Magnesium Diboride (MgB2) Superconductor Research [1 ed.] 9781614703068, 9781604565669

Citation preview

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

MAGNESIUM DIBORIDE (MGB2) SUPERCONDUCTOR RESEARCH

No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central, rendering legal, medical or any other professional services.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

MAGNESIUM DIBORIDE (MGB2) SUPERCONDUCTOR RESEARCH

SOUTA SUZUKI Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

AND

KOUKI FUKUDA EDITORS

Nova Science Publishers, Inc. New York

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2009 by Nova Science Publishers, Inc.

All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA MgB2 superconductor research / Souta Suzuki and Kouki Fukuda (editors). p. cm. ISBN H%RRN 1. High temperature superconductors. 2. Magnesium diboride. 3. High temperature superconductivity. I. Suzuki, Souta. II. Fukuda, Kouki. QC611.98.H54M45. 2008 537.6’23—dc22 2008013811

Published by Nova Science Publishers, Inc.

New York

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

CONTENTS

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Preface

vii

Chapter 1

MgB2 Superconductor Research Wei Du

Chapter 2

Synthetic and Phenomenological Approaches to 2 Dimensional High-Tc Superconductivity in the Layered Cuprates: Design and Creation of 2 Dimensional Hybrid Systems with Discrete Superconducting-Insulating and Superconducting-Magnetic Subsystems Soon-Jae Kwon

19

Chapter 3

Surveying the Vortex Matter Phase Diagram for Pristine MgB2, and Atomic Substituted Mg1-xAlxB2 and MgB2-xCx Single Crystals D. Stamopoulos and M. Pissas

77

Chapter 4

Nanocrystalline Microstructure of Mechanically Alloyed MgB2 Superconductor Precursor Powder for Bulk and Tape Fabrication and Implications on the Superconductivity W. Häßler, O. Perner, C. Fischer, K. Nenkov, C. Rodig, M. Schubert, M. Herrmann, L. Schultz, B. Holzapfel, IFW Dresden and J. Eckert

117

Chapter 5

Thermal Transients in MgB2 Conductors Antti Stenvall and Risto Mikkonen

133

Chapter 6

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2 Wei Yeu Chen and Ming Ju Chou

153

Chapter 7

Pinning Enhancement in MgB2 by Addition of Some Metallic Elements Yoshihide Kimishima

175

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

1

vi

Contents

Chapter 8

Doping Effects on the Superconducting Properties of Bulk and PIT MgB2 Adriana Serquis and Germán Serrano

211

Chapter 9

Optimization of Critical Current Density in MgB2 S.K. Chen and J.L. MacManus-Driscoll

247

Chapter 10

Microwave Response of Ceramic MgB2 Samples A. Agliolo Gallitto, G. Bonsignore, S. Fricano, M. Guccione and M. Li Vigni

273

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Index

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

293

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

PREFACE Magnesium diboride (MgB2) is an inexpensive and simple superconductor. Its superconductivity was announced in the journal 'Nature' in March 2001. Its critical temperature of 39 K is the highest amongst conventional superconductors. This material was first synthesized and its structure confirmed in 1953 but its superconducting properties were not discovered until half a century later. Though a conventional (phonon-mediated) superconductor, it is a rather unusual one. Its electronic structure is such that there exist two types of electrons at the Fermi level with widely differing behaviours, one of them being much more strongly superconducting than the other. This is at odds with usual theories of phonon-mediated superconductivity which assume that all electrons behave in the same manner. For this reason, theoretical understanding of the properties of MgB2 has not yet been achieved, particularly so in the presence of a magnetic field. This new book presents leading research in this field. Chapter 1 reports on the development of MgB2 superconductor and superconductivity, focusing on the experiments performed in the Mg-B system, the motivation behind them and their impact on basic research and device application. Combining the recent progress of MgB2 superconductor, especially MgB2 which has a relatively high Tc up to 39 K, it is systematically analyzed and summarized the current of superconductivity research and development of some prospects. It refers to the time from 2001 to 2007, with emphasis on the occurrences after the discovery of superconductivity in MgB2 in 2001. It involves MgB2 basic structure, theory research, crystal growth, polycrystalline synthesis, film preparation, and nanomaterials etc. The problems in MgB2 crystal growth is discussed on the basis of the chemical and thermodynamic information about Mg–B system. After comparing and analyzing the reported crystal growth methods, a novel technique for reproducible crystal growth of MgB2 at ambient pressure in Mg–B system is proposed from personal experience and elaborated. As explained in Chapter 2, the most challenging question on high-transition temperature (high-Tc) superconductivity is what interaction makes the transition temperature (Tc) high and mediates the electron pairing (Cooper pairing). Is electron pairing confined to only 2 dimensional (2 D) or effectively 3 dimensional (3 D) by interlayer interaction? Intercalation chemistry applied to high-Tc cuprate superconductors has provided a way of controlling the dimensionality as well as modifying the charge carrier density in the superconductively active copper-oxygen layer. The free modulation of interlayer distance in a layered high-Tc superconductor is of crucial importance for the study of the superconducting mechanism. 2 D

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

viii

Souta Suzuki and Kouki Fukuda

superconductors were achieved by intercalating a long-chain organic compound into bismuthbased cuprate superconductors. The long-chain organic compounds were incorporated into the layered cuprates with systematic increment of interlayer distance, while the atomic arrangement of each cuprate sheet was unchanged. The physico-chemical characterizations revealed that the orgnic-cuprate lamellar heterostructure shows high-Tc superconductivity even in the isolated cuprate layer, which was confirmed in microscopic scale by muon spin rotation/relaxation experiment as well as in macroscopic scale by d.c. magnetic susceptibility measurement. Although a remarkable increment of interlayer distance, to tens of angstroms, upon organic chain-intercalation, the superconducting transition temperature of the heterostructured system was nearly the same as that of the pristine material, suggesting the 2D nature of the high-Tc superconductivity. For a series of intercalation compounds, the electronic and geometric structures of the guest (inorganic or organic species) and the host (cuprate layer) have been investigated by the synchrotron radiation X-ray absorption spectroscopy, revealing that the electronic interaction between cuprate lattice and the incorporated species is responsible for the subtle change in the copper-oxygen layer and in turn Tc variation. In a structural view point, the intercalation compounds of high-Tc superconductors can be seen as a series of naturally grown superconducting-insulatingsuperconducting(S-I-S) superlattices, whose degree of coupling between superconductive layers may be systematically modified by adopting an appropriate guest. A novel heterostructured spin-system was developed by incorporating a spin-active species into bismuth-based cuprate layers, which showed extraordinary magnetic behavior of superconducting-paramagnetic dual magnetism. The unprecedented hybrid of high-Tc cuprate and paramagnetic species may provide not only a probe for high-Tc superconductivity but also a way of creating materials with spin- or magnetic field-dependent functionality unattainable from conventional solid-state materials. The recent discovery that the MgB2 compound is a superconductor with remarkably high critical temperature, Tc = 39:2 K has renewed the interest of the scientific community on superconductivity worldwide. This relatively high critical temperature classifies MgB2 as an intermediate-Tc superconductor opening new possibilities for its efficient utilization in various practical applications such as the design and construction of superconducting highfield magnets. In Chapter 3 the authors study in detail the properties of vortex matter phase diagram for MgB2 single crystals by means of local Hall and global SQUID magnetometry. Starting from the case of pristine MgB2 the authors extensively survey how the vortex matter phase diagram is modified upon substitution of Al for Mg, and C for B, that is for the case of Mg1-xAlxB2 and MgB2-xCx single crystals, respectively. The peak effect is observed in all cases of pristine, Al and C substituted MgB2. Referring to the local Hall ac-susceptibility measurements the dynamic behavior of the peak effect is systematically studied upon the variation of the excitation field’s characteristics. These data enable us to discuss the possible existence of various vortex phases on the H-T phase diagram such as the Bragg glass, the vortex glass and the vortex liquid. The influence of both thermal and quenched disorder on the vortex matter phase diagram is studied on the basis of relevant theoretical propositions. In this context, parameters that provide important information for the phenomenology of vortex systems, such as the anisotropy

γ , the upper-critical fields H cab2 ,c (T ) that determine the ultimate

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Preface

ix

transition to the normal state, and the concept of two-band superconductivity are discussed for the pristine and atomic substituted MgB2. Except for the importance for basic physics, surveying the vortex matter phase diagram is important for practical applications; since these vortex phases have extremely different dynamic transport response, their relative participation on the phase diagram determines the limitations for utilizing pristine, and atomic substituted MgB2 in practical application. As presented in Chapter 4, in order to enhance the reactivity of the starting substances and, therefore, to reduce the processing temperature for the MgB2 formation process as well as to improve the flux pinning abilities of the resulting material, the ambient temperature preparation technique of mechanical alloying was successfully applied starting with the elemental magnesium and boron powders. Processing in highly purified argon atmosphere hinders the contamination with oxygen and leads to grain refinement down to several nanometers. The high reactivity of the milled powders causes the formation of MgB2 at reduced temperatures. The result is a partially reacted precursor powder with clean particle surfaces and no oxide entry during processing. The milled powder mixture was hot pressed for a short time resulting in highly densified nanocrystalline single-phase bulk material with composition close to the stoichiometric ratio of MgB2, which exhibits good grain connectivity and low oxide content. The high density of grain boundaries which act as pinning centers enhances the upper critical field Hc2 and the irreversibility field Hirr as well as the critical current density Jc and the pinning force per unit volume Fp remarkably. Depending on the preparation parameters the critical temperature Tc is reduced to 30 - 35 K due to residual strain in the material and impurities stemming from the milling tools. Furthermore, monofilamentary Fe- as well as Cu-cladded and multifilamentary tapes with Fe sheath have been prepared by the PIT method using the mechanically alloyed partially reacted powder mixtures consisting of the constituents Mg, B and MgB2 as precursor. With this precursor the tapes can be annealed at relatively low temperatures of 773 – 873 K. Despite reduced Tc values of 30 - 35 K, maximum critical current densities Jc of 30 kA/cm2 and 9 kA/cm2 in external magnetic fields of 7.5 T and 10 T, respectively, are achieved at 4.2 K. The irreversibility fields Hirr of these tapes are 9.5 T and 4.2 T at 10 K and 20 K, respectively. Investigation of the microstructure by optical microscopy, SEM/WDX and XRD reveals that the high Jc values are mainly due to the remarkably small grain size of the MgB2 phase and defects, in particular precipitates of magnesium oxide. The properties of tapes with iron sheath are compared to those with Cu-sheath. The high critical temperature of MgB2 (39 K) offers increased range of operation temperature when compared to LTS materials. When operation temperature is raised from the liquid helium temperature (4.2 K) to the vicinity of 20 K the increased specific heat makes the operation of a superconductor much more stable. At 20 K hydrogen is the only possible liquid coolant. However, the use of hydrogen requires special care, especially if overpressure occurs in a cryostat and fast evacuation to air is required. Thus, cryocooler operation is preferred around 20 K due to its safety and simplicity. For an end user, cryocoolers require very little knowledge about cryogenics. Therefore, the wide commercialization prospects of MgB2 are mainly related to conduction cooled applications operating in the vicinity of 20 K. In addition, at least so far the properties and price of NbTi at 4.2 K are transcendent when compared to MgB2. During thermal disturbances, the cooling power of a cryocooler is negligible. Therefore, adiabatic stability considerations play an import role for system designs which

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

x

Souta Suzuki and Kouki Fukuda

utilize MgB2 superconductor and conduction cooling. In Chapter 5 the authors first consider the computation of the critical current for an MgB2 coil which includes conductor with ferromagnetic matrix. Then magnet stability under thermal transients is studied with a quench analysis algorithm. For conductor stability considerations, a numerical model to compute minimum propagation zones and normal zone propagation velocities for adiabatic MgB2 conductors is presented and verified with the measurement results. Magnesium diboride, MgB2 , has the highest Tc of 40 K for intermetallic compounds with anisotropic type-II superconductors. The promising potential in application has attracted numerous attentions on this novel material. In Chapter 6, the authors shall first investigate the quasiorder-disorder first-order phase transition or the peak effect and then study the anomalous Hall effect of superconducting MgB2 . It is well understood that the presence of impurities due to quenched disorder, doping or irradiation destroy the long-range order of flux line lattice, after which only short-range order, the vortex bundles, remains. If the applied magnetic field or the temperature increases, a first-order phase transition between the shortrange order and disorder in the vortex system eventually appears owing to enormous increase in the dislocations inside the short-range domains. The origin of peak effect is in this kind of first-order phase transition. The peak value of the critical current density J c , the exact peak

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

position and its corresponding half-width for a constant temperature as well as for a constant applied magnetic field, are obtained by calculating the critical current density explicitly. All the results are in good agreement with the experiments. The anomalous Hall effect for MgB2 is also studied based upon the theory of thermally activated motion of vortex bundles over a directional-dependent energy barrier. It is shown that the directional-dependent potential barrier renormalizes the Hall and longitudinal resistivities and the Hall anomaly is induced by the competition between the Magus force and the random collective pinning force of the vortex bundle. The Hall and longitudinal resistivities as functions of temperature and applied magnetic field for the thermally activated motion of vortex bundles are obtained. The double sign reversal, or reentry phenomenon, is also investigated. These studies are essential because they might provide some important information for their future applications. As explained in Chapter 7, the study on the pinning property is very important for the applications of high Tc superconductor MgB2 [1] at liquid hydrogen or 4He gas refrigerator temperature of about 20 K. Many authors have been tried to enhance the pinning force in the MgB2 superconductor by chemical modification using several kinds of element. The critical current density Jc at 20 K of liquid hydrogen temperature was about 104 A/cm2 for pure MgB2 at 20 K [2]. In this chapter, the magnetization curves M(H) of Mx(MgB2)1-x [M=Ag, Cu and Zn] and Mx(SiC)0.1-x(MgB2)0.9 [M=Ag, Cu, Nb and Pt] sintered under ambient pressure, and Cux(MgB2)1-x sintered under high pressure are analyzed to estimate the critical current density Jc by the extended critical state model. In the earlier papers [3-12], the author presented the analytical expressions of magnetization M and AC magnetic susceptibility χ ac by some critical state models for type-II superconductors, and indicated the importance of lower critical field Hc1 and surface equilibrium (reversible) magnetization Meq to analyze the magnetization curve and magnetic susceptibility. One of the most important issues for MgB2 magnet applications is the simultaneous enhancement of its critical current density (Jc) and the upper critical field (Hc2). Thus, on one hand, the pinning force may be improved by the incorporation of defects (nano particle

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Preface

xi

doping, chemical substitutions, etc.). On the other hand, the doping level affects the intraband scattering coefficients and the diffusivity of the two bands of this peculiar superconductor, and these changes may cause a significant Hc2 variation. In Chapter 8 the authors first present a review of different kind of doping and substitutions in the superconducting properties of MgB2 bulk samples. In particular, they analyze the correlated enhancement of Hc2 and critical current densities Jc obtained by SiC, single (sw) or double (dw) wall carbon nanotubes (CNT) doping, to understand the role of C substitution and other defects in MgB2 superconducting properties. In second place the authors describe our recent progress in the processing, microstructures and superconducting properties of MgB2 conductors prepared by PIT. Several sheath materials (stainless steel, copper and titanium) are used to fabricate SiC doped MgB2 wires and tapes. The microstructure and phase composition of the samples are followed by Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM) and X-Ray Diffractometry (XRD). Critical temperatures (Tc), Jc and Hc2 are determined by magnetization and transport measurements. The correlation between the superconducting properties and the microstructural characteristics is discussed. Chapter 9 focuses on the optimisation of critical current density, Jc of bulk polycrystalline MgB2 through studies of the influence of boron precursor powder, nominal Mg non-stoichiometry and by chemical modification. On the influence of the nature of the boron precursor on the superconducting properties of MgB2, Jc’s of samples made from crystalline boron powders are around an order of magnitude lower than those made from amorphous precursors. X-ray, superconducting transition temperature, Tc and resistivity studies indicate that this is as a result of reduced current cross section due to the formation of (Mg)B-O phases. The influence of Mg content was investigated in a series of samples with systematic variation of nominal Mg non-stoichiometry. Jc(H) was found to be influenced significantly with nominal Mg content while Tc remained unchanged. Mg deficient samples show a higher degree of disorder as inferred from the Raman spectroscopy, residual resistivity ratio and x-ray diffraction. The Mg-deficient samples also showed higher Hirr and Hc2 compared to samples with larger nominal Mg contents. Finally, GaN and Dy2O3 additions into MgB2 during the in situ reaction (owing to enhanced intragranular crystallinity and pinning, respectively) enhance Jc at 6K and 20K up to 5T without changing Tc appreciably. In Chapter 10, the microwave response of ceramic MgB2 has been investigated as a function of temperature and external magnetic field by two different techniques: microwave surface impedance and second-harmonic emission measurements. The measurements of the surface resistance have shown that microwave losses in MgB2 are strongly affected by the magnetic field in the whole range of temperatures below Tc, even for relatively low field values. The results have been accounted for in the framework of the Coffey and Clem model hypothesizing that in different temperature ranges the microwave current induces fluxons to move in different regimes. In particular, the results at temperatures close to Tc have been quantitatively justified by assuming that fluxons move in the flux-flow regime and taking into account the anisotropy of the upper critical field. At low temperatures, the field dependence of the surface resistance follows the law expected in the pinning limit; however, an unusually enhanced field variation has been detected, which could be due to the peculiar fluxon structure of MgB2, related to the presence of the two gaps. The measurements of the secondharmonic signals have highlighted several mechanisms responsible for the nonlinear

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

xii

Souta Suzuki and Kouki Fukuda

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

response. At low magnetic fields and low temperatures, the nonlinear response is due to processes involving weak links. At temperatures close to Tc, a further contribution to the harmonic emission is present; it arises from the modulation of the order parameter by the microwave field and gives rise to a peak in the temperature dependence of the harmonicsignal intensity.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

In: Magnesium Diboride (MgB2) Superconductor Research ISBN: 978-1-60456-566-9 Editors: S. Suzuki and K. Fukuda © 2009 Nova Science Publishers, Inc.

Chapter 1

MGB2 SUPERCONDUCTOR RESEARCH Wei Du1 School of Environment and Material Engineering, Yantai University, Yantai 264005, P. R. China

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Abstract This article reports on the development of MgB2 superconductor and superconductivity, focusing on the experiments performed in the Mg-B system, the motivation behind them and their impact on basic research and device application. Combining the recent progress of MgB2 superconductor, especially MgB2 which has a relatively high Tc up to 39 K, it is systematically analyzed and summarized the current of superconductivity research and development of some prospects. It refers to the time from 2001 to 2007, with emphasis on the occurrences after the discovery of superconductivity in MgB2 in 2001. It involves MgB2 basic structure, theory research, crystal growth, polycrystalline synthesis, film preparation, and nanomaterials etc. The problems in MgB2 crystal growth is discussed on the basis of the chemical and thermodynamic information about Mg–B system. After comparing and analyzing the reported crystal growth methods, a novel technique for reproducible crystal growth of MgB2 at ambient pressure in Mg–B system is proposed from personal experience and elaborated.

Introduction In 1911, the Netherlands scientists Kamerlingh Onnes first discovered superconductivity in Hg with 4.2 K, revealed this phenomenon, and created a new field of superconductor research and application. The ensuing 70 years of research, scientists fixed attention on metals and alloys conductor, and superconducting transition temperature (Tc) raised to 23 K (Nb3Ge). In 1979, a new class of superconductors-(TMTSF)2PF6 with Tc only 0.9 K were discovered in the organic conductors, although this organic salt superconducting transition temperature is 0.9 K, the low-dimensional properties, low electron density and conductivity

1

E-mail address: [email protected] (Du, W.). Tel: +86-13235351100 (Corresponding author).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

2

Wei Du

anomalies frequency relations of organic superconductors, and organic superconductors discovery indicates a new superconductivity research areas to happen. Subsequently, the new organic superconductor (BEDT-TTF)2ReO4 was synthesized, and its Tc is 2.5 K. Since then some other new organic superconductors have been discovered, such as κ-(BEDTTTF)2Cu(NCS)2 with the Tc of 10.4 K; κ-(BEDT-TTF)2Cu[N(NC)2]Br with the Tc of 12.4 K; κ-(BEDT-TTF)2Cu[N(NC)2]Cl with the Tc of 12.8 K under 300 MPa pressure. In 1986, the two Swiss scientists Bednorz and Müller investigated the electrical properties of La2BaCuO4 oxide ceramic, and found superconducting transition at 30 K which caused a sensation in the world at that time, and then it set off a high-temperature superconductivity chase. In 1991, K3C60 superconductor (Tc = 18K) was synthesized by Bell Labs, has been conducted a number of studies in this respect, with the exception of (ICl)xC60 (Tc = 60K) and IxC60 (Tc = 57K) of Tc are high, the rest of the Tc are relatively low. After several years of research, oxide superconductors HgBa2Ca2Cu3O8's Tc has been reached to138 K (the highest Tc is 160 K under high pressure), the application of oxide superconductors has already made a fine figure in some respects. Oxide superconductor’s superconducting mechanism is put in front of condensed matter physicists about the most meaningful and challenging one of the topics, because the electronic interaction in such materials is very strong, it seems that electronic move behavior can not be made clear by knowledge of solid state physics. To understand the high-temperature superconductivity mechanism may lead to understand the large class of the materials physical nature of electronic-related materials, and at the same time has a leap in two areas of science and technology. Due to its characteristics, oxide superconductors subject to many restrictions in the application. These features include very small coherence length lead to low condensed energy and flux pinning energy, flux system becomes two-dimensional and easy to move as a result of copper oxides layered structure, ceramic materials are easy to brittle and high prices of raw materials result in the high costs of application. So, new superconductor exploration seems increasingly urgent. The discovery of superconductivity in the binary metallic boride, MgB2[1], has led to a flurry of research activities directed mainly toward understanding the fundamental properties and fabrication of crystals[2] wires[3], tapes[4], and thin films[5] of this material for practical applications. The remarkably high Tc (39 K) of this material coupled with the advantages of a high coherence length (50 Å)[6], weaklink-free grain boundaries[7], high critical current densities in the range of 4-20 K, and large energy gap[8], makes MgB2 a promising candidate for applications in superconducting devices. Although MgB2 early in the 1950s had been successful synthesized [9], the superconductivity was not found before 2001. As a light main group representatives compound superconductors, MgB2 and AlB2 are identical in crystal structure, but its superconducting transition temperature is higher than alloy superconductor Nb3Ge’s, and is also higher than the limit superconducting transition temperature (29.2 K) predicted by the BCS theory.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

MgB2 Superconductor Research

3

1. MgB2 Crystal Structure MgB2 has very simple graphite-typed crystal structure with the space group of P6/mmm as shown in figure 1. It consists of alternating hexagonal closed-packed layers of Mg atoms and graphite-like honeycomb layers of B atoms. B atoms arranged at the corners of a hexagon with three nearest neighbor B atoms in each plane. The Mg atoms are located at the center of the B hexagon, midway between adjacent B layers, and lattice parameters a = b = 3.086 Å,

c = 3.524 Å at room temperature [1].

2. Electronic Structure of MgB2

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Several properties of MgB2 appear closely related to high-Tc superconducting cuprates: a low electron density of states, a layered structural character, and the presence of rather light atoms (like oxygen in cuprates) facilitate high phonon frequencies [10]. Mg is fully ionized in this compound; however the electrons donated to the system are not localized on the anion, but rather are distributed over the whole crystal [11]. These analyses establish a mixed-bonding behavior with ionic bonding between Mg and B, covalent bonding between B atoms, and metallic bonding between Mg and Mg like that in sp metals [10]. These bands are incompletely filled bonding σ bands with predominantly boron px ,py character. The pz bands mainly in the unoccupied state are derived from the interlayer π bonding orbitals which also have interlayer couplings between adjacent atomic orbitals in the c direction.

Figure 1. MgB2 crystal structure.

Further, although the electronic structure of this material has three-dimensional character, the B–B σ bands derived from B px,py electrons (believed to be important for the superconductivity) reflect two-dimensional character. MgB2 structure has negatively charged honeycomb-shaped B planes which are reminiscent of highly negatively charged Cu–O planes in the high-Tc cuprates. Hole carriers that dominate the transport properties exist in the B atoms plane. Zone boundary phonon calculations show that this band feature is very sensitive to the E2g mode (B-bond stretching) [10]. Strong bonding induces strong electron-ion scattering and hence strong electron-phonon

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

4

Wei Du

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

coupling. An additional benefit is the high frequency of the boron vibrations (while the force constants remain reasonably soft). Superconductivity is mainly due to boron [11]. Band structure calculations indicate that Mg is substantially ionized, and the bands at the Fermi level derive mainly from B orbitals [11]. Strong bonding with an ionic component and considerable metallic density of states yield a sizable electron-phonon coupling. MgB2 the energy band structure is obtained from detailed theoretical calculations [11]: a double degenerated flat band structure (shown by arrow in figure 2) exists above the Fermi surface along Γ-Α (Δ) direction, the band along Κ-Γ (Λ) direction and intersect with Fermi surface, which is σ band. The electronic and phononic structures and the electron-phonon interaction have been calculated throughout the Brillouin zone ab initio [12]. MgB2 has holes in the bonding σ-bands; and the total interaction strength is dominated by the coupling of the σ-holes to the bond-stretching optical phonons (E2g mode). Like the holes, these phonons are quasi two-dimensional and have wave-vectors close to Γ-Α. MgB2 seems to be an intermediate-coupling e-ph pairing s-wave superconductor according to Eliashberg theory evaluation.

Figure 2. Band structure of MgB2 with the B p character. The radii of the red (black) circles are proportional to the B pz (B px,y ) character.[11].

3. Superconducting Mechanism in MgB2 Whether the anomalously high Tc can be described within the conventional BCS (Bardeen– Cooper–Schrieffer) framework [13] has been debated. The superconducting transitions in the MgB2 materials synthesized under a variety of conditions seem to be at around the limit of Tc as suggested theoretically several decades ago for BCS. The key to understanding superconductivity is that superconductivity can be explained whether within conventional BCS electron-phonon mechanism or by a more exotic one. Boron atoms isotope effect

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

MgB2 Superconductor Research

5

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

experiment [14] in MgB2 demonstrates that the superconducting transition temperature obviously depend on the atomic quality, people gradually believe that electron-phonon coupling plays very important role in the superconducting formation. Further discovered, attempts to increase Tc in MgB2 by chemical substitution (such as electron-doping Al [15,16] and C [17,18]; hole-doping Li [19-22]; equivalent doping Mn [23] and Zn [24]; theoretical calculations show that Cu [25] and Li [19-22] doping would increase Tc in MgB2 by chemical substitution, but experimental verification of these ideas has been not thus far been successful.) only make superconducting temperature drop. Therefore, one believes that magnesium diboride superconductors might be one of a large number of binary alloy superconductors, and superconductivity will be completely attributed to the BCS mechanism of conventional superconductors. However, human imagination and the natural facts are always some gaps. The Eliashberg formalism [26,27] is a more general extension of the original formulation of the BCS theory, which is based on the mechanism for pairing that involves an attractive interaction between electrons mediated by lattice vibrations. This approach is able to reproduce successfully the superconducting transition temperature of MgB2 after detailed material properties are used. This particular study provides only the transition temperature Tc, and does not give information on the superconducting. MgB2 has many different properties with conventional BCS superconductor, specifically in the following aspects: (1) BCS theory can explain the Tc of conventional elements and alloy superconductors, but can not accurately predict that MgB2 may emerge superconducting transition critical temperature with more than 30 K. (2) The partial isotope exponent for boron is αB=0.26 [14]. The Mg isotopic coefficient is very small in total isotope effect, and which resulting in MgB2 total isotope coefficient (αMgB2) is only 0.32 [28] different with 0.5 of the BCS theoretical prediction. This value of αMg (0.02) proves that vibration modes of Mg atoms have a small contribution on Tc, but boron layers will be the key to understand superconducting mechanism in MgB2. (3) The specific heat of MgB2 along with temperature changes put up very anomalous behavior [29]. (4) Theoretical calculations show that more than one band cross the Fermi level [30], The E2g phonon mode involving in-plane B motion provides the strongest coupling and is highly anharmonic, and this mode may also have significant two-phonon coupling. A detailed examination of the energy associated with the formation of charge-carrying pairs, referred to as the ‘superconducting energy gap’, should clarify why MgB2 is different. A lot of experiments (such as specific heat [31,32], high-resolution photoemission [33], Raman spectra [34], Raman scattering spectra [35], point-contact spectroscopy [36,37]) indicated that multiple gaps may exist in MgB2. Yang H. D. et al. [38] found anisotropic swave or multi-component order parameter using polycrystalline MgB2 prepared by high pressure synthesis, which unambiguously indicates a fully opened superconducting energy gap. The results direct experimental evidence for the multiple superconducting energy gaps in MgB2.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

6

Wei Du

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 3. The superconducting energy gap of MgB2. a, b, The superconducting energy gap on the Fermi surface at 4 K given using a colour scale (a), and the distribution of gap values at 4 K (b). The Fermi surface of MgB2 consists of four distinctive sheets. Two σ sheets (‘cylinders’), derived from the σ-bonding px,y orbitals of boron, are shown split into eight pieces around the four vertical Γ-Γlines. Two π sheets (‘webbed tunnels’), derived from the π-bonding pz orbitals of boron, are shown around Κ–Μ and H–L lines (upper and lower Κ–Μ lines are equivalent). The superconducting energy gap is~7.2 meV on the narrower σ cylindrical sheet, shown in red, with variations of less than 0.1 meV. On the wider σ cylindrical sheet, shown in orange, the energy gap ranges from 6.4 to 6.8 meV, having a maximum near Γ and a minimum near A. On the π sheets, shown in green and blue, the energy gap ranges from 1.2 to 3.7 meV. The density of states at the Fermi energy is 0.12 states per (eV atom spin), 44% of which comes from the σ sheets and the other 56% comes from the π sheets. c, Local distribution of the superconducting energy gap on a boron plane and on planes at 0.05, 0.10 and 0.18 nm above a boron plane, respectively [39].

According to the evidence of multiple gaps, Choi, H. J. et al., [39] carried out a detailed model calculation (ab initio) on MgB2 with a two-gap structure assume. The two-band model [30,39] may be theoretically described as follows: (1) The Fermi surface consists of two sheets (2D coaxial cylinders parallel to c*) from the σ-bonding states of boron px,y orbitals, and two sheets (3D webbed tunnels) from the π-bonding states of boron pz orbitals. Electrons in the σ-bands are strongly coupled to phonons confined within the honeycombed boron layer and give rise to a large gap, whereas a relatively small gap opens in the π-band due to the weak electron-phonon coupling [Figure 3]. (2) The resulting superconducting energy gap has s-wave symmetry (that is, the gap is of the same sign and non-zero everywhere on the Fermi surface), but the size of the gap changes greatly on the different sections of the Fermi surface. Later, the present high-resolution angle-resolved photoemission spectroscopy (ARPES) experiment [40] has succeeded in resolving σ and π bands and directly observing the superconducting gaps as shown figure 4. The typical size of crystals used in ARPES measurements is about 100×100×10 mm3 [41].

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

MgB2 Superconductor Research

7

Figure 4. Experimental band structure near EF of MgB2 obtained by ARPES. a, ARPES spectra of MgB2 measured at 45 K along the ΓΚΜ (AHL) direction in the Brillouin zone (inset to a) with 28-eV photons. b, ARPES-intensity plot of MgB2 as a function of wave vector and binding energy. White arrows A, B and C indicate the location of Fermi-level crossing points for the π,σ and surface bands. Inset to b shows the schematic view of the band dispersion; S indicates surface. The σ and the surface bands have a large gap of 6-7 meV whereas the π band shows a small gap of 1-2 meV [40].

According to this particular band structure, various physical properties of MgB2 can be obtained easily. Choi H. J. et al., [39] have calculated the specific heat from the free energy of the superconducting state. The overall shape and magnitude of their calculated specific-heat curve agrees very well with the experimental data, especially below 30 K [29,31,38]. The present ARPES results [40] that the large gap observed by surface-sensitive techniques such as tunneling spectroscopy may be due to both the σ and the surface bands, because the gap size is almost the same for the two bands. A large variation in the size of the large gap may stem from the various surface conditions, depending on the surface preparation method. Although why the surface band exhibits a similar gap size to the σ band is unclear at present,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

8

Wei Du

the proximity of the two bands in the momentum and energy spaces as seen in Figure 4 may account for it, because the interaction between the surface and σ bands is expected to be larger than that between the surface and π bands. Two superconducting energy gaps theory will not only give possible explanation for the various seemingly contradictory results obtained from the electronic tunneling spectroscopy, angle-resolved photoelectron spectroscopy, neutron scattering spectroscopy, and specific heat experiments, but play an important guiding in the search for new superconductors with the higher superconducting transition temperature in the materials with similar electronic structure containing elements B, C, N, etc.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

4. Mg-B System Phase Diagram Among magnesium borides, MgB2 phase is reported to be the most unstable, because it starts to decompose at T>850–900°C. To determine the stability region of MgB2 and to construct the equilibrium phase diagram of Mg-B system, accurate thermodynamic data for MgB2 and other magnesium borides are required [2]. The experimental phase diagram for the Mg-B system is not available yet and the diagram at P=1 bar presented in Massalsky’s edited compilation [42] was substantially based on the assessments of Spear [43]. Recently Liu et al., reported thermodynamic analysis of the Mg-B system with the calculation of temperaturecomposition, pressure-composition and pressure-temperature phase diagrams (as shown figure 5) [44]. The calculations are based on the known crystal structure and thermodynamic data of three intermediate phases (MgB2, MgB4 and MgB7) in addition to the Mg and β-B. The results of calculation for P=1 bar are quite consistent with the published [42]. Calculations for different pressure ranges showed that due to the high volatility of magnesium, MgB2 is thermodynamically stable only under Mg-overpressure. According to these calculations, the MgB2 is decomposed into MgB4 and Mg vapor at 1545°C under the 1 atm Mg partial pressure, but at 1 Torr the decomposition T decreases down to 912°C. At present, the reported experimental data of MgB2 decomposition in vacuum are not consistent and estimated evaporation co-efficient of Mg from MgB2 varies from 10-4 [45] to 5 ×10-2 [46].

5. MgB2 Crystal Growth In spite of the chemical and structure simplicity, growth of the high quality single crystals of MgB2 for fundamental studies has been proved to be very difficult because of the nonreproducibility of Mg evaporation during the process. The origin of this problem is related to the chemical and thermodynamic features of Mg-B system [42, 44] and the extra vapor pressure of Mg over its melting point. There have been several reports of single crystals growth of MgB2 [41,47-53] since 2001, and MgB2 single crystals are synthesized mainly by heat treatment in sealed metal containers [41,47,48] or by sintering at high temperature (> 1400°C) and pressure (2-5 G Pa) [49-52]. Single crystals can be obtained in sub-millimeter size with different Tc [41, 47, 53], and their shapes are mostly irregular. Until now, both single crystal size and shape seem to depend strongly on the method of preparation. So, a new

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

MgB2 Superconductor Research

9

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

practice is introduced to grow MgB2 single crystal by evaporating flux method in order to investigate the habit of crystal growth [54].

Figure 5. Temperature–composition phase diagrams of the Mg–B system under the pressures of (a) 1 atm, (b) 1 Torr, and (c) 1m Torr. [44].

As we all known, Mg vapor pressure increases with the temperature over its melting point (heat of fusion 8.954 kJ/mol, heat of evaporation 127.4 kJ/mol). All the metals Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

10

Wei Du

presented single atomic or molecular ideal crystal properties after gasification, which satisfied physical relation between vapor pressure and temperature (only for metals):

− Δ vap H θ C A lg P = + B = + 2.303RT 2.303R T *

(1)

If every thermal data of MgB2 are provided for the above mentioned equation, the following equation can be obtained [55, 56]:

lg( PMg / KPa ) = 6.99 −

6818 T

(2)

According to the equation (2) and the phase diagram of Mg-B system [42], MgB2 crystals may be grown from a lot of Mg as flux, that is to say, a small quantity of MgB2 is resolved in a mass of Mg flux at high temperature. At the same time, MgB2 crystals grow and separate out along with the evaporation of Mg with the temperature increasing. In the present work, we introduce Mg as the flux and marketed MgB2 powder as the raw material, and vaporize Mg flux by increasing temperature slowly, which cause the local solution supersaturating and MgB2 single crystal growing and separating out. This is the practicable solution imaginable to grow MgB2 crystals because vapor pressure of MgB2 is far below that of Mg, and antioxidation of MgB2 is superior to that of Mg. The Well hexagonal plate-shaped single crystal with the size of about 100 μm was successfully prepared by optimizing temperature program.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

6. Polycrystal Preparation of MgB2 The polycrystalline form of MgB2 can be prepared by sealing a mixture of Mg and B with Mg:B = 1:2 in a tantalum tube [14] or Mg flakes and submicron amorphous B powder mixed and pressed into pellets placed on Ta foil [57], or amorphous B powder and Mg turnings in the atomic ratio 1:1 (The B powder was pressed into small pellets under 500 MPa ) wrapped in Ta foil [58] using solid state reaction at least heated to 900°C in a tube furnace under ultra high purity Ar. Shi L et al., [59] reported a novel convenient chemical route to synthesize ultrafine MgB2. The reaction was carried out in an autoclave at 600°C and can be described as follows: MgCl2 +2NaBH4 → MgB2+2NaCl + 4H2.

7. Thin Film of MgB2 [60] The MgB2 films are especially important not only in the superconducting circuits and devices, but also as a possible pre-stage for the preparation of the MgB2 tapes and wires in the industry at lower lost and simpler process.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

MgB2 Superconductor Research

11

There have already been many reports on the synthesis of superconducting MgB2 films [5,61-72]. There are two complicating problems related to the preparation of superconducting MgB2 films. These are the high sensitivity of Mg to oxidation and the high Mg vapor pressure required for the thermodynamic stability of the superconducting MgB2 phase. The former problem can be avoided by depositing MgB2 films either in an ultrahigh vacuum or in a reducing atmosphere containing hydrogen. The latter problem is more serious, and there are two ways to overcome it. One is two-step synthesis, in which amorphous B (or Mg-B composite) precursors are ex-situ annealed at high temperatures with high Mg vapor pressure usually in a confined container [61-65]. This two-step process produces good crystalline films with good superconducting properties although it may not be favorable for multilayer device fabrication. The other is in-situ (as-grown) synthesis, in which films are grown in-situ at low temperatures of around 300°C at the relatively low Mg vapor pressure (10-5~10-6 Torr) that is compatible with many vacuum deposition techniques. In-situ synthesis makes multilayer deposition feasible although in most cases it only produces poor crystalline films with a Tc of ~ 35 K, which is slightly below the bulk value [69-72]. This is because good epitaxial growth is impeded due to the limited growth temperatures below ~300°C. By employing a special combination of physical and chemical vapor deposition techniques, Zeng et al., have achieved the in-situ epitaxial growth of MgB2 films at around 750°C at a high Mg vapor pressure (10100 mTorr) [5]. However, it remains to be seen whether this method is as suitable for multilayer deposition as conventional physical vapor deposition. An effective approach to produce controlled quality, thick MgB2 film is therefore especially important for the purpose of electronic devices and large-scaled superconducting industrial applications. Very thick, ~40μm, clean, and highly textured MgB2 film with (101) oriented micro-crystals was effectively grown on an Al2O3 substrate [73]. The fabrication technique was by the hybrid physical-chemical vapor deposition (HPCVD) using B2H6 gas and Mg ingot as the sources. Recently, Li Qi et al., [74] reported a large normal-state magnetoresistance with temperature-dependent anisotropy in very clean epitaxial MgB2 thin films (residual resistivity much smaller than 1μΩcm) grown by HPCVD. The magnetoresistance shows a complex dependence on the orientation of the applied magnetic field, with a large magnetoresistance (Δρ /ρ0=136%) observed for the field H ⊥ ab plane. The angular dependence changes dramatically as the temperature is increased, and at high temperatures the magnetoresistance maximum changes to H || ab. They attribute the large magnetoresistance and the evolution of its angular dependence with temperature to the multiple bands with different Fermi surface topology in MgB2 and the relative scattering rates of the σ and π band, which vary with temperature due to stronger electron-phonon coupling for the σ bands. In order to achieve high quality film, the relationship between the deposition mechanism and the controlling parameters in the synthesis process need further study.

8. Mgb2 Nanomaterials One of the most interesting characteristics of the superconducting compound is that grain boundaries in the polycrystalline MgB2 do not appear to significantly decrease the overall critical current (jc) in a marked contrast to the cuprate high-Tc-superconductors, where high angle grain boundaries universally act as weak links and dramatically reduce the intergranular

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

12

Wei Du

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

critical currents [75]. As such, it is conceivable that fabrication of nanostructured MgB2 would improve its electrical properties by providing strong pinning centers and simultaneously will improve its mechanical properties by dramatic reduction of grain size to the nano-level. Gümbel et al., [76] attempted to fabricate nanostructured MgB2 by mechanical alloying (MA) of elemental Mg and amorphous B powders in a planetary ball mill followed by hot-pressing at about 700°C. The nanograin size of MgB2 estimated from the XRD peak broadening was found to be ~15 nm in the hot-pressed sample. Very high jc values have, indeed, been observed in this nanocrystalline material due to grain boundaries acting as flux lines pinning centers [76]. Varin R.A. and Chiu Ch. [77] reported the results of the synthesis of nanocrystalline MgB2 (estimated crystallite (nanograin) size is on the order of ~23 nm with a minimal lattice strain.) superconducting compound by mechano-chemical reaction followed by post-annealing. Superconducting nanowires, and other 1D nanostructures, can ideally be used as lowdissipation interconnects in superconducting devices making it desirable to grow MgB2 nanowires and other nanostructures on a substrate. Recently, Nath M. and Parkinson B. A. [78] have grown superconducting nanohelices of MgB2 (Tc ≈ 32 K) on Si (as shown in figure 6) and other substrates. An interesting and useful feature of the MgB2 nanohelices is that their growth does not require any foreign catalyst particle as in classical vapor-liquid-solid growth (the growth is self-catalyzed by Mg), thus minimizing the possibility of catalyst substitution (possibly altering Tc). Superconducting nanocoils and solenoids (with iron nanorod cores) may have practical applications as nanoactuators or in flexible superconducting cable.

Figure 6. SEM images of MgB2 nanohelices grown on Si substrates [78].

9. Element Doped MgB2 In the high Tc cuprates, chemical doping has been widely used to investigate the dependence of superconducting properties on the structure. Chemical doping in MgB2 is performed by different groups and various results have been presented. The partial substitution of Al or Li

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

MgB2 Superconductor Research

13

for Mg leads to the decrease or the loss of superconductivity [15,79]. Prikhna, et al., [80] reported the preparation of Ti-doped MgB2 with high critical current density. They believe that Ti may act as a sintering assistant and fine particles of the Ti-rich phase may be responsible for flux pinning, i.e., no new phase was observed. Yet, other elements were shown to have no effect on Tc, as reported for Be-doped MgB2 [25,81]. Guo J. D. et al., [82] have selected Au as the substitution element for Mg considering the similar radii, with a slightly lower transition temperature and broader transition width. Experiments and theories have predicted phonon-mediated s-wave BCS superconductivity with a double energy gap σ and π bands. The MgB2 lattice structure consists of alternating layers of boron and magnesium atoms. The boron atoms form a honeycomb lattice and the magnesium atoms a triangular lattice halfway between the boron layers. Immutability of translation of the lattice structure has an important influence on the energy bands of crystals. The formation of Cooper pairs and phonon frequency depend on the crystal lattice vibration. However, local defects have an impact on the vibration, and thus weaken the formation rate of Cooper pairs. Mg atoms or ions play an important role in MgB2 superconducting properties. Kortus et al., [11] concluded that Mg was fully ionized in MgB2; however, the electrons donated to the system were not localized at the anion, but were distributed over the whole crystal. An and Pickett [83] suggested that the B2 layers provide a strong differentiation between B states (σ versus π) that results in the Mg2+ layer giving a 3.5 eV σ-π energy shift, driving self-doping of the σ bands. Furthermore, according to [15, 79] the superconducting transition temperature of MgB2 is reduced through electron [15] or hole doping [79], which indicates that the superconducting MgB2 phase is placed very near a structural instability at slightly higher or lower electron concentrations.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

10. Applications Like the conventional superconductor Nb, MgB2 is a phononmediated superconductor, with a relatively long coherence length [6]. These properties make the prospect of fabricating reproducible uniform Josephson junctions, the fundamental element of superconducting circuits, much more favorable for MgB2 than for high-temperature superconductors. The higher transition temperature and larger energy gap [8,84] of MgB2 promise higher operating temperatures and potentially higher speeds than Nb-based integrated circuits. Nb-based superconductor integrated circuits using rapid single flux quantum logic have demonstrated the potential to operate at clock frequencies above 700 GHz. However, the Nb-based circuits must operate at temperatures close to 4.2 K, which requires heavy cryocoolers with several kilowatts of input power, and is not acceptable for most electronic applications. Circuits based on high-temperature superconductors (HTS) would solve this problem, but 21 years after their discovery, reproducible HTS Josephson junctions with sufficiently small variations in device parameters have not been produced. An MgB2-based circuit will operate at about 25 K, achievable by a compact cryocooler with roughly onetenth of the mass and the power consumption of a 4.2 K cooler of the same cooling capacity. The ultimate limit on device and circuit speed depends on the product of the junction critical current, Ic, and the junction normal-state resistance, Rn. Because Ic Rn is proportional to the energy gap of the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

14

Wei Du

superconductor, the larger energy gap in MgB2 could lead to even higher speeds (at very high values of critical current density) than in Nb-based superconductor integrated circuits [5]. For microwave applications [85], MgB2 holds promise for filling a niche between lowtransition-temperature (low-Tc) superconductors such as Nb and high-transition-temperature (high-Tc) oxides such as YBa2Cu3O7-δ (YBCO). The fact that MgB2 is a very good metal with relatively high electrical conductivity and the possibility to prepare samples with no weak links represent significant advantages with respect to oxide high-Tc superconductors. The highquality thin films have been especially encouraging [86]. They demonstrate classic swave-like order parameter, which leads to an exponential drop of surface resistance below about Tc/2 in optimized samples, and very low residual surface resistance of 19 mV measured at 5 K and 7.2 GHz. The material looks rather promising for niche applications because grain boundaries do not appear to be deleterious to the continuity of the current path and Josephson junction fabrication suggests these materials may also be promising for a range of electronic applications. Microwave surface impedance measurements are extremely interesting because the order parameter in MgB2 is thought to be of s-wave symmetry, which suggests that the residual losses ought to be low and the temperature dependence of the surface resistance ought to be weak, similar to the classical superconductors such as Nb, but usable at a 25-30 K operating temperature [87].

References

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[1]

Nagamatsu, J., Nakagawa, N., Muranaka, T., Zenitani, Y., Akimitsu, J. Nature 2001, 410, 63-64. [2] Lee, S. Physica C 2003, 385, 31-41 [3] Jin, S., Mavoori, H., Bower, C., van Dover, R. B. Nature 2001, 411, 563-567. [4] Kumakura, H., Matsumoto, A., Fujii, H., Togano, K. Appl. Phys. Lett. 2001, 79, 2435. [5] Zeng, X., Pogrebnyakov, A. V., Kotcharov, A., Jones, J. E., Xi, X. X., Lysczek, E. M., Redwing, J. M., Xu, S., Li, Q., Lettieri, J., Schlom, D. G., Tian, W., Pan, X., Liu, Z-K. Nat. Mater. 2002, 1, 1-4. [6] Finnemore, D. K., Ostenson, J. E., Bud’ko, S. L., Lapertot, G., Canfield, P. C. Phys. Rev. Lett. 2001, 86, 2420-2422. [7] Larbalestier, D. C., Cooley, L. D., Rikel, M. O., Polyanskii, A. A., Jiang, J., Patnaik, S., Cai, X. Y., Feldmann, D. M., Gurevich, A., Squiteri, A. A., Naus, M. T., Eom, C. B., Hellstrom, E. E., Cava, R. J., Regan, K. A., Rogado, N., Hayward, M. A., He, T., Slusky, J. S., Khalifah, P., Inumaru, K., Haas, M. Nature 2001, 410, 186-189. [8] Tsuda, S., Yokoya, T., Kiss, T., Takano, Y., Togano, K., Kito, H., Ihara, H., Shin, S. Phys. Rev. Lett. 2001, 87, 177006-1-177006-4. [9] Jones, M. and Marsh, R. J. Am. Chem. Soc. 1954, 76, 1434-1436. [10] Ravindran, P., Vajeeston, P., Vidya, R., Kjekshus, A. and Fjellvåg, H. Phys. Rev. B 2001, 64, 224509-1-224509-15. [11] Kortus, J., Mazin, I. I., Belashchenko, K. D., Antropov, V. P. and Boyer, L. L. Phys. Rev. Lett. 2001, 86, 4656-4659 [12] Kong,Y., Dolgov,O.V., Jepsen, O., Andersen, O. K. Phys. Rev. B 2001, 64, 020501-1020501-4

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

MgB2 Superconductor Research

15

[13] Bardeen, J., Cooper, L. N. and Schrieffer, J. R. Phys. Rev. 1957, 108, 1175–1204 [14] Bud’ko, S. L., Lapertot, G., Petrovic, C., Cunningham, C. E., Anderson, N. and Canfield, P. C. Phys. Rev. Lett. 2001, 86, 1877-1880. [15] Slusky, J. S., Rogado, N., Regan, K. A., Hayward, M. A., Khalifah, P., He, T., Inumaru, Loureiro, S. M., Haas, M. K., Zandbergen, H. W., Cava, R. J. Nature 2001, 410, 343345. [16] Barabash, S. V. and Stroud, D. Phys. Rev. B 2002, 66, 012509-1-012509-4. [17] Takenobu, T., Ito, T., Chi, D. H., Prassides, K., Iwasa, Y. Phys. Rev. B 2001,64, 134513-1-134513-3. [18] Ribeiro, R. A., Bud’ko, S. L., Petrovic, C., Canfieldet, P. C. Physica C 2003, 384, 227-236 [19] Rosner, H., Kitaigorodsky, A., Pickettet W. E. Phys. Rev. Lett. 2002, 88, 127001-1127001-4 [20] Dewhurst, J. K., Sharma, S., Ambrosch-Draxl, C., Johansson, B. Phys. Rev. B 2003, 68, 020504(R)-1-020504-4. [21] Fogg, A. M., Chalker, P. R., Claridge, J. B., Darling, G. R., Rosseinsky, M. J. Phys. Rev B 2003, 67, 245106-1-245106-10. [22] Bharathi, A., Jemima Balaselvi, S., Premila, M., Sairam, T. N., Reddy, G. L. N., Sundar, C. S., Hariharan, Y. Solid State Communications, 2002, 124, 423–428. [23] Xu, S., Moritomo, Y., Kato, K., Nakamura, A. J. Phys. Soc. Jpn. 2001, 70, 1889-1891. [24] Kazakov, S. M., Karpinski, J., Karpinski, J. Solid State communications 2001, 119, 1-5 [25] Mehl, M. J., Papaconstantopoulos, D. A., Singh, D. J. Phys. Rev. B 2001, 64, 140509(R)-1-140509-4. [26] Eliashberg, G. M. Zh.Eksp.Teor.Fiz. 1960, 38, 966-976, Sov.Phys.JETP 1960, 11, 696-702. [27] Allen, P. B., Dynes, R. C. Phys. Rev. B 1975, 12, 905-922. [28] Hinks, D. G., Claus, H. and Jorgensen, J. D. Nature 2001, 411, 457-460 [29] Wang, Y., Plackowski, T., Junod, A. Physica C 2001, 355, 179-193. [30] Liu, A. Y., Mazin, I. I., Kortus, J. Phys. Rev. Lett. 2001, 87, 087005-1-087005-4 [31] Bouquet, F., Fisher, R. A., Phillips, N. E., Hinks, D. G., Jorgensen, J. D. Phys. Rev. Lett. 2001, 87, 047001-1-047001-4 [32] Bouquet, F., Wang, Y., Sheikin, I., Plackowski, T., Junod, A. Phys. Rev. Lett. 2002, 89, 257001-1-257001-4 [33] Tsuda, S., Yokoya, T., Kiss, T., Takano, Y., Togano, K., Kito, H., Ihara, H., Shin, S. Phys. Rev. Lett. 2001, 87, 177006-1-177006-4 [34] Chen, X. K., Konstantinovi, M. J., Irwin, J. C., Lawrie, D. D., Franck, J. P. Phys. Rev. Lett. 2001, 87, 157002-1-157002-4. [35] Quilty, J. W., Lee, S., Tajima, S., Yamanaka, A. Phys. Rev. Lett. 2003, 90, 207006-1207006-4 [36] Szabó, P., Samuely, P., Kačmarčík, J., Klein, T., Marcus, J., Fruchart, D., Miraglia, S., Marcenat, C., Jansen, A. G. M. Phys. Rev. Lett. 2001, 87, 137005-1-135007-4. [37] Gonnelli, R. S., Daghero, D., Ummarino, G. A. Phys. Rev. Lett. 2002, 89, 247004-1247004-4. [38] Yang, H. D., Lin, J.-Y., Li, H. H., Hsu, F. H., Liu, C. J., Li, S.-C., Yu, R.-C., Jin, C.-Q. Phys. Rev. Lett. 2001, 87, 167003-1–167003-4.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

16

Wei Du

[39] Choi, H. J., Roundy, D., Sun, H., Cohen, M. L., Louie, S. G. Nature 2002, 418, 758–760. [40] Souma, S., Machida, Y., Sato, T., Takahashi, T., Matsui, H., Wang, S.-C., Ding, H., Kaminski, A., Campuzano, J. C., Sasaki, S., Kadowaki, K. Nature 2003, 423, 65-67. [41] Machida, Y., Sasaki, S., Fujii, H., Furuyama, M., Kakeya, I., Kadowaki, K. Phys. Rev. B 2003, 67, 094507-1-094507-4 [42] Massalski, T. Binary Alloy Phase Diagrams, second ed., ASM International: Materials Park, OH, 1990, pp1298-1302 [43] Spear, K.E. In Refractory Materials Aper, A.M., Ed., Academic Press: New York, 1976, Vol. 6-IV, pp 6-10 [44] Liu, Z.-K., Schlom, D.G., Li, O., Xi, X.X. Appl. Phys. Lett. 2001, 78, 3678-3680. [45] Fan, Z.Y., Hinks, D.G., Newman, N., Rowell, J.M. Appl. Phys. Lett. 2001, 79, 87-89. [46] Brutti, S., Ciccioli, A., Gigli, G., Manfrinetti, P., Palenzona, A. Appl. Phys. Lett. 2002, 80, 2892-2894. [47] Xu, M., Kitazawa, H., Takano, Y., Ye, J., Nishida, K., Abe, H., Matsushita, A., Tsujii, N., Kido, G. Appl. Phys. Lett. 2001, 79, 2779-2781. [48] Du, W., Xu, D., Zhang, H., Wang, X., Zhang, G., Hou, X., Liu, H., Wang, Y. Journal of Crystal Growth 2004, 268, 123-127. [49] Lee, S., Mori, H., Masui, T., Eltsev, Y., Yamamota, A., Tajima, S. J. Phys. Soc. Jpn. 2001, 70, 2255-2258. [50] Lee, S., Yamamoto, A., Mori, H., Eltsev, Yu., Masui, T., Tajima, S. Physica C 2002, 378, 33-37 [51] Lee, S., Masui, T., Mori, H., Eltsev, Yu., Yamamoto, A., Tajima, S. Supercond. Sci. Technol. 2003, 16, 213-220. [52] Angst, M., Puzniak, R., Wisniewski, A., Jun, J., Kazakov, S. M., Karpinski, J., Roos, J., Keller, H. Phys. Rev. Lett. 2002, 88, 167004-1-167004-4. [53] Cho, Y.C., Park, S.E., Jeong, S.Y., Cho, C.R., Kim, B.J., Kim, Y.C., Youn, H.S. Appl. Phys. Lett. 2002, 80, 3569-3571. [54] Du, W., Xu, H., Zhang, H., Xu, D., Wang, X., Hou, X. , Wu, Y., Jiang, F., Qin, L. Journal of Crystal Growth 2006, 289, 626-629. [55] Mironov, A., Kazakov, S., Jun, J., Karpinski, J. Acta Cryst. C 2002, 52, 95-97. [56] Qu, Y. Iron and Steel making Theory, Metallurgy Industry Publishing Company: Beijing, 1980, pp35-38 [57] Rogado, N., Hayward, M. A., Regan, K. A., Wang, Yayu, Ong, N. P., Zandbergen, H., John, W., Rowell, M., Cava, R. J. J. Appl. Phys. 2002, 91, 274-277 [58] Klie, R. F., Idrobo, J. C., Browning,N. D., Serquis, A., Zhu, Y. T., Liao, X. Z., Mueller, F. M. Appl. Phys. Lett. 2002, 80, 3970-3972 [59] Shi, L., Gu, Y., Qian, T., Li, X., Chen, L., Yang, Z., Ma, J., Qian, Y. Physica C 2004, 405, 271–274 [60] Ueda, K., Naito, M. J. Appl. Phys. 2003, 93, 2113-2120 [61] Kang, W. N., Kim, Hyeong-Jin, Choi, Eun-Mi, Jung, C. U., Lee, Sung-Ik Science 2001, 292, 1521-1523. [62] Eom, C. B., Lee, M. K., Choi, J. H., Belenky, L. J., Song, X., Colley, L. D., Naus, M. T., Patnaik, S., Jiang, J., Rikel, M., Polyanskii, A., Gurevich, A., Cai, X. Y., Bu, S. D., Babcock, S. E., Hellstrom, E. E., Larbalestier, D. C., Rogado, N., Regan, K. A.,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

MgB2 Superconductor Research

[63]

[64] [65] [66]

[67] [68] [69] [70] [71]

[72] [73]

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[74] [75] [76] [77] [78] [79] [80]

[81] [82] [83] [84]

17

Hayward, M. A., He, T., Slusky, J. S, Inumaru, K., Hass, M. K., Cava, R. J. Nature 2001, 411, 558-560. Paranthaman, M., Cantoni, C., Zhai, H. Y., Christen, H. M., Aytug, T., Sathyamurthy, S., Specht, E. D., Thompson, J. R., Lowndes, D. H., Kerchner, H. R., Christen, D. K. Appl. Phys. Lett. 2001, 78, 3669-3671. Moon, S. H., Yun, J. H., Lee, H. N., Kye, J. I., Kim, H. G., Chung, W., Oh, B. Appl. Phys. Lett. 2001, 79, 2429-2431. Zhai, H. Y., Christen, H. M., Zhang, L., Paranthaman, M., Cantoni, C., Sales, B. C., Fleming, P. H., Christen, D. K., Lowndes, D. H. J. Mater. Res. 2001, 16, 2759-2762. Zeng, X. H., Sukiasyan, A., Xi, X. X., Hu, Y. F., Wertz, E., Tian, W., Sun, H. P., Pan, X. Q., Lettieri, J., Schlom, D. G., Brubaker, C. O., Liu, Zi-Kui, Li, Q. Appl. Phys. Lett. 2001, 79, 1840-1842. Christen, H. M., Zhai, H. Y., Cantoni, C., Paranthaman, M., Sales, B. C., Rouleau, C., Norton, D. P. , Christen D. K. , Lowndes, D. H. Physica C 2001, 353, 157-161. Blank, D. H. A., Hilgenkamp, H., Brinkman, A., Mijatovic, D., Rijnders, G., Rogalla, H. Appl. Phys. Lett. 2001, 79, 394-346. Ueda, K. and Naito, M. Appl. Phys. Lett. 2001, 79, 2046-2048. Saito, A., Kawakami, A., Shimakage, H., Wang, Z. Jpn. J. Appl. Phys. 2002, 41, L127-129. Grassano, G., Ramadan, W., Ferrando, V., Bellingeri, E., Marre, D., Ferdeghini, C., Grassano, G., Putti, M., Siri, A. S., Manfrinetti, P., Palenzona, A. and Chincarini, A. Supercond. Sci. and Tech. 2001, 14, 762-764 Jo, W., Huh, J. -U., Ohnishi, T., Marshall, A. F., Beasley, M. R. and Hammond, R. H. Appl. Phys. Lett. 2002, 80, 3563-3565. Chen, C., Wang, X., Lu, Y., Jia, Zh., Guo, J., Wang, X., Zhu, M., Xu, X., Xu, J., Feng, Q. Physica C 2004, 416, 90-94 Li, Q., Liu, B. T., Hu, Y. F., Chen, J., Gao, H., Shan, L., Wen, H. H., Pogrebnyakov, A.V., Redwing, J. M. and Xi, X. X. Phys. Rev. Lett. 2006, 96, 167003-1-167003-4 Klie, R.F., Idrobo, J.C., Browning, N.D., Regan, K.A., Rogado, N.S., Cava, R. J. Appl. Phys. Lett. 2001, 79, 1837–1839. Gümbel, A., Eckert, J., Fuchs, G., Nenkov, K., Müller, K.-H., Schultz, L., Appl. Phys. Lett. 2002, 80, 2725–2727. Varin, R.A., Chiu, Ch. Journal of Alloys and Compounds 2006, 407, 268–273 Nath, M. and Parkinson, B. A. J. Am. Chem. Soc. 2007, 129, 11302-11303 Zhao, Y. G., Zhang, X. P., Qiao, P. T., Zhang, H. T., Jia, S. L., Cao, B. S., Zhu, M. H., Han, Z. H., Wang, X. L. and Gu, B. L. Physica C 2001, 361, 91-94 Prikhna, T.A., Gawalek, W., Savchuk, Ya.M., Moshchil, V.E., Sergienko, N.V., Habisreuther, T., Wendt, M., Hergt, R., Schmidt, Ch., Dellith, J., Melnikov, V.S., Assmann, A., Litzkendorf, D., Nagorny P.A. Physica C 2004, 402, 223-233 Oguchi, T. J. Phys. Soc. Jpn. 2002, 71, 1495-1500. Guo, J.D., Xu, X.L., Wang, Y.Z., Shi, L., Liu, D.Y. Materials Letters 2004, 58, 37073709 An, J. M. and Pickett, W. E. Phys. Rev. Lett. 2001, 86, 4366-4369 Schmidt, H., Zasadzinski, J. F., Gray, K. E. and Hinks, D. G. Phys. Rev. Lett. 2002, 88, 127002-1-127002-4

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

18

Wei Du

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[85] Findikoglu, A. T., Serquis, A., Civale, L., Liao, X. Z., Zhu, Y. T., Hawley, M. E. and Mueller, F. M. Appl. Phys. Lett. 2003, 83, 108-110 [86] Jin, B. B., Klein, N., Kang, W. N., Kim, H. J., Choi, E. M., Lee, S. I., Dahm, T. and Maki, K. Phys. Rev. B 2002, 66, 104521-1-104521-6 [87] Zhukov, A. A., Purnell, A., Miyoshi, Y., Bugoslavsky, Y., Lockman, Z. and Berenov, A. Appl. Phys. Lett. 2002, 80, 2347-2349

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

In: Magnesium Diboride (MgB2) Superconductor Research ISBN: 978-1-60456-566-9 Editors: S. Suzuki and K. Fukuda © 2009 Nova Science Publishers, Inc.

Chapter 2

SYNTHETIC AND PHENOMENOLOGICAL APPROACHES TO 2 DIMENSIONAL HIGH-TC SUPERCONDUCTIVITY IN THE LAYERED CUPRATES: DESIGN AND CREATION OF 2 DIMENSIONAL HYBRID SYSTEMS WITH DISCRETE SUPERCONDUCTINGINSULATING AND SUPERCONDUCTING-MAGNETIC SUBSYSTEMS

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Soon-Jae Kwon1 Advanced Materials Lab., Samsung Advanced Institute of Technology, Giheung-Gu, Yongin-Si, Gyeonggi-Do 446-712, Korea

Abstract The most challenging question on high-transition temperature (high-Tc) superconductivity is what interaction makes the transition temperature (Tc) high and mediates the electron pairing (Cooper pairing). Is electron pairing confined to only 2 dimensional (2 D) or effectively 3 dimensional (3 D) by interlayer interaction? Intercalation chemistry applied to high-Tc cuprate superconductors has provided a way of controlling the dimensionality as well as modifying the charge carrier density in the superconductively active copper-oxygen layer. The free modulation of interlayer distance in a layered high-Tc superconductor is of crucial importance for the study of the superconducting mechanism. 2 D superconductors were achieved by intercalating a long-chain organic compound into bismuth-based cuprate superconductors. The long-chain organic compounds were incorporated into the layered cuprates with systematic increment of interlayer distance, while the atomic arrangement of each cuprate sheet was unchanged. The physico-chemical characterizations revealed that the orgnic-cuprate lamellar heterostructure shows high-Tc superconductivity even in the isolated cuprate layer, which was confirmed in microscopic scale by muon spin rotation/relaxation experiment as well as in macroscopic scale by d.c. magnetic susceptibility measurement. Although a remarkable increment of interlayer distance, to tens of angstroms, upon organic 1 E-mail address: [email protected]/[email protected].

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

20

Soon-Jae Kwon chain-intercalation, the superconducting transition temperature of the heterostructured system was nearly the same as that of the pristine material, suggesting the 2D nature of the high-Tc superconductivity. For a series of intercalation compounds, the electronic and geometric structures of the guest (inorganic or organic species) and the host (cuprate layer) have been investigated by the synchrotron radiation X-ray absorption spectroscopy, revealing that the electronic interaction between cuprate lattice and the incorporated species is responsible for the subtle change in the copper-oxygen layer and in turn Tc variation. In a structural view point, the intercalation compounds of high-Tc superconductors can be seen as a series of naturally grown superconducting-insulating-superconducting(S-I-S) superlattices, whose degree of coupling between superconductive layers may be systematically modified by adopting an appropriate guest. A novel heterostructured spin-system was developed by incorporating a spin-active species into bismuth-based cuprate layers, which showed extraordinary magnetic behavior of superconducting-paramagnetic dual magnetism. The unprecedented hybrid of high-Tc cuprate and paramagnetic species may provide not only a probe for high-Tc superconductivity but also a way of creating materials with spin- or magnetic field-dependent functionality unattainable from conventional solid-state materials.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

1. Introduction Since the discovery of high transition temperature (high-Tc) superconductivity in the layered cuprates, intensive and extensive efforts have been put into superconductivity research, which continues today. There was therefore great excitement when Bednorz and Müller discovered superconductivity in La-doped Ba cuprate at 36 K in 1986, [1] and Wu et al. found it in a related O-doped Y-Ba cuprate at 93 K, [2] which could not be understood by the conventional Bardeen-Cooper-Schrieffer (BCS) theory. [3] Since then superconductivity has been found in a large number of similar Bi-, Tl-, and Hg-based cuprate materials at temperatures up to 135 K. These superconductors have been attracted, because they have the possibility of a wide range of application and the relevant science is fascinating. The most challenging question on high-Tc superconductivity is what interaction makes the transition temperature (Tc) high and mediates the electron pairing (Cooper pairing): Is electron pairing confined to only 2 dimensional (2 D) or effectively 3 dimensional (3 D) by interlayer interaction? Apart from their high temperature superconducting transitions, the cuprate superconductors have a common structural feature which make them distinguished from typical low-Tc metal superconductors. These oxide compounds contain copper-oxygen sheets with the formula CuO2; however, such as bismuth and thallium play a key role in this new class of superconductors. These CuO2 planes contain mobile charge carriers and are thought to be the active part of the superconductivity. The carriers are usually sharply confined in the planes, and this makes the interaction between the planes relatively weak. For this reason the cuprate often have extremely anisotropic properties, in both the normal and the superconducting state, with poor conduction in the c- direction. In this respect, it is generally assumed that the normal and superconducting state properties of the layered high-Tc cuprates derive from the charge and spin dynamics in the CuO2 plane, while the other structural components in the unit cell function either as inert “spacers” or as charge “reserviors” that regulate the charge density in the CuO2 plane. Consequently, a lot of theoretical models ignore the effects of interlayer coupling, and attempt to discover essential phenomena of the layered cuprate by exploring the properties of an isolated CuO2 plane. “Single layer models”, including the marginal Fermi liquid, [4] antiferromagnetic Fermi liquid, [5] and ordinary Fermi liquid [6] models of the high-Tc cuprates, generally assume that the essential physics of

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

21

the cuprates is described by the properties of a single CuO2 plane. Uemura et al., suggested that the Tc’s are governed mainly by the in-plane charge carrier density. [7, 8] On the other hand, “interlayer coupling” descriptions assume that either interlayer Josephson tunneling [9-11] or interlayer pairing [12,13] contributes to superconductivity. Experimental studies of YBa2Cu3O7/PrBa2Cu3O7 superlattices show that superconductivity with a depressed Tc persists in essentially isolated pairs of nearest-neighbor CuO2 planes (“bilayers”). [14-17] However, it is not known whether the depressed Tc in these superlattices is due to a loss of interbilayer coupling, [14,15] a reduction in the in-plane carrier concentration, [16] or an increase in anisotropy. [18] The representative description of this theoretical model is given by Wheatley et. al., where the interlayer coupling between the CuO2 planes enhances the superconductivity. [9] While better understanding is achieved both theoretically and experimentally of the superconductivity, the validity of the proposed models has remained unconfirmed due to the lack of experimental evidences. If the degree of interlayer coupling can be controlled, it will be informative to understand the relation between interlayer coupling and the superconductivity. In this regard, the intercalation into high-Tc superconductor is expected to be quite effective because it allows us to control the strength of interlayer coupling. Intercalation technique has been widely applied not only to study chemical and physical properties of low dimensional compounds but also to develop new nano-hybrid materials that cannot be prepared by conventional solid state methods. The essential advantage of this technique is to allow some degree of modification in geometric, chemical, electronic, and optical properties of host and guest. For low-Tc superconductors, Gamble et al. derived strongly anisotropic or two dimensional superconductivity by intercalating organic molecules into transition-metal dichalcogenides, MX2 (M = Ta, Nb, X = S, Se). [19-22] In high-Tc superconductors, the dimensionality of high temperature superconductivity has also been interesting subject for understanding the underlying high-Tc mechanism. Actually, there has been naïve question whether a few-unit-cell thick untrathin or unit-cell thick films, neither buffered nor covered with other materials like in YBCO/PrBCO superlattices, should have Tc lower or equal to or even higher than the bulk Tc. [23] However, for the empirical research, an ideal 2 D system is highly needed. In this respect, the intercalation chemistry applied to layered high-Tc superconductor can derive such an isolated single cuprate sheet without significantly perturbing the crystal and electronic structure of cuprate building block. Among the various high-Tc cuprates, Bi-based cuprate superconductors, Bi2Sr2Cam−1CumOy (m = 1, 2, and 3), [24,25] exhibit most anisotropic feature in crystal structure and electronic properties due to the weak van der Waals interaction between Bi2O2 double layers, which makes them suitable candidate for the intercalation reaction. There has been reported that inorganic species can be incorporated into the Bi-based cuprates. [26-29] However, intercalation of organic materials into these compounds has tremendous advantages for studying the high-Tc superconductivity as well as for the application of superconducting materials, since organic compounds show the widest variety of structural and chemical nature in that they have diverse size depending on the number of carbon atoms and in that their chemical species range from neutral molecule to various ions, even to radicals (with unpaired spin). First, the interlayer distance between the superconductive cuprate layer can be freely modulated by modifying the length of the organic intercalant, providing a clue to the unsettled problem, i.e. the relationship between interlayer coupling and high-Tc superconductivity. Second, the combination of organic

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

22

Soon-Jae Kwon

material and two dimensional cuprate lattice can be used for designing a new superconducting heterostructures with unprecedented physico-chemical properties. Third, some kinds of organic compounds, for example viologen, generate a spin-active species in a specific condition, which may contribute to solve the hotly debated issue on high-Tc superconductivity, spin interaction in the pairing mechanism, if only the spin-active radical can be hybridized with the layered high-Tc cuprates. The hybrid material that combines superconductivity with paramagnetism or ferromagnetism, will be useful for exploring the interplay between supercoductivity and magnetism, which, like oil and water, usually do not mix. Although many efforts have been devoted to prepare organic intercalated high-Tc superconductors by many chemist and material scientists, most of the trials are proved to be failed except few erroneous reports. [30, 31] This difficulty is mainly due to the geometric hindrance upon intercalation of organic molecules into rigid oxide lattice. Here some chemical intuitions are needed to overcome this energy barrier. In this respect, it was devised a new intercalation method of interlayer complexation, where a complex formation reaction was ignited in-between the two dimensional solid matrix with the interlayer gallery space acting as nano-scale reactor. [32-34] In this work, synthetic and physico-chemical studies were systematically carried out for the Bi2Sr2Cam−1CumOy interstratified with inorganic and organic species. Since the present organic-inorganic nanohybrids have the fashion of superconducting-insulating-superconducting (S-I-S) multilayers with controllable thickness of insulating layer, it is expected that the proposed theories of high-Tc superconductivity can be empirically tested. The intercalation compounds of high-Tc superconductors can be seen as a series of naturally grown S-I-S superlattices, whose degree of coupling between superconducting layers may be systematically modified by adopting an appropriate guest. We have also developed a hetetrostructured spin-system by intercalating a spin-active species (with unpaired electron spin S = 1/2; free radical in terms of chemistry) into high-Tc cuprate Bi2Sr2CaCu2Oy, in which the doped-antiferromagnetic (superconducting) and paramagnetic subsystems coexist in a unified system. [35, 36] The magnetic heterostructures showed superconducting-paramagnetic dual magnetism, although high-Tc superconducting and magnetic layers interstratified in the molecule level. To characterize the crystal structure of the intercalation compounds, X-ray diffraction and high-resolution transmission electron microscopic (HREM) analyses have been carried out. The X-ray absorption near edge structure (XANES) and the extended X-ray absortion fine structure (EXAFS) were applied to probe the electronic configuration, bonding character, and the local structural evolutions of host lattice and guest species. The electronic interaction between the cuprate block and guest layer was also theoretically examined by performing approximated molecular orbital (MO) calculations based on the extended Hückel method, which was compared with the experimental results from the XANES/EXAFS. The superconducting properties were investigated in both macroscopic and microscopic scale by the d.c. magnetic susceptibility measurement using superconducting quantum interference device (SQUID) and by the muon-spin resonance (μSR) analysis, respectively.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

23

2. Brief Introduction of Theoretical Models for High-Tc Superconductivity 2.1. Interlayer Coulomb-Coupling Model Harshman et al., tried to explain high-Tc superconductivity assuming BCS theory as the appropriate frame work, putting importance on the interlayer Coulomb interaction. [37] In this theoretical model, interplanar distance d, as well as the properties relevant to a single sheet such as the 2D carrier density n2D, the 2D effective mass mab*, the 2D Fermi energy EF2D were taken into account. According to the previous study for the multi-quantum well structures, it was suggested that “the behavior of the system is critically dependent only on the planar electron density and the spacing between the layers. [38] Küchen et. al., showed that the dilute electron gas in 3D is unstable against formation of Cooper pairing, [39] suggesting Tc would increase if the carriers were confined to planar conducting sheets and if interplanar coupling were included. One condition for optimizing the pairing would be to have n2Dd2 = β1,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

where β1 is order unity and n2D is equal to mab*/me. A requirement for a significant interaction between particles in separate planes is thus to have the spacing between the charges in one plane match the distance between planes, i.e., dkF ≈ √2π. It will also be necessary that the interplanar Coulomb interaction, VI = e2/εd, have the proper size relative to the 2D Fermi energy. If VI is too large, the carriers in neighboring planes will behave as if they belonged to only a single plane; if VI is too small, it will be too weak to yield an interplanar bound state. This condition becomes to be

where rs = √2(kFao*)-1, or equivalently, d =

πβ1 rso ao* = β 2 ao* . In the BCS theory, Tc is

given by kBTc = 1.14 =ωc (e1/Λ-1)-1, where, Λ [=N(0)V] is the BCS coupling constant, and in this 2 D case, N(0) = 1/EF2D is the density of states per unit area at the Fermi surface. If it is assumed that =ωc ≈ EF2D, then we can find Λ ≈ 0.3 for the high-Tc superconductors, corresponding to weak coupling. If the BCS interaction V is some fraction of VI and the cutoff energy of the excitation spectrum =ωc is proportional to the 2D Fermi energy EF2D, it is given

In this scheme, the Tc is inversely proportional to the interlayer distance or coupling strength. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

24

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

2.2. Anderson’s Interlayer Interaction Model Based on the anisotropic nature of normal and superconducting properties of layered cuprates, Anderson proposed some postulations on high-Tc superconductivity. [40] (1) All the relevant carriers of both spin and electricity reside in the CuO2 planes and derive from the hybridized O 2p–Cu dx2-y2 orbital which dominates the binding in these compounds. The O 2p orbitals hybridize strongly with Cu 3d’s but it is the antibonding linear combinations of the two which are relevant. For Cu2+/3+ mixed valent compound, the detail of antibonding Cu (3d)-O(2p) is slightly split due to the differences in energy level for Cu2+ and Cu3+, respectively. (2) Magnetism and high-Tc superconductivity are closely related, in a very specific sense: i.e., the electrons which exhibit magnetism are the same as the charge carriers. In most cuprate superconductors, δ = 0 (pure Cu++ oxidation state) is an antiferromagnetic insulator, with relavtively high TNeel if not frustrated. It is a Mott-Hubbard insulator with at least a 2 volt charge-transfer gap. The present view is that a relatively sharp transition occurs at δ ∼ 0.1 to a metallic state which always is superconducting, with a Tc which is initally finite. The metallic state is particular; when it turns into a more normal metal, with excessive doping, Tc goes down. From optics and photoelectron spectroscopy(PES), it is clear that the carriers appear in the Mott-Hubbard gap in proportion to the doping. NMR data show that the hyperfine couplings of the metallic carriers are identical with those of the spins responsible for magnetism. (3) The normal metal well above Tc results from the planar one-band. The most vital experimental evidence lies in the giant anisotropy of resistivity ρc/ρab. The resistivity perpendicular to the planes extrapolates to ∞ at T = 0 and is in all cases well above the Mott limit h/e2kF. This means that there is no coherent electronic transport in the c-direction. The absence of coherent c-axis electron motion in the cuprate layer compounds implies excess kinetic energy in this direction. This is due to the “confinement” property of incompressible quantum fluids such as the spinon gas. (4) The state is strictly two-dimensional and coherent transport in the third dimension is blocked. The two-dimensional state has separation of charge and spin into excitation which are meaningful only within their two-dimensional substrate; to hop coherently as an electron to another plane is not possible, since the electron is a composite object, not an elementary excitation. It seems required that Tc itself depends radically either on interactions between planes or with the substrate, and is not a purely 2dimensional effect. There are simply no indications of a unique, purely two-dimensional type of superconductivity. It is true that 2 D fluctuation effects of a fairly conventional type exists above Tc in YBCO and in fact in all the “multilayer” systems such as Bi2212 and Tl2212. It is proposed that pairs or triplets of layers do become superconducting by dint of their interlayer coupling and behave like a single conventional superconducting layer. The KosterlitzThouless behavior often seen is consistent with this idea. (5) Interlayer hopping is either the mechanism of or at least a major contributor to superconducting condensation energy. Along the c-axis there is a great barrier in conductivity: there is no coherent motion of electrons in the c-direction. This means that there is, in the normal state, a missing energy of order t⊥2/t||, which is regained in the superconducting state. There is, therefore, a contribution to the condensation energy which is not a theoretical but an experimental fact and comes from the interlayer tunneling energy. It is natural to identify this as the source of condensation energy. As a consequence, whatever the normal state physics, the mechanism of interlayer tunneling deconfinement is bound to account for Tc. Josehson-type, two-electron transport is not

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

25

blocked because the spinon fluid is a pair condensate, so that singlet pair tunnel freely. This motivates superconductivity as a 2 → 3 dimensional crossover. Anderson et. al. argued that Tc is proportional to t⊥2/t|| where t⊥ is the frustrated interlayer tunneling matrix element. However, they presumed that the actual nature of the pairing wave function is determined not by the basic interlayer mechanism which raises Tc but by the “residual interactions” whatever may they caused by phonons, spin-fluctuations, or other source. The idea is to amplify the pairing mechanism within a given layer by allowing the Cooper pairs to tunnel to an adjacent layer by the Josephson mechanism. This delocalization process of the pair gives rise to a substantial enhancement of pairing only if the coherent single particle tunneling between the layers is blocked, which is argued to be the case on phenomenological as well as theoretical grounds. In this respect, the presence of bilayers or triple layers in the high-Tc cuprates is important for raising the Tc values as shown in Figure 1.

2.3. The Spin Gap in Cuprate Superconductors

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

The spin gap can be thought of as spinon (uncharged) pairing, which occurs independently at each point of the 2 D Fermi surface because of the momentum selection rule on interlayer superexchange and pair tunneling interactions. The spin excitations are always describable as spinons, even for free electrons. The spin part is always a spinon, the charge is a bosonized Luttiger liquid. Spinons in 2 D are paired but gapless. What the nonexistence of a phase transition when we lower temperature (T) to the interplanar scale, tells us is that the spin gap state has the same symmetry.

Figure 1. Anderson's interlayer coupling model, where λ1 and λ0 represent the interblock and intrablock coupling, respectively. (Source: Reprinted with permission from [9]).

It must leave the crucial fact of Fermi or Luttiger liquid intact. Spinons are always effectively paired. [41] It is natural that spinons are more easily paired in the underdoped Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

26

Soon-Jae Kwon

regime, because the spinon velocity becomes progressively lower as we go toward the Mott insulator; therefore the density of state is higher, χpair larger, on the underdoped side. The basic description either of a Fermi or a Luttiger liquid is the independence of different Fermi surface points. If we are go smoothly from a two-dimensional electron liquid to a gapped state without change of symmetry-without introducing any new correlations-it must be done without coupling the different Fermi surface points, that is, we need interactions which conserve two-dimensional momenta kx, ky. There is only one source of such interactions, namely, the interlayer tunneling.

Two different hypotheses have been put forward for the “spin gap” phenomenon exhibited by the bilayer structures of cuprate superconductors.(As in the layered materials of YBCO and Bi2212). Strong and Anderson have proposed that the interlayer pair tunneling Hamiltonian produces a correlated state with pairing on each layer for each momentum k, but the different k’s are independently phased, pair tunneling. [42]

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Millis and Monien and coworkders have proposed that what is occurring is pair formation between the two layers with one of the pair on each layer, motivated by the interlayer antiferromagnetic superexchange. [43]

Both postulate “preformed BCS pair” states as the essential nature of the gap phenomenon. And both theories have one vital element in common: the coherent motion of single electrons between the two layers must be blocked. Antiferromagnetic “superexchange” interaction exists only if the single-particle kinetic energy is frustrated, and is a consequence of the second-order, virtual action of this kinetic energy, causing hopping of electrons between the relevant sites. This two-particle tunneling process is the basis of the interlayer theory.

2.4. Spin Interactions in High-Tc Superconductors Emery et. al. insisted that the properties of high-Tc cuprate superconductors are consistent with a model in which the charge carriers are holes in the O(2p) states and the pairing is mediated by strong coupling to local spin configurations on the Cu site, CuII↑⎯O+↑⎯

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

27

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

CuII↑⎯O⎯ CuII↓. According to this model, anisotropic electron-pairing is produced by exchange of spin-fluctuations as shown in Figure 2. [44] The interchange of a and b lowers the energy, and real bound pair (spin polaron) will form. There is an instantaneous magnetic moment at a, which is somewhat smaller than the full moment since the spins are delocalized. It is opposite to the spin of one of the other O(2p) holes. Exchange of the holes at b and c may be accomplished by an (ab) interchange, followed by an (ac) interchange. In this regard, the hole moving in an antiferromagnetic back ground leaves spin-flip in its wake. A new approach to the theory of high-temperature superconductivity is supposed, based on the two-dimensional antiferromagnetic spin correlations, observed in these materials over distances large compared to the lattice spacing. The spin ordering produces an electronic pseudogap ΔSDW which is locally suppressed by the addition of a hole. This suppression forms a bag inside which the hole is self-consistently trapped.

Figure 2. Spin-interacting model in the copper-oxide plane by Emery et al. (Source: Reprinted with permission from [44]).

Two holes are attracted by sharing a common bag. (Spin-bag mechanism). In the Resonant-valence-Bond (RVB) approach, [45,46] it is assumed that the spin 1/2 and charge (+e) of each hole are separated and become independently excitated, just like a hole in polyacetylene which splits into a spinless positively charged soliton and a spin-1/2 neutral soliton. The spinless charge objects of the RVB approach are presumed to be condensed in three dimensions, in the presence of interplanar hopping by boson pairs. There are two qualitative effects of the hole on the spin order. First, the spin of the hole couples to the spin density of the antiferromagnetic background through an exchange interaction. [44] While this

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

28

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

effect is similar to the conventional spin-polaron effect in which an electron is coupled to an array of localized Heisenberg spins, the spin polaron has a ferromagnetic core while the spin bag reduces antiferromagnetic order inside. Second, the added hole locally depletes the electronic charge density. Of course the hole and its surrounding bag move through the crystal and act as a fermionic quasiparticle, having charge +e and spin-1/2. The spin effect also leads to the local suppression of ΔSDW and reinforces the charge effect. It is reasonable when two such quaiparticles interact that the effective potential arising from the shared bag will be attractive and have a range of order the bag size l. This attraction is opposed by the Coulomb repulsion. It is found that the net effective interaction is attractive leading to a pair condensation because the short-range nature of the Coulomb potential permits the holes to avoid the electrostatic repulsion yet remain within the bag. The resulting bag provides a strong attraction to a second hole over a distance ξSDW which appears to be sufficiently large enough to lead to high-temperature superconductivity, spin-bag mechanism. [47] Mook et al., suggested that fluctuations of spins give rise to magnetic excitations of cuprate material, and might mediate the electron pairing (Cooper pairing) that lead to superconductivity. [48] In this scheme, undoped parent compound is insulating antiferromagnets and chemical doping induces metallic and superconducting behavior due to the spin fluctuation. According to Ioffe et. al., in the actual cuprate material, thermal and quantum fluctuations in each plane may effect the superconducting properties, [49] where they assert that pseudogap is caused by pairing without long-range phase coherence. There was a suggestion that the conducting carriers (probed by infared spectroscopy) are strongly coupled to a resonance structure in the spectrum of spin fluctuations (measured by neutron scattering). According to Carbotte et. al., the coupling strength inferred from those results is sufficient to account for the high transition temperatures of the copper oxides, highlighting a prominent role for spin fluctuations in driving superconductivity in these cuprate materials. [50]

2.5. One Dimensional (1-D) Stripe Model Considerable attention has been paid to the possible formation of spin-charge stripes in highTc superconductors. There was proposed a model that spatial modulation of the spin and charge density induces charged domain walls in the copper-oxide sublayer which is related to superconductivity in the copper oxides. This was based on the theoretical prediction that strongly interacting two-dimensional electron system self-organizes into one-dimensional substructures. [51] Stripes are a complex form of electronic self-organization that occurs in close proximity to the superconductivity found in the layered cuprates. The gap of the electronic spectrum for the underdoped cuprates is believed to be closely related to the stripes. Stripes are particularly well developed at low dopings, and fade away where superconducting Tc’s are highest. [52] Figure 3a and 3b comparatively depict the standard model for the cuprate superconductors formed by a superlattice of Josephson coupled homogeneous CuO2 layers and the recently proposed model for the cuprate superconductors formed by a superlattice of quantum stripes in the CuO2 plane, respectively. Unlike conventional metals in which the charge distribution is homogeneous, doped holes are confined in each stripe, the stripe picture

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

29

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

asserts that the charge carriers are segregated into one-dimensional (1D) domain walls. At the same time, the electronic spins in the domain between the walls order antiferromagnetically with a π phase shift across the domain wall as shown in Figure 3b. [52] Here the charge distribution cannot be detected directly by neutrons; instead, the modulation of atomic positions associated with the charge modulation (a charge-density wave) can be measured. [53]

Figure 3. (a) Pictorial view of the standard model for the cuprate superconductors formed by a superlattice of Josephson coupled homogeneous CuO2 layers. (b) Pictorial view of the proposed model for the cuprate superconductors formed by a superlattice quantum stripes in the CuO2 plane (Source: Reprinted with permission from [56]).

There is growing experimental evidence that the superconducting CuO2 plane is not homogeneous at a mesoscopic scale. Stripes of undistorted lattice (U-stripes) of width L running in the x direction are intercalated by stripes of distorted lattice (D-stripes) of width W forming a superlattice of stripes with period λp = L + W, have been found as shown in Figure 3b. The width L in the Bi212 system has been first measured by joint Cu K-edge EXAFS and electron diffraction. [54, 55] The period λp has been determined to be ~ 25 Å in most of the cuprate superconductors at optimum doping, with λp ~ ξo, satisfying the condition for Josephson coupling in the plane. In the present model, the separation W between the stripes is large enough to neglect single particle hopping along y but shorter or of the order of the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

30

Soon-Jae Kwon

superconducting coherence length in order to allow Josephson coupling in the superconducting phase. [56]

3. Crystal and Electronic Structures of High-Tc Superconductors

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

3.1. Electronic Structure of Cuprate Superconductors The common structural feature of high-Tc superconductors is the existence of copper-oxygen layer embedded in-between the inonocovalent spacer or charge reservoir layers. Since these compounds are derived from the Perovskite or Perovskite-related oxides whose chemical bonds between metal and oxide ions are considerably ionic, the electronic structure of high-Tc cuprate superconductors can be understood based on the ionic model. In highly covalent oxides, the real charge on oxygen is actually less than one; however, the oxidation state remains –2 by definition. Divalent copper usually forms four short bonds to O2- which are nearly coplanar with Cu2+. However, it is also common to have a fifth oxygen ligand to Cu2+ forming a square pyramidal coordination or a fifth and sixth oxygen forming a distorted octahedron. The fifth and sixth oxygens are normally at longer distances, i.e., the central copper ion experiences Jahn-Teller distortion. An another feature common to copper oxides is the availability of mixed oxidation states, for instance, Cu2+/3+ in La2-xSrxCuO4 and Cu1+/2+ in Nd2-xCexCuO4. It is essential for metallic properties and for superconductivity that the two oxidation states should be present on one crystallographic site. For example, YBa2Cu3O6 is neither metallic nor superconducting because Cu1+ and Cu2+ occupy distinct crystallographic sites and there is no mixed valency on either site. On the other hand, YBa2Cu3O7 is metallic and superconducting, and this is related to Cu2+,3+ mixed valency in the CuO2 sheets. The mixed valency situation may be equally well described in terms of bands. The band of copper is the Cu 3dx2-y2-O 2p band. Both of these are σ* bands. For the lowest oxidation state (Cu1+), this band is filled; for the highest oxidation state (Cu3+), this band is empty. According to simple band structure considerations, metallic properties are expected for any partial filling of this σ* band in copper oxides. While metallic properties are indeed observed for most of the intermediate band fillings, insulating properties are always found for the halffilled band, i.e., the situation for pure Cu2+. There are two competing mechanisms to produce an insulating state for the half-filled σ* band. One is through valency dispropertionation, and this is the case for another mixed valent oxide, BaBiO3, i.e., 2Bi4+ → Bi3+ + Bi5+. If Bi4+ had not disproportionated in BaBiO3, it is expected that this compound to be metallic because it would have a half-filled band. The real charges on Bi3+ and Bi5+ are very much lower than the oxidation states due to covalency effects. Thus, the real charge difference between Bi3+ and Bi5+ is much less than two. The disproportionation situation of BaBiO3 is termed as charge density wave (CDW). There is another way to achieve an insulating state for the half-filled band, and that is through antiferromagnetic ordering. This happens for all of the copper oxides which contain copper only as Cu2+. Thus, spin pairing of electrons on Cu or Bi sites is always related to the insulating state of the Cu2+ and Bi4+. In the case of Bi4+, spin pairing occurs on alternate Bi sites creating Bi3+ and Bi5+. The magnetic situation in the Cu2+ oxides may also be described as a spin density wave (SDW). Sleight referred to the two competing mechanism for

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

31

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 4. Schematic picture of the hybridized Cu-O bands arising in a copper-oxides with various local symmetries around copper ion. On the top, atomic positions are schematically shown. The atomic 3d and 2p orbitals, at the right and left sides, are split by the Jahn-Teller distortion. (Source: Reprinted with permission from [62]).

localization at the half-filled band as disproportionation and magnetic. [57] For instance, it can be said that if BaBiO3 did not become insulating through disproportionation, it would have become a BaBi4+O3 antiferromagnetic insulator. However, muon spin rotation experiments have completely ruled out such an unlikely possibility. [58] It can be also said that, if Cu2+ oxides did not become antiferromagnetic, the hypothetical half-filled band metals do not exist due to electron-electron correlations which cause band splitting. The π* band is placed so that it is always below the Fermi level. The consensus from nuclear resonance studies is also that there are carriers in only the σ* band. [59] For significantly covalent compounds, such as the copper and bismuth oxides, it is not assumed that valence electrons should be assigned to either the cations or to oxygen. Rather these electrons are in the bonds between the cations and anions. Each atoms in the CuO2 sheets contributes nearly equally to the states near the Fermi level. In fact, it is known that the mobile holes must spend significant time on both copper and oxygen in order to explain the delocalization of the holes. The oxidation state situation in the oxidized copper oxides is O2- and mixed Cu2+-Cu3+ by definition. This does not mean that the charge on copper has greatly increased beyond that of a pure Cu2+ oxide. The electron was not removed from copper, but rather an antibonding electron was removed from the Cu-O bond. According to charge transfer model for the copper-oxide, the oxidation state of copper can be expressed as

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

32

Soon-Jae Kwon α | 3d9> + β |3d10L>, α2 + β2 = 1

where the |3d10L> configuration corresponds to localized covalent holes, L meaning a hole in the ligand.[60] Due to the characteristic electronic configuration of Cu-O bond, the bending of Cu-O-Cu bonds and resulting buckling of the CuO2 sheets may be of importance to superconducting properties. In the ionic limit, the CuO2 plane composed of ions would be expected to be flat and square. However, the Cu2+-O2- bond is highly covalent and the strongly antibonding nature of the π-bond cannot be ignored. This antibonding interaction is strongest for 180 o Cu-O-Cu angle and is relaxed as the bond angle bends away from 180 o. [57] For the Cu-O-Cu bond, it is a π* interaction between oxygen p-orbitals and Cu filled 3d orbitals. When the Cu-O-Cu bond is close to 180 o, it is unstable and exhibits soft-mode behavior. All the copper oxide-based superconductors commonly have holes in the conduction band that could be represented as Cu3+ or O1-. Without holes, as in La2CuO4 and in YBa2Cu2O6, no superconductivity have been observed, they are just antiferromagnetic insulators or metals. A very interesting possibility for creating Cu3+ exists with the (A3+O)mA2+2Can-1CunO2n+2 phases where A3+ is Bi or Tl.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

3.2. Electronic and Crystal Structures of Bi-Based High-Tc Cuprate Superconductors The discovery of high-Tc superconductivity in a new material which contains no reare-earth element promises to provide useful insights into the pairing mechanism in these unusual cuprates. Bismuth is the new element which distinguishes the material, Bi2Sr2Cum-1CumOy (Bi2201, Bi2212, and Bi2223 for m=1, 2, and 3, respectively), [24,25] from the 40 K class, La2-xSrxCuO4, and the 90 K class of YBa2Cu3O7. The Bi-based cuprate compounds are much more layer-like and have a pronounced micaceous nature, related to the lone-pair of electrons (6s2) on Bi3+, which are not present in Tl3+. This lone pair of electrons normally hybridizes with 6p levels and moves off to one side of the Bi3+ cation thus forcing very weak bonds to oxygen on that side. Lone pairs of many Bi3+ cations are pointed essentially toward the direction of the interlayer spacing between the two adjacent Bi-O double layers. These layers are far apart (3.7 Å) and only weakly bonded to each other. The analogous Tl-O layers in Tlbased cuprates have much shorter interlayer spacings (2.0 Å) and thus are much more strongly bound to each other. As shown in Figure 5a, these Bi-based superconductors have mica-like crystal structure and, accordingly, highly anisotropic electronic property. Here we can see that that electron delocalization along the c-axis be much easier in the Tl phase relative to the Bi one. This new material shows a superconducting onset as high as 120 K, and does not require prolonged high-temperature processing. In ionic materials Bi usually assumes +3 and +5 states and if one assumes that only the +3 configuration occurs, it might be supposed that Bi acts much like the trivalent rare earths in providing electrons of the CuO2 plane and stabilizing a structure which is largely ionic in character. The band calculations done by Krakauer et al. provided evidence that Bi is qualitatively different from the rare-earth ions in these cuprates, which may account for the distinct properties exhibited by this new materials. [61,62] According to the band calculation studies, [63,64] it was suggested that BiO bands dip below EF and the Bi, unlike the Sr and Ca ions, is not fully ionized retaining an appreciable amount of valence charge. This bismuth bonds in a covalent-metallic fashion with

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

33

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

the neighboring O2 and O3 ions, and as a result Bi-O layer plays an important role not only in doping the CuO2 layer but also in providing an additional coupling of superconducting pairs along the c-axis. The valence charge density in the (100) and (110) planes is pictured in Figure 5b.

Figure 5. (a) Crystal structure of Bi-based cuprate superconductor Bi2212. (b) Contours of the constant valence charge density in two high-symmetry planes of Bi-based cuprate (Bi2212) (Source: Reprinted with permission from [61]).

There is a quite appreciable electron density around the Bi ion, and it is bonded both to the in-plane O3 ion and to the O2 ion which binds the Bi and Cu atoms. A remarkable feature is the charge separation between the two Bi-O planes as well as the similar separation between the two Cu-O planes. This decoupling of the structure into rather isolated CuO1-O2BiO3 separated on the CuO side by Ca atoms accounts for the extreme lack of dispersion in the band structure, as well as the lamellar, micaceous character of the material. [65] It has been well known that the intercalation reaction occurs in highly anisotropic lamella structure in which the interlayer binding forces are fairly weak compared to the strong ionocovalent intralayer ones. Among the known high-Tc superconducting materials, the Bi-based cuprates, Bi2Sr2Cam–1CumOy, are suggested to be the best candidate for a host compound in intercalation reaction, since the Bi2O2 layers in these compounds are weakly interacted each other only by van der Waals-type interaction.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

34

Soon-Jae Kwon

4. High-Tc Superconductors in the 2 D Limit: [(Py-Cnh2n+1)2hgi4]Bi2Sr2Cam-1cumoy (M=1 And 2) The free modulation of interlayer distance in a layered high transition temperature (high-Tc) superconductor is of crucial importance not only for studying the mechanism of high-Tc superconductivity but also for the practical application of superconducting materials. Here two-dimensional superconductors have been achieved by intercalating long-chain organic compounds into Bi-based high-Tc cuprates, based on the novel synthetic strategy of interlayer complexation in which the complex formation reaction was ignited in-between the two dimensional solid matrix. Although the intercalation of organic chain increases the interlayer distance remarkably, to tens of angstroms, the superconducting transition temperatures of the intercalates remained nearly the same as those of the pristine materials, suggesting the 2 D nature of the high-Tc superconductivity. In addition, the novel synthetic method adopted in this work is surely useful for developing a new class of hetetrostructures with unprecedented physico-chemical properties.

4.1. Research Motivation Since the appearance of layered cuprate superconductor, much attention has been given to elucidating the origin of high-Tc superconductivity such as interlayer coupling effect [9,14,37] or in-plane charge carrier density [7, 8, 66], or both. According to the model of Wheatley, Hsu, and Anderson (WHA), the superconducting transition temperature of a layered cuprate superconductor is expressed as:

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Tc = λo + λ1

(1)

where λo is the interlayer coupling between nearest CuO2 planes (intrablock coupling) and λ1 is interlayer coupling between next-nearest planes (interblock coupling). [9] However, Uemura et al. suggested a close correlation between Tc and 2 D carrier density (ns/m*: m* = effective mass) in the layered high-Tc superconductor. [7] Extensive and intensive research efforts have been concentrated on these issues both in theoretical and empirical fields. Now the issues are still controversial due to the lack of experimental evidence. In order to solve such problems, a way is needed to freely modulate the interlayer distance without perturbing the superconducting oxide block. If we can control the strength of interlayer coupling, i.e. interlayer distance, it will be informative in understanding the relation between interlayer coupling and superconductivity in the layered cuprates. In this regard, the intercalation into high-Tc superconductors is expected to be quite effective because it allows us to control the strength of interlayer distance. In addition, intercalation can also provide useful ways of preparing high-Tc superconducting nanohybrids with multi-functional properties since it can also enables us to combine the heterogeneous chemical species into a unified chemical system. The Bi-based cuprate superconductors have weakly bound Bi2O2 double layers which make it possible to intercalate various guest species without introducing any significant changes to the superconducting block. Actually, there have been researches on the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

35

intercalation into layered high-Tc superconductors, [26-31] but the basal increment in these compound were limited to only a few angstroms. Here, for the first time, we have developed new model compounds where organic modulation layers are intercalated into Bi2O2 double layers of the high-Tc cuprate superconductors, Bi2Sr2Cam-1CumOy (m = 1 and 2; Bi2201 and Bi2212).[32-36] In such intercalates, the interlayer distance of superconductive CuO2 layer can be easily controlled by changing the number of carbon atoms in the organic chain. The present organic intercalates with remarkable layer separation can be regarded as two-dimensional (2D) limit cuprate superconductors, taking into account the small out-of-plane coherence length (ξc) in the pristine materials. [67] The organic intercalates are also regarded as weakly coupled Josephson multilayers, where the barrier width greatly influences on the diamagnetic shielding fraction. In this respect, the present organic-inorganic hybrids can be an ideal model compounds to investigate the low-dimensional superconducting theory such as KosterlitzThouless (KT) transition [68] and Lawrence-Doniach model [69] in high-Tc materials. Emphasis is especially placed on the synthetic strategy applied to develop the present organic-inorganic superconducting nanohybrids. In the present study, the long-chained organic compounds were intercalated into Bi-based high-Tc cuprates in the form of the complex salt, bisalkylpyridinium tetraiodomercurate (Py-CnH2n+1)2HgI4 based on the novel synthetic strategy of interlayer complexation. The relation between structural anisotropy and the superconducting transition temperature or between interlayer distance and the superconducting shielding fraction is discussed. To characterize the crystal structure of the intercalation compounds, X-ray diffraction and high-resolution transmission electron microscopic (HREM) analyses have been carried out. In order to probe the electronic configuration, bonding character, and the local structural evolutions of host lattice and guest, the X-ray absorption spectroscopic (XAS) analyses such as X-ray absorption near edge structure (XANES) and the extended X-ray absorption fine structure (EXAFS) were applied. The electronic interactions between the cuprate block and guest species were also theoretically examined by performing perturbational molecular orbital (MO) calculations based on the extended Hückel method, which was compared with the experimental results obtained from the XANES/EXAFS. The bulk superconductivity was investigated by the d.c. magnetic susceptibility measurements using superconducting quantum interference device (SQUID), and the microscopic superconducting property was probed by the muon-spin resonance/relaxation (μ-SR) technique, respectively. From these experimental and theoretical approaches, the possibility of two dimensional (2 D) high-Tc superconductivity is suggested.

4.2. Synthesis and Measurements The pristine Bi2Sr2Cam-1CumOy (m = 1 and 2) compounds [24,25] were synthesized by conventional solid state reaction. At first, the powder reagents of Bi2O3, SrCO3, La2O3, CaCO3, and CuO were thoroughly mixed with molar ratios of Bi:Sr:La:Cu = 2:1.6:0.4:1 for m = 1 and Bi:Sr:Ca:Cu = 2:1.5:1.5:2 for m = 2, respectively. And the obtained mixtures were calcined at 800 °C for 12 hours in air, and then, the pre-fired materials were pressed into 13 mm disk-shaped pellets and finally sintered with intermittent grindings. Depending upon the compositions, the different final heating conditions were adopted to obtain the single phasic

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

36

Soon-Jae Kwon

samples. That is, the pristine Bi2Sr2CuOy (Bi2201) and Bi2Sr2CaCu2Oy (Bi2212) compounds were prepared by heating for 40 hours in air at 890 and 860 °C, respectively. Since the stoichiometric Bi2Sr2CuOy compound possesses an overdoped hole concentration, a part of Sr2+ ion (20 %) was substituted with La3+ one to induce the highest Tc with optimum hole concentration. [70] The intercalation of organic chain into the pristines was achieved with the following stepwise synthesis. First, the HgI2 intercalated Bi2Sr2Cam-1CumOy (m = 1 and 2; HgI2-Bi2201 and HgI2-Bi2212) compounds were prepared by heating the guest HgI2 and the pristines in a vacuum-sealed Pyrex tube, as reported previously.[27,28] Then, the intercalation of organic chain was carried out by the solvent-mediated reaction between HgI2 intercalates and alkylpyridinium iodide. The reactants of alkylpyridinium iodides, Py-CnH2n+1I (n = 1, 2, 4, 6, 8, 10, and 12), were obtained by reacting alkyliodide with 1 molar equivalent of pyridine in a solvent, in which pyridine is alkylated by primary alkyliodides forming ionic salt compounds; Py + CnH2n+1I → Py+-CnH2n+1·I-. This organic-salt formation reaction results from the nucleophilic property of nitrogen lone-pair in the pyridine molecule, which is an SN2-type nucleophilic substitution reaction in terms of organic chemistry. [71] For the alkyliodide with short alkyl-chains (n = 1, 2), the salt formation reaction was easily proceeded in diethyl-ether solvent at room temperature, while it needed a condition of reflux in hexane for the longchained alkyliodide. (n ≥ 4). Then, the HgI2 intercalates were mixed with two excess of PyCnH2n+1I, to which a small amount of dried acetone (0.5 ml per 1 g of the mixture) was added. Each solvent containing mixtures was reacted in a closed ampoule at 40 °C for 6 hours and washed with a solvent blend of acetone and diethyl-ether (1:1 volumetric ratio) in order to remove the excess reactant of Py-CnH2n+1I. For the organic-salts of short alkylchain, PyCnH2n+1·I (n = 1, 2), solid state reaction at 90∼100 °C was also possible for the organic-salt intercalation. The resulting products were dried in vacuum. The samples are all air-stable. The formation of single phase stage-1 intercalates was confirmed by powder X-ray diffraction (XRD) analyses and also by cross-sectional view of high-resolution electron microscope (HREM) images. In the present organic-inorganic nanohybrids, the thinning process for the TEM measurement was not accessible by the ion-milling method because the energy exerted by the accelerated ions gives rise to structural deformation during the milling process and hampers the clear observation of structural features. In this respect, the particles of these samples were dispersed in a resin (G1-Exopy) and sliced by the ultramicrotomy with the thickness of 40 ~ 80 nm. The XAS measurements were measured on the beam lines 7C and 10B at the Photon Factory, National Laboratory for High Energy Physics (KEK-PF) in Tsukuba. The applied synchrotron X-ray radiation was provided from a storage ring of a 2.5 GeV electron beam with a current of ca. 300−360 mA. The electronic interaction between the host and the guest was also theoretically studied by performing molecular orbital calculations based on the extended Hückel method. The effect of intercalation on superconductivity was examined by d.c. magnetic susceptibility measurements using Quantum Design superconducting quantum interference device (SQUID) magnetometer with an applied field of 10 gauss.

4.2.1. Synthetic Strategy Long-chained organic compounds are outstanding guest molecules which are expected to freely regulate the interlayer distance of layered materials, so that they are excellent agents

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

37

for inducing two dimensional electronic systems due to their insulating nature against electronic conduction and to the modifiable length. Bi-based cuprate superconductors, Bi-SrCa-Cu-O, are classified into van der Waals type layered compounds whose building blocks are weakly bound between adjacent Bi-O layers. Neutral polar organic or inorganic molecules are generally incorporated into these van der Waals type layered materials with partial charge transfer between host and guest species. In this chemical point of view, many researches have been carried out to intercalate inorganic or organic guests into these layered compounds based on the model of host-guest charge transfer interaction. It has been known that halides and metal-halides could be intercalated into the Bi-based cuprates, [26-29] where the host lattice plays a role of soft Lewis-acid and the guest species a role of soft Lewis-base (Hard-SoftAcid-Base; HSAB). Thereafter a lot of attempts have been made to intercalate various organic molecules into Bi-based cuprates on the basis of HSAB concept. But most of trials were found only to be failed, which might be due to a severe geometric hindrance of bulky organic molecule and/or due to the rigidity of host lattice. Consequently, some chemical intuitions are needed to overcome this energy barrier. Here we have devised a novel synthetic strategy of interlayer complexation reaction. Taking into account the coordinately unsaturated state of mercury in HgX2-intercalates, [28] it is reasonably expected that the intercalated mercuric halide species could be further ligated by organic/inorganic ligands in the interlayer space of Bi-based cuprates. In general, the driving force of intercalation reaction is thought to be the chemical interaction between host and guest. In the present synthetic scheme, however, the major driving force of intercalation is considered to be a negative enthalpy change during the formation of tetraiodomercurate complex anion, HgI42-: HgI2 + 2I → HgI42-, ΔH = -95.8 kJ/mol [72] and, in the course of this reaction, the organic cation is also inserted into the Bi2O2 layer to meet the condition of charge neutrality. As diffusion goes on, alkyl-chains change their packing forms to make up a stable intercalation compound, which is accompanied with a large expansion of the basal spacing of the intercalate. Considering the ionic character of guest species, it is suggested that there is a partial distortion of local charge (local charge separation) in the Bi-O charge reservoir plane, giving rise to a weak electrostatic attraction between guest and host. The chemical species, which is further ligated to intracrysalline HgI2, is iodide (I-) and the counter cation is alkylpyridinium. There is a possibility that similar intercalation processes may be applied to many organic-iodide salts.

4.2.2. Structure Analyses Figure 6 represents the powder XRD patterns for the pristine Bi2212, HgI2 intercalate and (Py-CnH2n+1)2HgI4 ones (n = 1, 6 and 12), respectively. There is no trace of the pristine phase in the XRD patterns of all the present intercalates, indicating that HgI2 and organic complexes are intercalated homogeneously into host lattice. According to the least-square fitting analysis, each intercalated organic spacer layer expands the unit cell along the c-axis by 10.8, 11.3, 13.7, 17.7, 22.9, 26.7, and 31.6 Å for n = 1, 2, 4, 6, 8, 10, and 12, respectively. To investigate the evolution of superconductivity in a single CuO2 layer, the organic intercalation compounds of Bi2201, (Py-CnH2n+1)2HgI4-Bi2201, were also prepared, where the basal increment (Δd) corresponds to 10.9, 13.1, 22.4, and 31.9 Å for n = 1, 4, 8, and 12, respectively. From the relation between the hydrocarbon chain length and interlayer distance d in the organic intercalates, it is found that d is linearly proportional to the number of aliphatic carbon atoms (n) in the range of n = 4 to 12 of Py-CnH2n+1 as shown in Figure 7a.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

38

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Based on the calculated slope of Δd/n = 2.42 Å, it is suggested that the bilayered alkyl chains are stabilized in-between Bi2O2 layer with a tilting angle of ~ 70 o with respect to the basal plane.

Figure 6. Powder X-ray diffraction patterns for (a) the pristine Bi2212, (b) HgI2-Bi2212, and (PyCnH2n+1)2HgI4-Bi2212 series with (c) n = 1, (d) n = 6, and (e) n = 12, respectively. arb. units, arbitrary unit. (Source: Reprinted with permission from [32]).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

39

Figure 7. (a) Interlayer distance (d) as a function of the number of carbon atoms in aliphatic chains for (Py-CnH2n+1)HgI4-Bi2201 ({) and (Py-CnH2n+1)2HgI4-Bi2212 (z). (b) Schematic structural models of the (Py-C10H21)2HgI4-Bi2201 and (c) the (Py-C10H21)2HgI4-Bi2212, where the anions (HgI42-) are sandwiched between pyridinium cations but omitted here for simplicity. (Source: Reprinted with permission from [32]).

The formation of single phase stage-1 intercalates was confirmed also by cross-sectional view of HREM images. Figure 8a shows a HREM image and its Fourier diffractogram of the cross-section of an organic-inorganic nanocomposite obtained by ultramicrotomy. It appears to feature well-aligned planes with periodic arrangement of dark line and bright one, where the discrete bright lines represent the intercalated organic bilayers. The basal spacing estimated by the present HREM image (d ≈ 47 Å) is well consistent with that from XRD analysis. Moreover, the high-resolution plane view of the organic intercalate (n = 12) and its electron diffraction pattern illustrating atomic arrangement of the [100]Bi2212 and [010]Bi2212 orientations show that the cuprate lattice is not perturbed upon organic intercalation (Figure 8b).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

40

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 8. (A) An HREM image of the thin cross-section of a (Py-CnH2n+1)2HgI4-Bi2212(n=12) particle and (inset) its Fourier diffractogram revealing periodic arrangement of the layered nanocomposite. The basal spacing (1/2c ≈ 47 Å) is consistent with the XRD and c* represents [001]Bi2212 orientation. (B) A high-resolution plane view of the organic intercalate (n=12) and (inset) its electron diffraction pattern, where the organic material (Py-CnH2n+1)2HgI4 on the surface of the sectioned plane was cleaned with chloroform. (Source: Reprinted with permission from [32]).

4.2.3. D.C. Magnetic Susceptibility Measure Figure 9 shows the temperature dependent d.c. magnetizations of the pristine Bi2212 and its intercalates, measured in zero-field-cooled (ZFC) mode at an applied magnetic field of 10 Oe, in which the in-set represents the magnetic behaviors of the samples at around Tc of the pristine (78 K). In spite of a remarkable expansion of basal spacing, all of the organic intercalates exhibit superconductivity with the onset Tc of 81 ~ 82 K, which is higher than those of the iodine intercalate [26, 73, 74] (Tc ≈ 63 K, Δd ≈ 3.6 Å) and of the HgI2 one (Tc ≈ 68 K, Δd ≈ 7.2 Å), even slightly higher than that of the pristine (Tc ≈ 78 K). Because the organic intercalates are prepared by the reaction between HgI2-intercalate and alkylpyridinium iodide, there should be, if any, the same amount of unintercalated remnant of the pristine Bi2212 in both type of intercalates, resulting in similar magnetic behavior near the transition temperature (78 K) of the pristine. However, HgI2-Bi2212 and (Py-CnH2n+1)2HgI4-Bi2212 are found to exhibit different magnetic behavior at around 78K (in-set in Figure 9). Furthermore, the organic intercalates show higher Tc, on-set values compared to the HgI2-intercalate. The depressed Tc value upon HgI2 intercalation is recovered by the intercalation of organic-salt, which can be understood as a result of charge restoration of the host block. Because of the ionic-bonding character of the guest species itself (PyCnH2n+1)2HgI4, it is hard to expect a electronic charge transfer from host block and to intercalant layer, in contrast to the halogen or mercuric halide intercalates [26-28]. Here we investigate the applicability of the WHA model (Tc = λo + λ1) to the Bi2212 intercalation compounds. While the intercalation of inorganic or organic guests have little effect on the intrablock coupling (λo), the strength of the interblock coupling (λ1) is remarkably reduced compared to the pristine Bi2212. The Tc depression upon I2 and HgI2 intercalation left a

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

41

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

possibility of the interlayer coherent hopping mechanism suggested by Wheatly, Hsu, and Anderson, [9] where coherent hopping of the valence bond pair between CuO2 layers mediates interlayer quasi-particle (or pair) tunneling and stabilizes the superconductivity, consequently, raising the Tc. For the long-chain organic intercalated Bi2212, however, such an interlayer tunneling mechanism can not be applicable, because the layer separation is large enough to prohibit interlayer electronic or spin interactions. In addition, the carbon back-bone of the intercalated organic chain is a genuine insulator with sp3-hybrid orbital in chemistry view point and can not mediate the electronic or spin interaction between the interblock CuO2 planes. In this regards, it is reasonable to conclude that the WHA model may not be appropriate for explaining high-Tc superconductivity in the layered cuprate compounds.

Figure 9. Temperature dependence of zero-field-cooled (ZFC) magnetization (M) with an applied magnetic field of 10 G, measured with a superconducting quantum interference device (SQUID) magnetometer. Each data represents for Bi2212 („), IBi2212 (‹), HgI2-Bi2212 (c), and (PyCnH2n+1)2HgI4-Bi2212 series [ n = 1(z), 2( ), 4({), 6(U), 8(‘), 10(„), 12(V)], respectively. The data show clearly that the shielding magnetization decreases sharply as the lattice expansion along the c-axis increases. (Inset) The normalized magnetizations for the samples, in which the arrow indicates the on-set Tc of organic intercalates. (Source: Reprinted with permission from [32]).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

42

Soon-Jae Kwon

Figure 10. (a) The onset Tc’s as a function of interlayer distance of each samples [(i) Bi2212, (ii) IBi2212, (iii) HgI22-Bi2212, and (Py-CnH2n+1)2HgI4-Bi2212 series with (iv) n = 1, (v) n = 2, (vi) n = 4, (vii) n = 6, (viii) n = 8, (ix) n = 10, and (xi) n =12], showing its insensitivity to interlayer distance. The opencircle represent Bi2212 series. (b) The diamagnetic shielding fraction and calculated volume ratio of CuO2 bi-layer for Bi2212 series as a function of interlayer distance. The dashed lines are guides to the eye. (Source: Reprinted with permission from [32]).

In order to investigate the evolution of superconductivity in single-layer superconductor, magnetizations were also measured for the organic intercalates of (Py-CnH2n+1)2HgI4-Bi2201. The superconductivity of Bi2201 is also retained upon intercalation of long-chained organic derivatives. Moreover, while Tc is depressed (ΔTc ≈ 4 K) upon iodine and HgI2 intercalation, all of the organic intercalates of Bi2201 show superconductivity with onset Tc value of 27 − 28 K, comparable to the pristine Bi2201 (Tc ≈ 26 K) (Figure 10a). Such results allow us to conclude that the Tc in the layered cuprate is essentially governed by the intrinsic property of single CuO2 plane rather than by the interlayer electronic coupling effect. Since there is only one CuO2 plane per cuprate building block of Bi2201, the long organic-chain intercalated Bi2201 is believed to be a genuine single-layer superconductor due to the large interlayer distance with respect to the small c-axis coherence length in the layered high-Tc cuprates ( d » ξc). [75, 76] Based on these findings, it becomes clear that 2D single cuprate sheet in the organic intercalate exhibits high-Tc superconductivity. Figure 10a shows the relation between Tc and the separation between the CuO2 planes in adjacent blocks, where the Tc’s of the intercalates are insensitive to the interlayer distance but are mainly dependent on the nature of the intercalant.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

43

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Such findings are very interesting in the light of the interlayer coupling theory in high-Tc superconductivity, which predicts that Tc is proportional to the coupling strength between adjacent superconducting layers, that is, inversely proportional to the layer separation (kBTc ∝ (εd)-1). [37] The broadness of the superconducting transition observed for the organic intercalates (Figure 9) is attributed to the thermal and/or quantum fluctuations in the true 2 D superconductor. [77, 78] An isolated superconducting sheet would be described by the Kosterlitz-Thouless (KT) theory of phase transitions in 2 D systems, [25,45] where the vortex pairs remain bound below the mean-field Ginzburg-Landau (GL) transition Tc0. In structural aspect, the long organic-chain intercalated Bi2212 can be considered to be a 2 D superconducting system, since the 15.4 Å thick cuprate layers are separated by the organic spacer layers to a distance, more than 30 Å. In this respect, it is expected that the KosterlitzThouless theory is applicable to the present organic-inorganic superconducting nanohybrids. On the other hand, irrespective of Tc variation, the diamagnetic shielding magnitude diminishes monotonically with the basal increments. The superconducting shielding fractions of the pristine Bi2212 and its intercalates are represented in Figure 10b as a function of distance (d) between interblock CuO2 plane, where the shielding fraction decreases drastically as d increases. A modification of interlayer distance is found to have a more significant influence on the diamagnetic shielding fraction than on the volume fraction of CuO2 layer. The present superconducting compounds interstratified with organic spacer layer can be regarded as weakly coupled or decoupled Josephson multilayers, because their structures are periodic sequences with a fashion of superconductor-insulator-superconductor (SIS). In the present setup of magnetic property measurement, all of the grains in polycrystalline samples are randomly oriented with respect to the applied magnetic field. In this respect, such a decrease of shielding fraction with increasing d can be explained by the exponentially decreasing Josephson tunneling rate with increasing insulating barrier. [80] This explanation is supported by the previous magnetization study on the grain-aligned HgI2-Bi2212 [81], where the shielding fractions of the aligned samples at 10 K are found to be 67 % for the pristine Bi2212 (d ≈ 12 Å) and 61 % for HgI2-Bi2212 (d ≈ 20 Å) whereas those of nonaligned samples are determined to be ∼42 % for the former and ∼21 % for the latter. That is, the diamagnetic shielding fraction differences between the pristine Bi2212 and the HgI2Bi2212 correspond to 21 % for the non-aligned samples and only 6 % for the alinged ones. The difference between the aligned sample and the non-aligned one is attributed to the contribution of c-axis tunneling, because the superconducting planes are perpendicular (inplane supercurrent) to the applied field in the former while they are randomly oriented (both in-plane and Josephson supercurrent) in the latter. In this postulation, the magnetizations of the aligned samples are not significantly affected by the thickness of insulating barriers, since only the in-plane supercurrents contribute to the superconducting diamagnetic shielding. (Figure 11a) For the non-aligned samples, the magnetizations would be significantly influenced by the thickness of insulating layers, because both in-plane and Josephson supercurrents contribute to the shielding supercurrent. (Figure 11b) When the magnetic field is perpendicular to the CuO2 plane, it is expected that the lower critical field, Hc1⊥, is not significantly changed depending on the layer separation. However, if the applied field is parallel to the layers, the magnitude of Josephson shielding current will be greatly influenced by the thickness of intercalant layers. If the insulating barrier layer is thin enough to allow

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

44

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Josephson current to flow, then the magnetic fluxes is partially shielded. (Figure 11c) When the intervening barrier layers are thick enough to prohibit Josephson tunneling, the energy cost for magnetic flux to penetrate parallel to the layers vanishes, thus Hc1∥ = 0, [82] i.e., the material is transparent to an applied magnetic field. (Figure 11d) The long organic-chain intercalated Bi2212 is believed to be the case of Figure 11d, by which the drastic decrease of diamagnetic shielding can be understood. From the above results and postulations, it is concluded that the increasing barrier thickness is mainly responsible for the drastic decrease of diamagnetic shielding fraction in the intercalated system. It is noted here again that experimental data strongly suggest a superconducting transition in the 2 D limit, both in bilayered CuO2 plane and monolayered CuO2 one. In addition, irrespective of Tc, the tunneling between the superconducting planes is sharply affected by the interlayer distance.

Figure 11. (a) Only the in-plane shielding supercurrent flows when the superconducting layers are aligned perpendicular to an applied magnetic field. (b) Both the in-plane and out-of-plane (tunneling) shielding supercurrents flow in the randomly oriented particles. (c) A finite Josephson current flows if the insulating layer-thickness is thin enough to allow Cooper-pair tunneling. (d) There is no Josephson shielding current if the insulating layer-thickness is thick, resulting in no shielding effect.

The muon spin rotation and muon spin relaxation (μSR) measurements have been carried out for the organic-inorganic nanohybrid superconductor, in order to investigate the superconducting volume faction, superconducting transition temperature, and magnetic behaviors in the heterostructured multilayer. The sample (2-cm diam with 1.5-mm-thick disk) was mounted in a cryostat with its face perpendicular to the incident muon beam, where the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

45

sample disk was shaped by pressing the polycrystalline powder, (Py-C12H25)2HgI4-Bi2212. (The data are not shown here) μSR provides a reliable method of determining Tc, since relaxation rate σ(T) increases suddenly below Tc with decreasing temperature and because the μSR signal clearly reflects the superconducting volume fraction. [7] Compared to other methods, μSR measurements have several advantages: (1) The concentration of superconducting carriers ns can be directly studied. (2) μSR signals are volume proportional; the results are relatively insensitive to small impurity phases. (3) The extrapolated values of σ (T→0) can be determined very accurately. The muon spin rotation spectrum for the (Py-C12H25)2HgI4-Bi2212 measured at 10 K (data not shown here), there observed a long-lived component and a fast relaxing one. The long-lived component corresponds to either non-superconducting or weakly superconducting (with small ns/m*) volume, which is about 30 % of the sample. μSR is a powerful method for detecting static magnetic order since the muons are acts as miniaturized bar-magnets. The resulting muon decay-time histogram reflects the local magnetic fields seen by the implanted muons. In this work, the static magnetic order is thought to be the vortex fluxes in the mixed state type-II superconductor. Therefore, the existence of long-lived component is attributed to the non-vortex state, that is, homogeneous magnetic field in the nonsuperconducting medium. These postulations can be rationalized by the orientation effect and structural feature of the organic-inorganic nanohybrid. Here we assume two extreme cases of orientation. When the superconducting plane is perpendicular to the external magnetic field Hext, the mixed state will be induced forming a flux-line lattice. These magnetic fluxes cause a fast depolarization of the muon spins, contributing to the fast relaxing component. On the other hand, if the applied magnetic field Hext is parallel to the CuO2 planes (Hext//ab), then Hext will penetrate the sample homogeneously due to the absence of Josephson current across the superconducting layers. Accepting that the flux-line (or vortex) cores are located between the supercoducting CuO2 planes, [83] the supercurrent circulating around the core have to flow in the CuO2 planes and tunnel between them. In the 2 D description, like in the present case, the superconducting order parameter is large in the CuO2 planes, but almost uniformly zero between the layers. According to Kes et al., the field parallel to the planes penetrates in the form of Josephson vortices with mutual distance a ≈ φo/Bs, where s is the distance between the CuO2 planes and B is an applied magnetic field. [82] Since the screening is very weak, both Hc1 and the magnetizations are extremely small, that is, the field penetrates between the decoupled superconducting layers as if the material is “magnetically transparent.” Due to the 2 D nature of the present organic-inorganic nanohybrid, a magnetic component parallel to the superconducting layers would induce no flux-line lattice. In this respect, it is quite reasonable that the layers parallel to the external magnetic field would not significantly perturb the muon spin precession pattern, allowing an appreciable amount of long-lived component. The temperature dependence of the muon spin relaxation rate σ was measured from 100 K to 10 K, where it is observed a gradual increase of muon spin relaxation rate below T = 80 K, and a sharp change near T = 10 K. The on-set transition temperature 80 K is consistent with the value obtained by d.c. magnetization measurement. The gradual increase of relaxation rate imply that there is an inhomogeneous distribution of Tc’s in the sample, which is also identical to the broad superconducting transition for the (Py-C12H25)2HgI4-Bi2212. Besides the possibility of inhomogeneous Tc distribution, the gradual increase of relaxation rate for the high temperature region (∼80K) and the sharp change for the low temperature

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

46

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

(∼10K) may be related to the thermal fluctuations of vortex lines in 2 D superconducting system [83, 84], where vortex decoupling occurs between adjacent CuO2 bi-layers due to a remarkable layer separation of 44 Å in the present intercalate, increasing the nonsuperconducting normal core. [85] In this scheme, the thermodynamic motion of the vortex lines (vortex melting) cause the dissipation of supercurrent, exhibiting broad superconducting transition. In the same context, the quenching of vortex motion (vortex freezing) at low temperature will reduce the dissipation effect, increasing superconducting volume fraction. For the 2 D limit superconducting system (Py-C12H25)2HgI4-Bi2212, a sharp increase of muon spin relaxation rate σ at 10 K indicates a kind of phase transition, that is to say, flux-line freezing from liquid- like phase into crystalline lattice. For the pristine Bi2212, however, the flux-lines appear to behave 3 D like at relatively high temperature. [86] In this respect, it is suggested that the organic intercalation into the Bi2212 significantly modifies the fieldtemperature (H-T) phase diagram which is relevant to the flux-line phase transition of mixed sate superconductors. Nevertheless, more researches both in theoretical and experimental field are needed to assess the effect of dimensionality on the flux-line behavior.

4.2.4. X-Ray Absorption Analysis (XAS) Although it is well expected that the electronic interaction between the adjacent cuprate blocks would be minimized in the intercalation compounds due to the large increase of basal spacing, their superconducting transition temperatures are not dependent on the interlayer distance. As observed in the organic intercalates, the depressed Tc upon HgI2 intercalation has been restored to the value of the pristine compound, or even slightly higher, in spite of further basal increment. These results could not be understood on the view point of interlayer interaction scheme such as WHA model. [9] In order to understand not only the relation of Tc – lattice expansion and/or Tc – hole but also the effect of intercalation upon the geometric and electronic structures of the host and the guest, chemical interaction and crystal structure of these intercalates should be systematically investigated. However, these intercalation compounds have highly anisotropic crystal structure, which hampers the in-plane crystal structure by the XRD analysis. In this respect, XAS is the most powerful way of investigating not only an electronic structure of a specific atom by XANES but also a local structure around absorber atom by EXAFS due to its element selectivity. Here I LI-XANES analyses for iodine have been carried out to probe orbitals with p character which are primary orbitals interacting with host lattice. The white line, corresponding to the transition from the 2s level to unoccupied np state above the Fermi level, gives a direct measure on the electronic interaction between host block and guest species, which is very informative in understanding the Tc variations upon intercalation. The changes of local structure around Hg have been followed by the curve fitting analysis for the Hg LIII-edge EXAFS spectra, where the twocoordinated HgI2 is transformed to HgI42- upon organic salt intercalation confirming the synthetic strategy. In addition to the XANES/EXAFS studies on the guest species, the Cu Kedge XANES and EXAFS spectra have been analyzed for the pristine and its intercalates in order to understand a relationship between the variation of electronic configuration of CuO2 layer and the Tc depression/increase upon intercalation. In this work, the XANES and EXAFS analyses are concentrated on the Bi2212 and its HgI2- and (Py-Me)2HgI4-intercalate (Me = – CH3).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

47

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

I LI-edge XANES

Figure 12. (a) I LI-edge XANES spectra for I2 (lightface solid line), HgI2 (lightface dashed line), HgI2Bi2212 (boldface dashed line), (Py-Me)2HgI4 (boldface dash-dot line), and (Py-Me)2HgI4-Bi2212 (boldface solid line), Py-MeI (boldface dash-dot-dot line) and KI (dotted line) and (b) their second derivative spectra.

Figure 12a and 12b show the I LI-edge XANES spectra and their second derivatives, respectively, for HgI2-Bi2212 and (Py-Me)2HgI4-Bi2212, together with the I2, HgI2, (PyMe)2HgI4, Py-MeI and KI as reference compounds. All the spectra except for KI and Py-MeI shows a pre-edge A called “white-line” in the range of 5185 ~ 5188 eV, assigned to the transition from 2s core level to empty 5p state. As can be seen in Figure 12b, the white-line feature is completely absent for the ionic species such Py-MeI and KI. In contrast to the ionic compounds, the HgI2 exhibits a small but distinct pre-edge peak, even though it has formal charge of –1. This white-line feature of the HgI2 is attributed to the formation of partially empty 5p state due to a strong covalent mixing between Hg 6s orbital and I 5pz one. [87] The high polarizabilities of soft I- and Hg2+ ion with an electronic configuration of [Xe]4f145d106s0 where d and f electrons shield the nucleus poorly, compared to the K+ ion with a [Ne]3s23p64s0 electronic configuration. According to the previous studies on the iodine intercalated Bi2212, it was revealed that a partial electronic transfer occurs from host lattice to the iodine forming a new intracrysalline iodine species I3-. [88] Upon HgI2 intercalation, the intensity of pre-edge peak A is also reduced, indicating that there happens a electron

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

48

Soon-Jae Kwon

transfer from host lattice to the intercalant HgI2 layer. On the other hand, for the (PyMe)2HgI4 intercalate, the pre-peak is remarkably depressed compared to the case of HgI2Bi2212. (Figure 12a) In this case, however, the reduction of pre-edge peak is not likely due to the charge transfer between the host lattice and the guest, because it is too drastic a change to be assigned as the charge transfer effect. Therefore, it is naturally supposed that electrons filling the empty I 5p state come from I- during the process of interlayer complexation, HgI2 + 2I- → HgI42-, where the complex anion HgI42- is formed by the charge transfer-type bond formation between HgI2 (intracrystalline) and I-. As shown in Figure 12b, the pre-edge peak of (Py-Me)2HgI4 intercalate shifts toward higher energy side compared with that of the HgI2 intercalate, indicating a drastic change in the electronic configuration. The change in the oxidation state of iodine can be also examined from variation of energy difference between the white line peak and the second absorption one at about 5190 eV corresponding to the transition to the unbound continuum state. From the peak positions in the second-derivative spectra, the transition energy of 2s → 5p (EWL) and 2s → continuum state are identical both for the (Py-Me)2HgI4-Bi2212 and free (Py-Me)2HgI4, confirming that the intercalated chemical species is converted from HgI2 to (Py-Me)2HgI4. According to the quantitative analyses for the I LI-edge XANES spectra, the I 5 p-orbital occupancies are determined to be 5p5.30 and 5p5.40 for the free HgI2 and the HgI2-Bi2212, respectively, indicating an electron transfer of 0.1 e- per iodine atom from the host lattice to the HgI2. For the (Py-Me)2HgI4 intercalate, the 5p-orbital occupancy is deduced to be 5p5.62, which implies that the electrons from two ligating I- (5p6) are delocalized in the HgI42- to give an average occupancy of p5.62. In this respect, the charge transfer effect from I- to HgI2 is more significant compared with that from the host lattice to HgI2. As a natural consequence of this change in I 5p-orbital occupancy, it is expected that the oxidation state of the CuO2 layer is more or less modified by the change in the electronic configuration of the guest. The systematic analysis of the I LI-edge XANES shows that the degree of electron transfer effect is more significant for the interlayer complexation than for the HgI2 intercalation, which is qualitatively correlated with the Tc recovery from the HgI2 intercalate to the organic-salt intercalates. Cu K-edge XANES/EXAFS

Figure 13. Continued on next page. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

49

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 13. (a) Cu K-edge XANES spectra for the Bi2212 (solid line), HgI2-Bi2212 (dashed line), (PyMe)2HgI4–Bi2212 (dash-dot line) and (b) their second derivatives. The peak P, A, B, C, and A’ correspond to 1s → 4d, 1s → 4pπ (d10L), 1s → 4pπ(d9), 1s → 4pσ(d9), and 1s → 4pσ(d9L), respectively. (Inset) Enlarged view of peak A’.

In order to understand the effect of intercalation on the electronic structure of superconducting CuO2 layer, we have measured the Cu K-edge XANES spectra for the pristine Bi2212 and its intercalates. Figure 13a and 13b represent the Cu K-edge XANES spline and the second derivative spectra for Bi2212, HgI2-Bi2212 and (Py-Me)2HgI4-Bi2212, respectively. The Cu K-edge XANES and EXAFS spectra for the long organic-chain intercalated samples, (Py-CnH2n+1)2HgI4-Bi2212 (n = 6, 8, 10, and 12), show the same spectral feature as that for (Py-Me)2HgI4-Bi2212. Therefore, the analysis for the organic-salt intercalate is concentrated on the (Py-Me)2HgI4-Bi2212. As shown in Figure 13a and 13b, all the spectra show the characteristic peaks of the Bi-based cuprate corresponding to the dipoleallowed (Δl = ± 1) transitions from core 1s level to unoccupied 4p states which are denoted as A, A′, B, and C, together with the pre-edge peak P. Among the peaks, the pre-edge peak P is assigned to the transition from core 1s level to the final state with unoccupied 3d states. [89] Even though this pre-edge feature is primarily forbidden by electronic dipolar selection rule (Δl ≠ ± 1), it can be attributed to a quadrupole-allowed transition and/or due to mixing of 4p and3d states. According to the previous XAS studies on the cuprate compound with various valence states and local symmetries of copper, the main-edge features A and B are assigned to the transition from 1s orbital to the out-of-plane 4pπ one, whereas the feature C is assigned as the transition to in-plane 4pσ one. From the polarized XANES studies, Kosugi et al. suggested that Cu K-edge spectra for the compounds with the local symmetries of square planar or tetragonally distorted octahedron could be separated to the 1s → 4pπ (out-of-plane) and 1s → 4pσ (in-plane) transitions and each transition shows twin-peak structure, in which the lower energy peak correspond to the transition to well screened core-hole final state involving shakedown process by ligand-to-metal-charge transfer (LMCT) and the higher-energy peak to the transition to poorly screened one. [90] In this respect, the lower energy peak A is assigned to the transition to the shake-down final state of |1s13d104pπ1L〉 (L represents a hole in the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

50

Soon-Jae Kwon

ligand shell) where an electron in oxygen p-orbital is transferred to the copper 3d one, whereas the peak B correspond to the final state of |1s13d94pπ1〉 without shake-down process. Thus, the final state of peak C is ascribed to be |1s13d94pσ1〉. In addition to these main-edge peaks A, B, and C, there can be seen a spectral feature at around 8985.7 eV (denoted as A’) corresponding to the transition from |1s23d8〉 state to the |1s13d94pσ1L 〉 one, which has been revealed as an indicator for the presence of Cu3+ ion. [89] Based on the above assignments, the effect of intercalation on the CuO2 layer was examined by comparing the Cu K-edge XANES derivative spectra for the pristine and its intercalates. There can be seen no appreciable difference in the edge energy and the peak intensity including A’ upon HgI2 intercalation, indicating that the changes in the electronic structure of CuO2 plane is too weak to be observed. However, for the organic-salt intercalate, the peak A’ is slightly shifted toward lower energy (Δ E ≈ 0.3 eV) as can be seen in the in-set of Figure 13b. This is interpreted as a partial reduction of Cu3+ ion upon (Py-Me)2HgI4 incorporation into the interlayer space of Bi2212. According to the electronic band calculations for the Bi-based cuprate superconductors, [62, 63] it has been suggested that the electronic structures of Bi-O and CuO2 sublayers are coupled through the chain-like orbital overlaps, Bi(6p)-O2(2p)-Cu(3d)-O1(2p)-Bi(6p)-O3(2p). It has been also reported that the Bi-O bands are sensitive to the geometry around bismuth atoms in Bi-based cupate. [91] In this scheme, the intercalant of (Py-Me)2HgI4 possibly contributes to the reduction of Cu3+ to a lower valence. The electronic interaction between host and guest could be also understood by performing the approximated molecular orbital (MO) calculations. In the cuprate superconductors, it has been well known that the charge carriers (mostly hole) exist in the band with Cu (dx2-y2) – O (2p) σ* antibonding character. [40,62] As can be seen in the Cu Kedge XANES derivative spectra (Figure 12b), all the spectra relevant to Cu2+ (d9) do not exhibit noticeable change. This can be explained by the Cu (dx2-y2) - O (p) molecular orbital (MO) diagram for the Cu2+/Cu3+ mixed valent system suggested by Anderson et al, where the upper antibonding MO is split to the corresponding valent state. [40] The antibonding MO relevant to Cu3+ is vacant, which is supposed to be filled by the electrons added. If the antibonding MO of Cu3+-O is partially filled, then the oxidation state of tri-valent copper would be slightly reduced due to the covalent mixing between Cu dx2-y2 and O 2p orbitals. By such a filling of Cu3+-O antibonding MO, the slight decrease in the peak energy for A’ is rationalized. As a consequence of the filling of antibonding obital, it is reasonably expected that the Cu-O distance is increased. Actually, the Cu K-edge XANES spectra cannot reflect very subtle changes in the oxidation state, since it does not feel out the orbital with d character that is directly relevant to the chemical bonding. In this regard, the changes in the oxidation state can be more precisely investigated by measuring the Cu-O bond distances. Although the crystal structure of cuprate superconductors has been mostly determined by X-ray diffraction analysis, it is not so easy to precisely determine the (Cu-O) bond length in these intercalates due to their highly anisotropic structural feature and low scattering factor of oxygen to the X-ray beam. In these point of view, the Cu K-edge EXAFS analysis is believed to be very effective way for determining the (Cu-O) bond since the EXAFS is element selective and the first shell for the nearest neighbor of oxygen around copper ion is separated from the other distant shells. [92, 93] Elaborate Cu K-edge EXAFS analyses have been carried out for the pristine Bi2212 and its HgI2- and (Py-Me)2HgI4-intercalate. The EXAFS oscillations are curve-fitted in order to

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

51

determine the (Cu-O) bond length. During the fitting procedure, only the bond distance and the Debye-waller factor were allowed as variables, whereas the coordination number was fixed to a crystallographic value to exclude an inaccuracy which may be caused by its strong correlation with Debye-Waller factor. The best lease- square fitting results are compared with the experimental spectra to give structural parameters as listed in Table 1. As shown in the table, the out-of-plane (Cu-Osr) bond distance is slightly increased (ΔR = 0.005 Å) upon HgI2 intercalation within the detection limit of EXAFS analysis, whereas the in-plane (Cu-Oeq) one is not significantly changed. Even though it is well known that the latter is closely related to the hole concentration of CuO2 plane, [94] its variation has been found to be minute even with considerable change in hole concentration accompanying large Tc modification. In this respect, HgI2 intercalation does not give rise to an appreciable change in the local structure around copper ion. Table 1. Results of nonlinear least square curve fitting for the first shell of Cu K-edge EXAFS spectra for the pristine Bi212 and its HgI2 and (Py-Me)2HgI4-intercalate Parameters

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

HgI2-Bi2212

(Py-Me)2HgI4-Bi2212

R

(Cu-Oeq) (Cu-Osr)

1.913 2.359

1.912 2.364

1.921 2.420

σ2

(Cu-Oeq)

3.83 × 10-3 Å2

3.53 × 10-3 Å2

2.75 × 10-3 Å2

(Cu-Osr)

1.11 × 10-2 Å2

1.00 × 10-2 Å2

1.37 × 10-2 Å2

(Cu-Oeq)

4

4

4

(Cu-Osr)

1

1

1

CNa a

Bi2212

The coordination numbers were fixed to crystallographic values due to their strong correlation with DebyeWaller factor.

Here it is supposed that two effects are competing: One is the competing bond effect where the HgI2 intercalation modifies the linear O3-Bi-Osr-Cu bond sequence into the I-BiOsr-Cu one and, as a result, weakens the Osr-Cu bond. The other one is the oxidation of copper ion due to the electronic charge transfer from the host lattice to the guest, in which case the copper ion of higher oxidation state reinforces the Cu-Osr bond. As a gross result, it is considered that the two effects are canceling each other. For the (Py-Me)2HgI4-intercalate, there are significant changes both in the in-plane and out-of-plane Cu-O bonds compared to those of the pristine. The in-plane (Cu-Oeq) bond is increased by 0.01 Å and, furthermore, the out-of-plane (Cu-Osr) bond by as much as 0.06 Å. Those are remarkable values in the crystallographic scale. The elongation of in-plane (CuOeq) bond seems to originate from the reduction of the CuO2 plane upon (Py-Me)2HgI4 intercalation, since the electrons transferred from the guest to the host lattice would contribute to the filling of Cu-O antibonding (pdσ*) orbitals, weakening the (Cu-Oeq) and (Cu-Osr) bonds. For the out-of-plane (Cu-Osr) bond, the two components, competing bond effect and chemical reduction of the CuO2 plane, seems to exhibit synergic effect: On one hand, the reduced copper oxidation state weakens the Cu-Osr bond. On the other hand, it is supposed that the interblock Bi-O3 bonding interaction is changed to nearly electrostatic interaction forming HgI42-···Bi-Osr-Cu bond sequence. Hence, in the viewpoint of competing bond

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

52

Soon-Jae Kwon

scheme, the Osr-Cu bond is further weakened with respect to the case of HgI2 intercalation. Although the Cu K-edge EXAFS fitting results imply that the CuO2 plane may probably be reduced upon organic-salt intercalation, the origin of electronic charge transfer from guest to host, opposite to the HgI2 intercalation, is not clearly understood. In order to further understand the effect of intercalation on chemical interaction between host and guest, the evolution of electronic configuration should be investigated in more detail for host lattice as well as for guest species. In this respect, the electronic structures of the host lattice and the guest have been theoretically calculated and compared with the experimental observations.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

4.2.5. Molecular-Orbital Calculations In order to understand electronic interaction between host lattice and guest, molecular-orbital (MO) calculation was carried out for the HgI2 intercalate and the (Py-Me)2HgI4 one. In the intercalation compounds of Bi-based cuprate superconductor, the Bi-O plane is the surface layer of cuprate building block, which is directly facing the intercalant layer. Therefore the chemical interaction between host and guest should be mainly affected by the relative electron donating or accepting ability, i.e. Lewis acidity and basicity, involving the orbitals of Bi-O layer and guest molecules. In the present Bi2212 intercalated with organic salt, while the organic cation PyMe+ is intercalated in the form of (Py-Me)2HgI4, its contribution to the Lewis acid-base interaction is supposed to be negligible compared to the highly polarizable HgI42- anion. In this context, the molecular orbitals (MO’s) of the HgI2 molecule and the HgI42- anion were calculated on the basis of geometric parameters such as coordination number and bond length (Hg-I), which were derived from the Hg LIII-edge EXAFS analyses of the corresponding intercalates, and compared to the energy level of the Bi-O layer, which was approximated as Bi2O42- cluster. In this study, the MO calculations were performed by the extended Hückel tight-binding band calculation method.

Figure 14. HOMO’s and LUMO’s of Bi2O42-, HgI2, and HgI42-. The dotted lines represent the preferred interactions between the HOMO’s and LUMO’s. (Source: Reprinted with permission from [33]).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

53

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

In Figure 14, the relative energy levels in the Bi2O42- cluster MO are represented, together with those in HgI2 and HgI42- MO’s. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the Bi2O42- cluster are determined to be 12.37 and -8.13 eV, respectively, whereas those of HgI2 molecule are −12.65 and −8.25 eV. For the pair of Bi2O42- and HgI2, the LUMO of each species is higher than the HOMO of the counterpart by more than 4 eV. The Bi2O42 (HOMO)- HgI2 (LUMO) perturbation will be more favorable than the case of Bi2O42- (LUMO)-HgI2 (HOMO) one, because the energy difference for the former (4.12 eV) is smaller than for the latter (4.52 eV). According to this reasoning, the HOMO of Bi2O42- behaves as a donor orbital and the LUMO of HgI2 as an acceptor orbital. The electrons therefore could be preferably transferred from the Bi2O42cluster to the HgI2 layer upon intercalation and, as a consequence, the Bi-O layer is slightly oxidized. [28] On the other hand, the calculated MO of HgI42- anion is markedly different from that of HgI2 molecule (Figure 14), due to the change in molecular structure and coordination number from linear HgI2 to tetrahedral HgI42-. The LUMO level is raised from −8.25 eV for the HgI2 to −4.68 eV for the HgI42-, whereas the HOMO level is only slightly changed from −12.65 to −12.47 eV. Consequently the HgI2 (HOMO)-Bi2O42 (LUMO) interaction should be more favored than the HgI2 (LUMO)-Bi2O42- (HOMO) one, where the HOMO of HgI42- acts as the donor orbital and the LUMO of Bi2O42- as acceptor orbital leading to a partial electron transfer from HgI42- anion to Bi2O42- cluster, i.e. to the Bi-O layer. Based on the concept of HOMO-LUMO interaction as mentioned above, it is found that the Bi-O layer can function as either a Lewis base for the HgI2 molecule or a Lewis acid for the HgI42- anion. Such theoretical results have been actually confirmed by the Bi LIII-edge and I LI-edge XANES analyses for the HgI2 intercalate and the (Py-Me)2HgI4 one. [33] Thus the perturbational MO approach provides a tentative but simple solution to the problems of electronic charge transfer between host and guest, which in turn gives a qualitative explanation for the Tc variations upon intercalation.

4.3. Conclusion A series of heterostructured nanohybrid between the Bi-based high-Tc superconductor and insulating organic moiety, have been successfully developed through a novel stepwise intercalation route. Until now, the interlayer coupling effects and low-dimensional properties of high-Tc superconductors have been investigated by the sequential deposition of alternating layers of a superconducting YBCO layer and an insulating PrBCO layer in vacuum. In such a YBCO-PrBCO superlattice compound, however, there exist other factors affecting Tc, such as strain effect by lattice mismatching, interdiffusion of Y and Pr atoms, proximity effect, and hole doping between sublattices, in addition to a change in the interlayer distance. The present organic-salt intercalation compound is different in its S-I-S multilayered structure and is an ideal model compound for studying high-Tc superconductivity, since the charge-carrying cuprate sheets are separated by the insulating organic layer with atomically clean interface. The organic-cuprate nanohybrid study has no substantial stress on the superconducting layer because of the weak interaction between host and guest. Furthermore, the hydrocarbon chain in the intercalant layer is a true insulator. In this regard, these intercalates have provided a clue that high-Tc superconductivity of layered cuprate is an intrinsic 2 D nature as in the case

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

54

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

of low-Tc TaS2-amine compounds. And the cuprate layers separated by an organic barrier are surely believed to be molecule-level thin films of a high-Tc superconductor, which are most suitable for studying the weakly coupled or decouple vortex behavior in type II superconductor because of their freely modifiable interlayer distance. In addition, the present multilayered superconductors are anticipated to be ideal model systems for understanding the c-axis properties of layered superconductors in relation to the still controversial issues in the high-Tc mechanism. From the physico-chemical characterizations, it is revealed that the anisotropy and electronic structures of layered cuprate can be controlled by intercalation reaction, because the interstratification of guest into the Bi2212 lattice modifies not only the layer separation between cuprate block but also the charge-carrier density of the superconducting layer. Both the partial oxidation and reduction of the cuprate block could be feasible depending on the nature of the intercalant. The main cause of Tc variation in the present intercalates is attributed to the modification of hole density in the CuO2 plane not only due to the hybridization between the Bi-O and Cu-O bands but also due to the electronic charge transfer between Bi-O layer and the guest, those which are empirically confirmed by the I LI-edge and Cu K-edge XAS analyses for the HgI2- and organic salt-intercalated Bi2212. Those variations in the electronic structure have been theoretically rationalized by the MO calculations for the host and the guest species, where the frontier orbital interactions between Bi-O layer and guest have dominant effect on the oxidation states of the host lattice and, in turn, Tc’s. It is expected that the organic-cuprate hybrids will prove substantial data for testing various existing theories explaining the 2D superconductivity. Moreover, the synthetic technique developed through this work is expected to be quite useful in the synthesis of many other organic-inorganic hybrid materials, [33-36] having advantageous properties both from crystalline inorganic solids and from organic components.

5. A Novel Hybrid of High-Tc Superconducting and CurieParamagnetic Subsystems The relationship between high-Tc superconductivity and dimensionality has been studied by interstratifying organic moiety into Bi-based cuprate layers, where the organic derivatives are incorporated in-between cuprate slabs in the form of organic salts and molecular complex. [32-35] Among organic materials, some organic molecules generate a spin-active species in a specific condition, which is called free radical in chemical terms. If only the spin-active radical can be hybridized with the high-Tc cuprate, it will surely contribute to solve the hotly debated issue on high-Tc superconductivity, spin interaction in the pairing mechanism. The hybrid material that combine superconductivity with paramagnetism or ferromagnetism, will be useful for exploring the interplay between superconductivity and magnetism, which, like oil and water, usually do not mix. In this respect, the ability to incorporate spin-species into the layered cuprate would be highly desirable for understanding the mechanism of high-Tc superconductivity. Here a novel heterostructured spin-system consisting of superconducting and paramagnetic sub-systems has been created, where free radicals (S = 1/2) are stabilized between Bi-based cuprate layers. The superconducting-paramagnetic dual magnetism observed in this work may provide a useful probe for investigating the mechanism of high-Tc

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

55

superconductivity. The stabilization of solid-state free radicals in-between superconductive layers is expected to provide a new class of magnetic heterostructures with unusual functionalities, which may play significant role in elucidating still unsettled issues on superconducting mechanism.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

5.1. Introduction The most challenging question on high-Tc superconductivity is what interaction makes the transition temperature (Tc) high and mediates the electron pairing. In the cuprate superconductors, the static antiferromagnetic order in the CuO2 plane usually disappears and is replaced by strong antiferromagnetic fluctuations upon hole doping, leading to superconducting transition. In this respect, it has been suggested that two-dimensional (2D) spin structure interrelated with the charge carrier density within the CuO2 plane is of crucial importance for the superconducting transition as well as for the Tc regulation. Intercalation chemistry applied to high-Tc cuprate superconductors have provided a way of controlling the dimensionality as well as modifying the charge carrier density in the superconductively active CuO2 layer. [26-28, 32-36] There have been reported that inorganic species can be intercalated into Bi-based high-Tc cuprates. [26-29] However, the incorporation of organic moiety [32-36] into the layered cuprate has tremendous advantage over inorganic species for studying high-Tc superconductivity as well as for creating materials with unusual features, since organic compounds show the widest variety of geometric and chemical nature ranging from neutral molecules to various ions, even to free radicals. Although the evolution of Tc in these intercalatin compounds has been mainly attributed to a change in the electronic structure of CuO2 plane, the micro-mechanism of Tc enhancement or suppression is still an open question. The hybrid material, if only the free radical with unpaired electron spin (S = 1/2) can be hybridized with the layered high-Tc cuprate, will contribute to solve the hotly debated issue on the superconductivity, because a free radical behaves as localized spin that can play a role of Cooper pair-breaker. Based on this methodology, it will also helpful to develop nanostructures in which the superconducting and paramagnetic subsystems interact to exhibit unusual physical properties. In an EPR spectroscopic study as an effort to elucidate the relationship between the superconductivity and the 2 D magnetic couplings involving 3d-transition metal ions (Cu2+/Cu3+), it is discovered a new type of heterostructured spin-system with discrete superconducting and paramagnetic subsystems.

5.2. Synthesis The pristine Bi2212 was synthesized by conventional solid state reaction with nominal composition of Bi2Sr1.5Ca1.5Cu2Oy. In an effort to avoid oxygen defect sites in the CuO2 plane and consequently to guarantee uniform spin-structure, the as-prepared compound was annealed at 500 °C in air 72 hours. [95, 96] The HgI2-intercalated Bi2212 (HgI2-Bi2212) was prepared by heating the HgI2 and the pristine Bi2212 in a vacuum-sealed Pyrex tube, as reported previously. [27] Then two types of organic intercalation compounds were prepared. One is (PyMe)2HgI4 (Py = pyridine; Me = -CH3) intercalated Bi2212, [32] which was

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

56

Soon-Jae Kwon

prepared by solid state reaction between the HgI2-Bi2212 and methylpyridinium iodide (PyMeI) at 100 °C for 12 hours. The other is (Me3S)2HgI4 intercalated one, [33] which was synthesized by solvent-mediated reaction between the HgI2-Bi2212 and trimethylsulfonium iodide (Me3SI) in acetonitrile solvent at 70 °C for 12 hours. The chemical formulae of the organic intercalates were determined to be [(PyMe)2HgI4]0.35Bi2Sr1.5Ca1.5Cu2Oy [(PyMe)2 HgI4-Bi2212] and [(Me3S)2HgI4]0.34Bi2Sr1.5Ca1.5Cu2Oy [(Me3S)2HgI4-Bi2212]. The characteristics of electronic spin interaction in each compounds has been investigated by EPR spectroscopy at room temperature. The magnetic properties of the samples have been measured in weak- and high-magnetic field at H = 20 G and H = 2 T, respectively, using superconducting quantum interference device (SQUID) magnetometer.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

5.3. Physico-Chemical Properties

Figure 15. Powder XRD patterns for (a) the pristine Bi2212, (b) HgI2-Bi2212, and (c) (Me3S)2HgI4Bi2212. (Source: Reprinted with permission from [33]).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

57

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Powder X-ray diffraction patterns for the pristine Bi2212, HgI2-Bi2212, and (Me3S)2HgI4-Bi2212 are shown in Figures 15a-15c, respectively. According to the leastsquare fitting analysis of (00l) reflection peaks, it is revealed that basal spacing is increased by 12.6 Å upon (Me3S)2HgI4-intercalation compared to the pristine Bi2212, while basal spacing is increased by 7.2 Å upon HgI2 intercalation. [32, 33] The existence of tetrahedral HgI42- unit is confirmed not only by micro-Raman spectroscopy but also by Hg LIII-edge EXAFS analysis for (Me3S)2HgI4-Bi2212. [33] Based on these results, the structural models for the (Me3S)2HgI4-Bi2212 was schematically illustrated in Figure 16.

Figure 16. (a) Schematic structural model for the (Me3S)2HgI4-Bi2212, where the isolated circle represents the trimethyl sulfonium cation, Me3S+. (b) Crystal structure of the free (Me3S)2HgI4.

Figure 17 shows the EPR spectra for the Bi2212 and its organic salt-intercalates. The asymmetric EPR spectral features of copper ion indicate a superposition of two anisotropic components, one sharp signal and a broad anisotropic one. For the (PyMe)2HgI4- and

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

58

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

(Me3S)2HgI4-intercalates, the intensity of Cu 3d EPR signal is significantly enhanced, at least by an order of magnitude compared to the pristine Bi2212, even though there have been several reports that superconducting cuprates are EPR silent. [97, 98] This drastic increase in Cu 3d EPR intensity may be explicable in terms of electronic exchange interactions between paramagnetic centers (Cu2+) in the d-transition metal compounds. [99-101] In this scheme known as exchange narrowing, the EPR spectra are characterized by a sharp EPR line, where strong electronic exchange in a lattice causes rapid motion of an individual spin throughout the crystalline array, in this case the CuO2 layer.

Figure 17. X-band EPR spectra for (a) the Bi2212, (b) the (Me3S)2HgI4-Bi2212, (c) the free (Me3S)2HgI4, and (d) (PyMe)2HgI4-Bi2212. The inset represents the enlarged EPR spectral line of (Me3S)2HgI4-intercalate at around 3500 G. All the EPR measurements were carried out at room temperature. (Source: Reprinted with permission from [35]).

Taking into account electronic charge transfer from the HgI42- to the host lattice upon organic-salt intercalation, [32, 33] it is reasonably expected that subtle changes in the geometric and electronic structure of copper reinforces the electronic exchange within the CuO2 plane and as a result 2 D dynamic spin-structure is substantially modified. [102] Although both type of organic salt-intercalates show similar Cu 3d EPR spectra, the (Me3S)2HgI4-intercalate exhibits a sharp resonant EPR peak centered at 3489 G (Figure 17b),

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

59

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

distinguished from the (PyMe)2HgI4-intercalate (Figure 17d). The peak-to-peak line width (ΔHpp) was determined to be 12 G and the g-factor was calculated to be g = 2.002, corresponding to the characteristic value for a free unpaired electron (S = 1/2), that is, free radical. This result indicates that the trimethylsulfonium cation (Me3S+) is the origin of the free radical, because the only difference between the two organic salt-intercalations is the organic cation incorporated in the form of complex salts, (PyMe)2HgI4 and (Me3S)2HgI4. The EPR spectrum of the free (Me3S)2HgI4 salt represents no sign of free radical. (Figure 17d) It is therefore reasonably concluded that the sharp resonant EPR peak of the (Me3S)2HgI4Bi2212 should result from the sulfonium cation Me3S+ under exotic chemical environment of interlayer space. This implies that there occurs an intermolecular charge-transfer [103] from the HgI42- to the Me3S+ as well as a charge-transfer from the HgI42- to the cuprate lattice, [32, 33], forming a meta-stable species of [Me3S⋅]0 and HgI4(2-δ)- in-between the cuprate blocks. Figure 18 shows the structural model of the (Me3S)2HgI4-intercalate, where it is anticipated that the 2 D array of paramagnetic spins may be converted into spin-aligned state by applying magnetic field. For this model, the existence of free radical can be verified by measuring temperature dependent magnetization at high magnetic field.

Figure 18. Schematic illustration of the (Me3S)2HgI4-Bi2212, where the tetrahedral unit and the arrow indicate the HgI42- and the unpaired electron spin, respectively. (Source: Reprinted with permission from [35]).

Figure 19a and 19b show the temperature dependent magnetization (M) for the (Me3S)2HgI4-Bi2212 (spin-active) and (PyMe)2HgI4-Bi2212 (spin-inactive), respectively. The (Me3S)2HgI4-intercalate shows the paramagnetic behavior from 300 down to 80 K at an applied magnetic field of H = 2 T. (Figure 19a), where the magnetization (M) increases towards lower temperature due to the alignment of the free radical spins. Thereafter, the magnetization declines to a minimum at 30 K owing to the superconducting transition at 80 K. In Figure 19a, the pit at around 30 K is an effect of interplay between diamagnetic shielding contribution of the superconducting host and the paramagnetic contribution of the guest. This superconducting-paramagnetic dual magnetism strongly suggests that the superconductivity is 2 D and confined to the metallic layers. Here interlayer coupling of the order parameter by Josephson tunneling seems to be unlikely, since the free radical spin in the interlayer space may act as scavengers for the Cooper-pair tunneling. Unlike the (Me3S)2HgI4-Bi2212, (PyMe)2HgI4-intercalate shows only typical superconducting transition at 80 K (Figure 19b), indicating the absence of spin-active paramagnetism. As can be seen in Figure 19a and 19b, both the (Me3S)2HgI4- and the (PyMe)2HgI4-intercalates exhibit magnetic

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

60

Soon-Jae Kwon

transition at around 20 K, which may be understood by the thermodynamic phase transition of magnetic flux-line (vortex) in the highly anisotropic type-II superconductors [84, 104-106].

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 19. Temperature dependence of zero-field-cooled magnetization (M) for (a) the (Me3S)2HgI4Bi2212 and (b) the (PyMe)2HgI4-Bi2212 in an applied magnetic field of 2 T. The dashed-line is a guide to the eye. The inset in (a) represents the enlarged view of paramagnetic behavior and the schematic illustration of spin-alignment in the intercalant layer. (Source: Reprinted with permission from [35]).

While the combined analysis of EPR measurement and high-field magnetization suggest a paramagnetism due to the intercalation-induced free radical spins, more reliable information is found in the χT-T plot. Figure 20a and 20b show the temperature dependent χTs (product of susceptibility and temperature) for the (Me3S)2HgI4- and (PyMe)2HgI4-Bi2212, respectively. Although the (Me3S)2HgI4-Bi2212 and (PyMe)2HgI4-Bi2212 represent different behaviors in the temperature dependent magnetization (M) under high magnetic field H = 2 T, a parallel behavior is observed in the χT for both types of intercalates. Here, it is worth noting that the χT-T plot for the (Me3S)2HgI4-intercalate appears to be shifted upward compared to the (PyMe)2HgI4-one. This upward shift of χT-T plot is predominantly attributed to the isolated free radical spins in the (Me3S)2HgI4-Bi2212, causing Curie-type paramagnetic contribution. In Figure 20a and 20b, both (Me3S)2HgI4- and (PyMe)2HgI4-intercalates show slightly increasing χT’s with decreasing temperature in the range 300-80 K, indicative of weak ferromagnetism. This weak ferromagnetism is attributed to the local ferromagnetic coupling between oxygen holes and adjacent Cu2+ (d9) electrons in the hole-doped CuO2 plane [107] As mentioned above, a comparative inspection of χT-T plots for the (Me3S)2HgI4- and (PyMe)2HgI4-intercalates reveals that the spin-active guest (free-radical) gives the Curie-

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

61

paramagnetism, which can also disentangle the magnetic effects of the superconducting host and of the localized free radical spins in the intercalant.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 20. χT’s as a function of temperature for the (a) the (Me3S)2HgI4-Bi2212 and (b) the (PyMe)2HgI4-Bi2212, respectively, which were derived from zero-field-cooled magnetization (M) in an applied magnetic field of 2 T. (Source: Reprinted with permission from [35]).

Figure 21. Zero-field-cooled (ZFC) d.c. magnetizations of the pristine Bi2212 and its intercalates measured with a superconducting quantum interference device (SQUID) magnetometer in a magnetic field of 20 G. Data points represent the Bi2212 ({), the HgI2-Bi2212 (†), and the (PyMe)2HgI4Bi2212 (U) and the (Me3S)2HgI4-Bi2212 (V).(Source: Reprinted with permission from [35])

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

62

Soon-Jae Kwon

Figure 21 shows the temperature dependent d.c. magnetizations for the pristine Bi2212 and its intercalates measured in a weak magnetic field of 20 G. For all the samples, there cannot be seen any sign of magnetic transition near at 20 K that would be, if any, indicative of secondary superconducting material. It is thus strongly suggested that superconductivity and paramagnetism can coexist in a molecule-level hybrid system. The nearly invariant onset Tc upon HgI2-intercalation (HgI2-Bi2212; Tc ≈ 78 K) is attributed to the air-annealed pristine Bi2212 (Tc ≈ 78 K) in this work. The (Me3S)2HgI4- and (PyMe)2HgI4-intercalate show onset Tc of 80 K, comparable to those of the high-field magnetic property measurements.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

5.4. Conclusion In summary, we have chemically created the heterostructured magnetic system that combines high-Tc cuprate and paramagnetic free radical, which is confirmed microscopically through EPR measurement and macroscopically through temperature dependent magnetization. The superconducting-paramagnetic dual magnetism and the prominent Cu 3d EPR signal in this system, indicate that the superconductivity is closely related to the 2D spin interaction within the CuO2 plane and the coupling between layers is not so important for the stability of the superconducting state. The unprecedented hybrid of Bi-based cuprate and free radical has electronically (host) and magnetically (guest) active parts, whose cooperation would possibly make the magneto-transport a very novel one. In this respect, the ability of incorporating free radical spins into metallic layers would be highly desirable from fundamental and technological aspects, particularly in the viewpoint of recently developing fields, magnetoelectronics or spintronics [108-112]. It would be interesting and challenging work to investigate tunneling magnetoresistance (TMR) [113] for the chemically prepared magnetic heterostructures, since spin- and magnetic field-dependent interlayer tunneling effect might be induced due to the possible control of spin degree of freedom in the intervening barrier layers by applying magnetic field.

6. Hybrid System of High-Tc Superconducting and Pauli-Type Paramagnetic Subsystems A superconducting-paramagnetic dual magnetic system has been chemically created by introducing molecular magnetic species into layered high-Tc cuprate, where the weak π-π interactions between planar π-conjugated radicals appear to form a Pauli-type paramagnetic subsystem in the interlayer space of cuprate blocks. The intercalation-induced free radicals lead to a heterostructured spin-system, providing not only a probe for high-Tc superconductivity but also a new way of creating materials with spin- or magnetic fielddependent functionality unattainable from conventional solid-state materials.

6.1. Introduction The intercalation technique, introducing a chemical species (guest) into a layered solid matrix (host), is a simple synthetic route to layered nanostructures available without high-cost

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

63

equipment and state-of-the-art skills. Previously, we found that organic cations could be intercalated into Bi-based high-Tc superconductor, Bi2212, in the form of complex-salt R2HgI4 (R = organic cation). [32,33] The readily exchangeable organic moiety allows for a versatile manipulation of nanohybrid materials with many different structures and functionalities. [32-36] Among various organic cations, the 1,1'-dimethyl-4,4'-bipyridinium (methylviolgen; MV2+) cation can form a one-electron reduced product (MV⋅+ radical) with one unpaired electron spin (S = 1/2) by thermal, electrochemical, and photochemical activations. [114-117] (figure 1).

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 22. Structures and chemical natures of MV2+ and MB+ cation. (Source: Reprinted with permission from [36]).

If Bi2212 can be interstratified with viologen radicals, the unpaired electron spins would be aligned under a magnetic field forming a two dimensional (2 D) array of spins. Therefore, the intercalation of radical spins into the layered cuprate may lead to novel magnetic behavior, conductivity or superconductivity due to the increased 2 D character of the layers as well as due to the paramagnetic nature of unpaired spins. In this respect, the above synthetic strategy is expected to provide a new way of developing hybrid nanomaterials in which the conducting and magnetic subsystems coexist, possibly giving rise to unprecedented structures and phenomena. Here the soft-chemical synthesis of a new heterostructured magnetic system is reported. It is found that viologen radicals are stabilized between the cuprate layers forming novel magnetic subsystem. In order to obtain more reliable information, the analyses were carried out in parallel for the intercalation compound of spin-inactive 1-methyl-4,4'-bipyridinium (MB+). Comparative analyses of electron spin paramagnetic resonance (EPR) spectroscopy and magnetization measurements have been performed for the Bi-based cuprate interstratified with spin-active and spin-inactive guests, which strongly suggests that superconductivity is confined to the metallic CuO2 layer and is most possibly relevant to the dynamic 2 D spin structure.

6.2. Synthesis The pristine Bi2212 was synthesized by solid-state reaction with a nominal composition of Bi2Sr1.5Ca1.5Cu2Oy. In the final synthetic step, the sample was quenched from 860 °C to room temperature in air with the intension of inducing oxygen defect sites within the CuO2 plane. Prior to viologen intercalation, mercuric iodide was intercalated into the Bi2212 as reported previously. [27, 28] Then the HgI2 intercalated Bi2212 (HgI2-Bi2212) was reacted with

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

64

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

methylviologen diiodide (MVI2), where intercalative complex-formation reaction, HgI2 + MVI2 → MVHgI4, proceeds in the interlayer space of 2 D lattices. The organic salt MVI2 was prepared by treating 4,4'-bipyridine and the iodomethane with 1:2 molar ratio in methanol at 50 °C. [118, 119] The resultant red crystals were washed with cold methanol and dried under reduced pressure. The 1-methyl-4,4'-bipyridinium iodide (MBI) was obtained by reacting 4,4'-bipyrine with 1 equivalent of iodomethane in benzene solution with subsequent purification. [120] The HgI2-Bi2212 was mixed with three molar excess reactant of MVI2, and a small amount of acetonitrile (0.2 mL per 1 g of the mixture) was added. This was reacted in a closed ampoule at 70 °C for 12 hours. This synthetic procedure was performed in a nitrogen (N2) atmosphere. After the reaction was finished, the excess reactant (MVI2) was removed by washing the sample with dimethyl sulfoxide and acetonitrile alternately. The resulting product was dried in vacuum. The product once synthesized is stable in air, because the host lattice prevents the viologen radical from reacting with molecular oxygen that otherwise acts as a radical scavenger. The same synthetic procedure was employed for MB+intercalation. The formation of the single-phase stage-I intercalate was confirmed by the powder X-ray diffraction (XRD) analyses using nickel filtered Cu-Kα radiation with a graphite monochromator. From electron probe microanalysis (EPMA) measurement and elemental analysis for C, H, and N, the chemical formula of viologen-intercalate is represented as (MVHgI4) 0.1Bi2Sr1.5Ca1.5Cu2Oy. Comparative Hg LIII-edge XANES analyses for the HgI2- and the viologen-intercalates revealed that, upon viologen intercalation, the twocoordinated linear HgI2 is transformed into a four-coordinated tetrahedral unit (HgI42-) in the interlayer space as reported previously, [33] confirming the intercalated species of MVHgI4. The superconducting and magnetic properties were investigated by temperature dependent d.c. magnetization measurements using superconducting quantum interference device (SQUID) magnetometer. The EPR spectra were measured at room temperature using an Xband EPR spectrometer, operating at 9.8 GHz with 100 KHz field modulation.

6.3. Physico-Chemical Properties Powder XRD patterns of the pristine Bi2212, HgI2-Bi2212, MVHgI4-Bi2212, and (MB) 2HgI4-Bi2212 are represented in Figure 23a-d, respectively. There is no trace of the pristine phase in the XRD patterns for all the present intercalates, indicating that mercuric iodide and organic-salt are incorporated homogeneously into the host lattice. From the least square fitting analysis, it is revealed that the basal spacing (d) increases from 15.3 Å for the pristine, to 22.5 Å (Δd = 7.2 Å) for the HgI2-Bi2212, and to 21.9 Å (Δd = 6.6 Å) for the MVHgI4-Bi2212. Despite the basal increment along c-axis upon intercalation, the in-plane (a and b) lattice parameters are invariant to those (a = 5.40 Å, b = 5.40 Å) of the pristine. Since the MVHgI4-intercalation was achieved by the reaction between the HgI2-Bi2212 and MVI2, a shrinkage of basal spacing upon in-situ MVHgI4 formation indicates a change of coordination around Hg. This is additionally indicated by the drastic increase of (002) peak intensities for the MVHgI4- and (MB)2HgI4-intercalates compared to the HgI2-one. The Hg LIII-edge XANES analysis also supports the geometrical change around Hg. In addition, it is a reasonable interpretation that the cuprate layers are parallel along the length of the MV2+ molecule, in which the anionic HgI42- units are located between the adjacent viologen cations. [121]

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Synthetic and Phenomenological Approaches…

65

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 23. Powder XRD patterns for (a) the pristine Bi2212, (b) HgI2-Bi2212, (c) MVHgI4-Bi2212, and (d) (MB)2HgI4-Bi2212. (Source: Reprinted with permission from [36]).

Figure 24. Schematic illustration for the preparation of MVHgI4-Bi2212. The structural models for the pristine Bi2212, HgI2-Bi2212, and MVHgI4-Bi2212 are also represented. (Source: Reprinted with permission from [36])

Figure 24 shows the structural models for the pristine, the HgI2- and the MVHgI4intercalates. The XRD pattern of the (MB)2HgI4-intercalate is similar to that of the MVHgI4one, except for the basal spacing of 22.1 Å (Δd = 6.8 Å). However, the physical properties are very different from each other.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

66

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 25. Temperature dependency of zero-field-cooled (ZFC) magnetizations for pristine Bi2212 (†), HgI2-Bi2212 ({), MVHgI4-Bi2212 (‘), and (MB)2HgI4-Bi2212 (U) in an applied magnetic field of 20 G. (Source: Reprinted with permission from [36])

Figure 26. (a) Temperature dependence of the molar magnetic susceptibility χm and (b) χmT of MVHgI4-Bi2212 ( )) and (MB)2HgI4-Bi2212 (z) at an applied magnetic field of 2 T, respectively. The in-set in (a) represents the enlarged view of the susceptibility χm for the MVHgI4-Bi2212 and the schematic illustration of the aligned electron spin in each viologen radicals under high field. The arrow in (b) indicates the ferromagnetic component resulting from the spin-clusters in the host, which is diminutive for the MVHgI4-intercalate compared with that for the (MB)2HgI4 one. (Source: Reprinted with permission from [36]).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

67

Figure 25 represents the zero-field-cooled (ZFC) d.c. magnetizations for the pristine Bi2212 and its intercalates in an applied magnetic field of 20 G.. HgI2-Bi2212 shows an onset Tc (Tc, on-set) of 68 K, representing a Tc drop of ~10 K with respect to the pristine phase. MVHgI4-Bi2212 exhibits a superconductivity with a broad range of transition temperature whereas the others show rather distinct on-set Tc values. The superconducting shielding fractions of the samples at 5 K are 46, 26, 31, and 20 % for the pristine phase, HgI2-Bi2212, (MB)2HgI4-Bi2212, and MVHgI4-Bi2212, respectively. The peculiar phenomenon observed for the MVHgI4-Bi2212 may be related with two possible factors. One is the change of the intrinsic property of the cuprate layer due to the physicochemical interaction between the host and the guest. The other is the unpaired electron-spin of the intercalation-induced MV⋅+ radical which might play a role of Cooper pair-breaker or scavenger for the pair-tunneling. At this point, it is not clear how the superconductivity of MVHgI4-intercalate is weakened. On the other hand, the intercalate of MB+ shows a Tc, on-set (78 K) comparable to that of the pristine Bi2212, that is, the (MB)2HgI4-intercalation raises the Tc, on-set by ~10 K with respect to HgI2-Bi2212. For the MVHgI4-intercalate, it is highly needed to closely investigate the interaction between superconductivity and the spin-activity of the guest, i.e., the relationship between superconductivity of the cuprate block, and possible magnetism of the intercalant layer. Previously, there was found a molecule-level hybrid of high-Tc superconductor and Curie-type paramagnetic layer, where noninteracting or isolated free radical spins are incorporated into the Bi-O double layers of Bi2212. [35] In this hybrid system of high-Tc superconductivity and Curie-paramagnetism, an unusually broad superconducting transition was not observed. Here it is worth noting that the local magnetic moment (free radical) itself is not the unique cause of the magnetic anomaly in the MVHgI4-Bi2212. Figure 26a represents the temperature dependent molar magnetic susceptibility χm(T) for the MVHgI4-Bi2212 (spin-active) and the (MB)2HgI4-Bi2212 (spin-inactive) in an applied magnetic field of H = 2 T. For MVHgI4-Bi2212, the molar magnetic susceptibility is small (≈ 600 × 10-6 emu mol-1) in a wide temperature range (300 - 80 K) with a weak upward curvature (Figure 26a, in-set), which is indicative of paramagnetism. On the other hand, (MB)2HgI4Bi2212 shows a negligible magnetic susceptibility in the normal state above Tc. Therefore it is valid that the paramagnetic contribution of the MVHgI4-intercalate observable in the normal state (T > Tc) should be attributed to the spin-active guest. As shown in Figure 26a, the magnetic susceptibility of MVHgI4-Bi2212 shows a shallow pit at around 40 K that may be attributed to a gross result of magnetic components from the host and the guest. The possible magnetic contributions in this case are (1) diamagnetic shielding contribution of the superconducting host, (2) ferromagnetism of local spin-clusters within the CuO2 plane, and (3) paramagnetic behavior of the spin-active guest. On the other hand, a deep pit at around 30 K for the (MB)2HgI4-intercalate is attributed to the combined effect of two intrinsic properties of the host only, i.e., the diamagnetic shielding of bulk superconductivity below Tc and the ferromagnetic component in the lower temperature end involving ferromagnetically coupled Cu-O clusters. Although the magnetic susceptibility χm(T) of the MVHgI4-intercalate implies a paramagnetic contribution from the guest (Figure 26a), more reliable information is found in the χmT-T plot. Figure 26 b shows that χmT for MVHgI4-Bi2212 decreases with decreasing temperature (300 - 80 K), indicative of Pauli-type paramagnetism. Curie-paramagnetism

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

68

Soon-Jae Kwon

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

would result from independent local moments, whereas the significant spin coupling results in correlated spins that must respond collectively to an applied field. [62] From the Pauli-type paramagnetic behavior for MVHgI4-Bi2212, it is reasonably expected that there should be electronic conduction paths as well as appreciable spin-spin interactions within the intercalant layer. The χmT-T plot can disentangle the magnetic effects of the local ferromagnetic domain (Cu-O clusters) in the host and of the spin-active guest. A comparative analysis of χmT behaviors for the MVHgI4- and the (MB)2HgI4-intercalates shows that the spin-active guest (MV⋅+) gives the Pauli-paramagnetic contribution at the expense of the ferromagnetic component of the host in the lower-end temperature region. A close inspection of temperature dependent magnetic susceptibilities (Figure 26a) and χmT-T plots (Figure 26b) strongly suggests that the magnetic behaviors below 30 K is strongly related to the local ferromagnetic (Cu-O) domains that can serve as pinning centres for the magnetic flux-lines (vortex-lines) in the field H > Hc1. In this scheme, the superconducting states in ferromagnetic domains are easily destroyed upon applying high magnetic field due to the absence of long-range order, which then give way to flux-penetration resulting in field-induced ferromagnetic centers. [122] In support of this interpretation, we cannot notice a ferromagnetic moment below around 20 - 30 K for the Bi2212 intercalates with an unbroken Cu-O network, [35] where a magnetic phase transition is observed at around 20 K possibly due to the decoupling of vortex-lines into 2 D pancake vortices, typically observable for the highly anisotropic high-Tc superconductors free of pinning centres. [105]

Figure 27. X-band EPR spectra of (a) pristine Bi2212, (b) HgI2-Bi2212, (c) MVHgI4-Bi2212, and (d) (MB)2HgI4-Bi2212. The dotted line indicates the resonance field of the free electron (ge = 2.002). (Source: Reprinted with permission from [36]).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

69

EPR study has been carried out for the Bi2212, the MVHgI4-Bi2212, and (MB)2HgI4Bi2212, in order to obtain microscopic information on the spin-active species such as free radicals and local ferromagnetic domains in the CuO2 plane. Figure 27 shows the EPR spectra for the Bi2212 and its intercalates. In all the samples, there can be observed typical Cu 3d EPR signals whose common spectral feature is a superposition of one narrow signal and a wide anisotropic one. These spectral components are relevant to axial g-values, g-parallel (g// = gzz) and g-perpendicular (g⊥ = gxx = gyy), [123] if we take into account the square pyramidal CuO5 symmetry in Bi2212. The Cu 3d EPR spectral lines exhibit lower resonance fields compared with that of the free electron, that is, g-factors from Cu 3d species are larger (g > 2.002) than ge = 2.002, as is typically observed for d-transition metal ions. [123] For both the MVHgI4- and (MB)2HgI4-intercalates, the intensity of Cu 3d EPRsignal centered at around 3300 G (g ≈ 2.1218) is significantly enhanced with respect to the pristine Bi2212, even though there have been reports that superconducting cuprates are EPR silent. [97, 98] The remarkable increase of Cu 3d EPR intensity is most possibly related to changes in the geometric and electronic structures of copper, which are closely correlated with both the Jahn-Teller distortion and the magnetic coupling between Jahn-Teller ions (Cu2+). On the other hand, the broad EPR line in the range 2000 - 4000 G observed initially in the pristine compound, is disappeared or revived depending on the chemical nature of the intercalant (Figure 27). The evolution of a broad EPR line can be phenomenologically explained in terms of a inhomogeneous line broadening in solids, which occurs as a result of interactions that affect the energies of the spin-states involving the EPR transitions. [123]. There have been reports that there occur magnetic islands or spin-clusters (Cu-octamers, tetramers, -dimers, and -monomers) in the sea of CuO2 plane due to oxygen defect sites in Cu-O network upon quenching the layered cuprates. [96, 124, 125] In these quenchinginduced magnetic islands, the spins of the oxygen holes and unpaired Cu 3d electrons (electrons in the dx2-y2 level) are ferromagnetically coupled or spin-polarized (S > 1/2) among themselves to ensure the minimum energy, where the static interaction of local spin-clusters and Cu 3d electron spins causes individual paramagnetic centers (Cu 3d9) to experience different effective magnetic fields (Heff). The extra magnetic field (HFC) from a ferromagnetically coupled spin-cluster (FC) is superimposed on the applied magnetic field (Ho), and in our case it is unlikely that all the copper ions will experience the same effective field (Heff = Ho + HFC). As the applied magnetic field is swept through the bulk sample, some of the paramagnets (Cu2+) in the spin-cluster come into resonance at a particular magnetic field. Thus the observed spectrum consists of a superposition of a large number of closely spaced resonances. This leads to unusually broad EPR signal (Figure 26a and 26d) and 6(d)) with a line shape which approximates closely to a Gaussian function. [123] When an oxygen defect is generated in the CuO2 plane, the linear O−Cu−O−Cu−O bonding sequence of Cu-O network is changed into O‹Cu"…"CuŒO one, where the thin line (−) represents for the normal Cu-O bond, the arrow (‹ or Œ) for the shortened Cu-O bond, the dotted line (") for the virtual Cu-Odefect bond, and the box (…) for the oxygen defect site. Thus the Cu-O bond opposite to the defect site is reinforced by the competing bond effect and consequently raises the energy of Cu(3dx2-y2) −O (2p) σ* antibonding level. Therefore the antibonding Cu2+−O MO states in the neighbor of oxygen defect sites are higher than that of the background CuO2 plane. As a consequence, if an electron is removed

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

70

Soon-Jae Kwon

from the antibonding MO of Cu2+(d9) −O(2p6) bond due to the electronic charge transfer from the cuprate host to the guest, the electron should be eliminated from the ferromagnetic (Cu−O) domains rather than from the normal CuO2 plane. As can be seen Figure 26, the intensity of the broad EPR line is vanished for the HgI2Bi2212 and the MVHgI4-Bi2212, whereas it is remarkably enhanced for the (MB)2HgI4Bi2212. For the cuprate high-Tc superconductors, it has been well known that charge carriers (mostly hole) are introduced into the band with Cu(3dx2-y2)−O (2p) σ* antibonding character. [40, 62] Therefore the suppression of broad ESR signal reflects the removal of electrons from spin-clusters of higher Cu2+−O σ* MO states, which diminishes the population of ferromagnetically coupled Cu 3d electrons. In particular, two types of organic salt-intercalates show distinctive contrast in the broad EPR line. This spectral contrast in each intercalate may be understood by considering the chemical nature of the organic cation. For the MVHgI4intercalate, it is supposed that there occurs an intermolecular charge-transfer [103] from the HgI42- to the viologen dication (MV2+) upon forming MVHgI4 complex in the interlayer space, owing to the electron-withdrawing character of the counter cation. For the (MB)2HgI4one, however, there seems to be an electronic charge transfer from HgI42- to the cuprate block [32, 33] rather than to the organic cation, because MB+ does not have the electronwithdrawing ability. The synchronized evolution of Tc,on-set (Figure 25) and the broad EPR component (Figure 27) indicates that the superconducting transition is determined by the electronic population in the local Cu-O domain with the higher Cu(3dx2-y2)−O (2p) σ* antibonding level. It is therefore supposed that the electronic interaction in the higher Cu−O σ* level facilitates the Cooperpairing at a higher temperature, whatever the mediating interactions maybe. With this reasoning, the energy level of the Cu(3dx2-y2)−O (2p) σ* antibonding MO is essentially determined by the local geometric environment around copper, which then confines the possible highest on-set Tc value, and the observable Tc is regulated by the electronic population therein. In more general terms, the systematic increment of on-set Tc with increasing number of CuO2 layers in the Bi- and Tl-based layered cuprates, might be closely related to the energy levels of Cu 3dx2-y2 which are sensitively affected by the Jahn-Teller perturbation around copper. In fact, there is a tendency of an increasing Jahn-Teller distortion on moving from a mono- to double- and to a triple-layered Cu-O plane, since the coordination around copper changes progressively from octahedral to square pyramidal and to square planar (middle CuO2 plane) geometry. In this scenario, the energy level of the Cu(3dx2-y2)−O (2p) σ* antibonding MO is fundamentally determined by intrinsic crystal system of each cuprate, which in turn determines the maximum Tc value, and the actual Tc is exhibited depending on the electronic population, i.e., doping content. Although the intercalated MV⋅+ radical was expected to show a sharp resonant EPR peak, [126] MVHgI4-Bi2212 does not show sharp EPR signal corresponding to a free radical. As can be seen in Figure 26a, however, paramagnetic behavior is evidently observed for the MVHgI4-intercalate. A noticeable paramagnetic moment implies the formation of weakly interacting spin-pairs between viologen radicals rather than the nonexistence of a radical cation, despite the absence of free radical EPR signal. In this instance, the individual spins in MV⋅+ molecules may be so arranged such that they no longer behave independently and are magnetically coupled.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

71

There have been reports that MV⋅+ radical molecules dimerize in solvents to form EPRsilent and diamagnetic spin-pairs through direct face-to-face overlapping of π-orbitals. [127,128] In our case, however, a direct π-π interaction between viologen molecules is unlikely, since the counter anions (HgI42-) are located between π-conjugated cations. [121] Therefore the spin-spin interaction between viologen radicals, if any, would be quite weak compared with the case of spin-paired dimers in solution. Furthermore, as the intercalated complex-salt MVHgI4 constitutes a two dimensional ionic layer in the interlayer space of Bi2212 slabs, a possible spin-spin interaction would not be restricted to a pair of MV⋅+'s but extends through the intercalant layer. Based on the observed paramagnetic behavior of MVHgI4-Bi2212 even without the free radical EPR signal, it is suggested that there exists a weak antiferromagnetic correlation among the neighboring spins of MV⋅+ radicals. Magnetic pathways, available through the indirect interaction between MV⋅+ molecules, may provide for moderate antiferromagnetic (AF) exchange or dipole-dipole interaction. [129] Due to the intervening anions (HgI42-) between adjacent cations, a possible interaction between MV⋅+ radicals is attributed to a dipole-dipole coupling [130] rather than to the AF exchange one. [131] The Pauli-type paramagnetism of the MVHgI4-intercalate in the high temperature range (Figure 26b) implies that the MV⋅+ radical spins respond to an applied magnetic field H = 2 T collectively rather than individually. There should be a Curie-type paramagnetism [35] in stead of a Pauli-type one, if the radical spins are independent to each other. In this respect, it is a reasonable interpretation that the MVHgI4 intercalant layer constitutes a paramagnetic system of weakly coupled spins. Here it is worth noting that the Pauli-type paramagnetism for the MVHgI4-Bi2212 is accompanied by an unusually broad superconducting transition, when compared with (MB)2HgI4-Bi2212. For the MVHgI4-intercalate, the correlated spins in the intercalant layer appears to be closely related with the Pauli-type paramagnetic behavior. Considering that there is no appreciable Tc suppression in the Curie-type paramagnetic intercalant, [35] the conducting pathways (metallic property) along intercalant layer in the MVHgI4-Bi2212 can be regarded as the most viable factor for the weakening of superconductivity. This phenomenon can be explained in the viewpoint of a proximity effect involving the interface between superconductive and electronically conductive layers. [132-134] In this scheme, as the conduction path is developed by the limited π-π interaction between MV⋅+ molecules, the superconducting proximity effect appears through the interfacial interaction between superconductive host and conductive intercalant layer. Taking into account a molecule-level hybrid of superconductive and conductive layers, there can be a leakage of Cooper-pairs into the conductive or metallic layers, which then may suppress the superconductivity of the superconductively active Bi2212 layer.

6.4. Conclusion A dual magnetic system of superconducting and paramagnetic subsystems has been created by a soft-chemical approach. From the comparative analyses of the magnetic, superconducting, and EPR characteristics for the two types of intercalation compounds, it is revealed that the unpaired electrons (S = 1/2) of π-conjugated (viologen) radicals are not fully localized but weakly interact to form a Pauli-type paramagnetic subsystem in the interlayer

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

72

Soon-Jae Kwon

space. For the viologen-intercalated compound, the interlayer space allows an organic guest to exhibit exotic chemical and/or physical properties that are quite different from the free MVHgI4 salt, while the physical properties of the cuprate host are significantly modified upon intercalation. A joint analysis of magnetic properties and EPR spectral features for the Bi2212 intercalates, suggests that the high-Tc superconductivity is closely related to the Cu-O σ* antibonding MO levels as well as to the electronic population therein. The stabilization of solid-state free radicals between (super)conductive layers could provide new approaches for preparing magnetic heterostructures with unusual magnetic or magneto-electric properties. Due to the peculiar layered nanostructure with discrete spin subsystems, the molecule-level hybrid of the cuparte layer and organic magnetic species is worth attracting attention as a model system for studying the high-Tc superconductivity.

Acknowledgements The author thanks Professor J. H. Choy for his academic inspiration on this work and valuable advices. He also thanks the Photon Factory, National Laboratory for High Energy Physics and is grateful to Professor M. Nomura for his help in X-ray-absorption experiments. Experimental help from Dr. M. Strongin (Brookhaven National Laboratory) in muon experiment is also acknowledged.

References

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

[14] [15] [16]

Bednorz, J. G.; Müller, K. A. Z. Phys. B 1986, 64, 189-193. Wu, M. K.; Ashburn, J. R.; Torng, C. J.; Hor, P. H.; Meng, R. L.; Gao, L.; Huang, Z. J.; Wang, Y. Q.; Chu, C. W. Phys. Rev. Lett. 1987, 58, 908-910. Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. Phys. Rev. 1957, 108, 1175-1204. Varma, C. M.; Littlewood, P. B.; Schmitt-Rink, S.; Abrahams, E.; Ruckenstein, A. E. Phys. Rev. Lett. 1989, 63, 1996-1999. Monthoux, P.; Pines, D. Phys. Rev. B 1993, 47, 6069-6081. Levin, K.; Kim, J. H.; Lu, J. P. ; Si, Q. Physica C 1991, 175, 449-522. Ihm, J.; Yu, B. D. Phys. Rev. B 1989, 39, 4760-4763. Wheatley, J. M.; Hsu, T. C.; Anderson, P. W. Nature 1988, 333, 121-121. Wheatley, J. M.; Hsu, T. C.; Anderson, P. W. Phys. Rev. B 1988, 37, 5897-5900. Chakravarty, S.; Sudbo, A.; Anderson, P. W.; Strong, S. Science1993, 261, 337-340. Tešanovič; Z. Phys. Rev. B 1987, 36, 2364-2367. Ye, Z.; Umezawa, H.; Teshima, R. Phys. Rev. B 1991, 44, 351-359. Li, Q.; Xi, X. X.; Wu, X. D.; Inam, A.; Vadlamannati, S.; McLean, W. L.; Venkatesan, T.; Ramesh, R.; Hwang, D. M.; Martinez, J. A.; Nazar, L. Phys. Rev. Lett. 1990, 64, 3086-3089. Lowndes, D. H.; Norton, D. P.; Budai, J. D. Phys. Rev. Lett. 1990, 65, 1160-1163. Terashima, T.; Shimura, K.; Bando, Y.; Matsuda, Y.; Fujiyama, A.; Komiyama, S. Phys. Rev. Lett. 1991, 67, 1362 -1365. Saito, K.; Kaise, M. Phys. Rev. B 1998, 57, 11786-11791.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

73

[17] Schneider, T.; Keller, H. Int’I J. Mod. Phys. B 1994, 8, 487-528. [18] Gamble, F. R.; DiSalvo, F. J.; Klemm, R. A.; Geballe, T. J. Science 1970, 168, 568570. [19] Gamble, F. R.; Osiecki, J. H.; Cais, M.; Pisharody, R.; DiSalvo, F. J.; Geballe, T. H. Science 1971, 174, 493-497. [20] Thompson, A. H.; Gamble, F. R.; Koehler Jr., R. F. Phys. Rev. B 1972, 5, 2811-2816. [21] Coleman, R. V.; Eiserman, G. K.; Hillenius, S. J.; Mitchell, A. T.; Vicent, J. L. Phys. Rev. B 1983, 27, 125-139. [22] Bozovic, I.; Eckstein, J. N. In Physical Properties of High Temperature Superconductors; Ginsberg, D. M.; World Scientific: Singapore, 1996, Vol. 5. [23] Maeda, H.; Tanaka, T.; Fukutomi, M.; Asano, T. Jpn, J. Appl. Phys. 1987, 27, L209L210. [24] Maeda, A.; Hase, M.; Tsukada, I.; Noda, K.; Takebayashi, S.; Uchinokura, K. Phys. Rev. B 1983, 41, 6418-6434. [25] Xiang, X. -D.; McKernan, S.; Vareka, W. A.; Zettl, A.; Corkill, J. L.; Barbee, T. W.; Cohen, M. L. Nature 1990, 348, 145-147. [26] Choy, J. H.; Park, N. G.; Hwang, S. J.; Kim, D. H.; Hur, N. H. J. Am. Chem. Soc. 1994, 116, 11564-11565. [27] Choy, J. H.; Hwang, S. J.; Park, N. G.; J. Am. Chem. Soc. 1997, 119,1624-1633. [28] Choy, J. H.; Park, N. G.; Kim, Y. I.; Hwang, S. H.; J. S.; Lee, H. I. Yoo, J. Phys. Chem. 1995, 99, 7845-7848. [29] Grigoryan, L. S.; Kumar, R.; Malik, S. K.; Vijayaraghavan, R.; Ajaykumar, K. S.; Shastry, M. D.; Bist, H. D.; Sathaiah, S. Physica C 1993, 205, 296-306. [30] Sathaiah, S.; Soni, R. N.; Joshi, H.C.; Grigoryan, L. S.; Bist, H. D.; Narlikar, A. V.; Samanta, S. B.; Awana, V. P. S. Physica C 1994, 221, 177-186. [31] Choy, J. H.; Kwon, S. J.; Park, G. S. Science 1998, 280, 1589-1592. [32] Kwon, S.J.; Choy, J. H.; Jung, D.; Huong, P. V. Phys. Rev. B 2002, 66, 224510. [33] Kwon, S.J.; Choy, J. H. Inorg. Chem. 2003, 42, 8134-8136. [34] Kwon, S.J.; Jung, D. Y. Solid State Commun. 2004, 130, 287-291. [35] Kwon, S.J.; Lee, Y. H.; Choy, J. H.; Kim, S. J. Supercond. Sci. Technol. 2005, 18, 470476. [36] Harshman, D. R.; Mills, A. P. Phys. Rev. B 1992, 45, 10684-10712. [37] Šwierkowski, L.; Neilson, D.; Szymaňski, J. Phys. Rev. Lett. 1991, 67, 240-243. [38] Küchenhoff, S.; Schiller, S. Physica B 1990, 165and166, 1033. [39] Anderson, P. W. The theory of superconductivity in the high-Tc cuprate superconductors; Princeton University Press: Princeton, NJ, 1997; p. 35. [40] Talstra, J. C.; Strong, S. P.; Anderson, P. W. Phys. Rev. Lett. 1995, 74, 5256-5259. [41] Chakravarty, S.; Sudbø, A.; Anderson, P. W.; Strong, S. Science 1993, 261, 337-340. [42] Millis, A. J.; Monien, H. Phys. Rev. Lett. 1993, 70, 2810-2813. [43] Emery, V. J. Phys. Rev. Lett. 1987, 58, 2794-2797. [44] Anderson, P. W.; Baskaran, G.; Zou, Z.; Hsu, T. Phys. Rev. Lett. 1987, 58, 2790-2793. [45] Anderson, P. W. Science 1987, 235, 1196-1198. [46] Schrieffer, J. R.; Wen, X. G.; Zhang, S. C. Phys. Rev. Lett. 1988, 60, 944-947. [47] Mook, H. A.; Dai, Pengcheng; Hayden, S. M.; Aeppli, G.; Perring, T. G.; F. Dogan, Nature 1998, 395, 580-582. [48] Ioffe, L. B.; Millis, A. J. Science 1999, 285, 1241-1244.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

74

Soon-Jae Kwon

[49] Carbotte, J. P.; Schachinger, E.; Basov, D. N. Nature 1999, 401, 354-356. [50] Zhou, X. J.; Bogdanov, P.; Keller, S. A.; Noda, T.; Eisaki, H.; Uchida, S.; Hussein, Z.; Shen, Z. X. Science 1999, 286, 268-272. [51] Zaanen, J. Science 1999, 286, 251-252. [52] Tranquada, J. M.; Sternlieb, B. J.; Axe, J. D.; Nakamura, Y.; Uchida, S. Nature 1995, 375, 561-563. [53] Bianconi, A.; Mossori, M. J. Phys. I (France) 1994, 4, 361-365. [54] Bianconi, A.; Missori, M.; Saini, N. L.; Oyanagi, H.; Yamaguchi, H.; Ha, D. H.; Nishihara, Y. J. Superconductivity 1995, 8, 545-548. [55] Perali,A.; Bianconi, A.; Lanzara, A.; Saini, N. L. Solid State Comm. 1996, 100, 181186. [56] Sleight, A. W. Science 1988, 242, 1519-1527. [57] Uemura, Y. J.; Sternlieb, B. J.; Cox, D. E.; Brewer, J. H.; Kadono, R.; Kempton, J. R.; Kiefl, R. F.; Kreitzman, S. R.; Luke, G. M.; Mulhern, P.; Riseman, T.; Williams, D. L.; Kossler, W. J.; Yu, X. H.; Stronach, C. E.; Subramanian, M. A.; Gopalakrishnan, J.; Sleight, A. W. Nature 1988, 335, 151-152. [58] Walstedt, R. E.; Warren, W. W. Science 1990, 248, 1082-1087. [59] Tolentino, H.; Medarde, M.; Fontaine, A.; Baudelet, F.; Dartyge, E.; Guay, D.; Tourillon, G. Phys. Rev. B 1992, 45, 8091-8096. [60] Krakauer, H.; Pickett, W. E. Phys. Rev. Lett. 1988, 60, 1665-1667. [61] Pickett, W. E. Rev. Mod. Phys. 1989, 61, 433-512. [62] Hybertsen, M. S.; Mattheiss, L. F. Phys. Rev. Lett. 1988, 60, 1661-1664. [63] Sterne, P. A.; Wang, C. S. Phys. Rev. B. 1988, 37, 7472-7475. [64] Subramanian, M. A.; Torardi, C. C.; Calabrese, J. C.; Gopalakrishnan, J.; Morrissey, K. J.; Askew, T. R.; Flippen, R. B.; Chowdhry, U.; Sleight, A. W. Science 1988, 239, 1015-1017. [65] Di Stasio, M. K.; Müller, A.; Pietronero, L. Phys. Rev. Lett. 1990, 64, 2827-2830. [66] Kleiner, R.; Müller, P. Phys. Rev. B 1994, 49, 1327-1341. [67] Kosterlitz, J. M.; Thouless, D. J. J. Phys. C 1973, 6, 1181-1203. [68] Lawrence, W. E.; Doniach, S. In Proc. 12th Intl. Conf. Low-Temperature Physics; Kanda, E.; Academic press, Kyoto, Japan, 1971; p. 361. [69] Groen, W. A.; de Leeuw, D. M.; Stollman, G. M. Solid State Commun. 1989, 72, 697700. [70] Streitwieser, A.; Heathcock, C. H.; Introduction to Organic Chemistry; 3rd Ed.; Macmillan Publishing Company: New York, NY, 1989; pp 161-165. [71] Arnek, R.; Poceva, D. Acta Chem. Scand. Ser.A 1976, 30, 59. [72] Xiang, X. D.; Zettl, A.; Vareka, W. A.; Corkill, J. L.; Barbee III, T. W.; Cohen, M. L. Phys. Rev. B 1991, 43, 11496-11499. [73] Xiang, X. D.; . Vareka, W. A; Zettl, A.; Corkill, J. L.; Cohen, M. L.; Kijima, N.; Gronsky, R. Phys. Rev. Lett. 1992, 68, 530-533. [74] Lee, W. C.; Johnston, D. C. Phys. Rev. B 1990, 41, 1904-1909. [75] Li, Q.; Suenaga, M.; Hikata, T.; Sato, K. Phys. Rev. B 1992, 46, 5857-5860. [76] Bancel, P. A.; Gray, K. E. Phys. Rev. Lett. 1981, 46, 148-152. [77] Martin, S.; Fiory, A. T.; Fleming, R. M.; Espinosa, G. P.; Cooper, A. S. Phys. Rev. Lett. 1989, 62, 677-680. [78] Halperin, B. I.; Nelson, D. R. J. Low. Temp. Phys. 1979, 36, 599-616.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Synthetic and Phenomenological Approaches…

75

[79] Clem, J. R.; Coffey, M. W. Phys. Rev. B 1991, 42, 6209-6216. [80] Bae, M. K.; Kim, M. S.; Lee, S. I.; Park, N. G.; Hwang, S. J.; Kim, D. H.; Choy, J. H.; Phys. Rev. B 1996, 53, 12416-12421. [81] Kes, P. H.; J. Aarts,; Vinokur, V. M.; van der Beek, C. J. Phys. Rev. Lett. 1990, 64, 1063-1066. [82] Tachiki, M.; Takahashi, S. Solid State Comm. 1989, 70, 291-295. [83] Nelson, D. R. Nature 1995, 375, 356-357. [84] Xue, Y. Y.; Cao, Y.; . Xiong, Q; Chen, F.; Chu, C. W. Phys. Rev. B 1996, 53, 28152818. [85] Zimmermann, P.; Keller, H.; Lee, S.L.; Savič, I. M.; Warden, M.; Zech, D.; Cubitt, R.; Forgan, E. M.; Kaldis, E.; Karpinski, J.; Krüger, C. Phys. Rev. B 1995, 52, 541 -552. [86] [87] Åkesson, R.; Persson, I.; Sandtröm, M.; Wahlgren, U. Inorg. Chem. 1994, 33, 3715-3723. [87] Huong, P. V.; Verma, A. L. Phys. Rev. B 1993, 48, 9869-9872. [88] Choy, J. H.; Kim, D. K.; Hwang, S. H.; Demazeau, G. Phys. Rev. B 1994, 50, 1663116639. [89] Kosugi, N.; Kondoh, H.; Tajima, H.; Kuroda, H. Chem. Phys. 1989, 135, 149-160. [90] Herman, F.; Kasowski, R. V.; Hsu, W. Y. Phys. Rev. B 1988, 38, 204-207. [91] Lottici, P. P.; Antonioli, G.; Licci, F. Physica C 1988, 152, 468-474. [92] DiMarzio, D.; Wiesmann, H.; Chen, D. H.; Heald, S. M. Phys. Rev. B 1990, 42, 294300. [93] Hwangbo, M. H.; Kang, D. B.; Toradi, C. C. Physica C 1989, 158, 371-376. [94] Ishida,T.; . Koga, K; Nakamura, S.; Iye, Y.; Kanoda, K.; Okui, S.; Takahashi, T.; Oashi, T.; Kumagai, K. Physica C 1991, 176, 24-34. [95] Singh, R. J.; Sharma, P. K.; Singh, A.; Khan, S. Physica C 2001, 356, 285-296. [96] Mehran,F.; P. W. Anderson, Solid State Commun. 1989, 71, 29-31. [97] ]Simon, P.; Bassat, J. M.; Oseroff, S. B.; Fisk, Z.; Cheong, S. W.; Wattiaux, A.; Schultz, S. Phys. Rev. B 1993, 48, 4216-4218. [98] Gorter, C. J.; Van Vleck, J. H. Phys. Rev. 1947, 72, 1128-1129. [99] Van Vleck, J. H. Phys. Rev. 1948, 74, 1168-1183. [100] Anderson, P. W.; Weiss, P. R. Rev. Mod. Phys. 1953, 25, 269-276. [101] Kochelaev, B. I.; Sichelschmidt, J.; Elschner, B.; Lemor, W.; Loidl, A. Phys. Rev. Lett. 1997, 79, 4274-4277. [102] Macfalane, A. J.; Williams, R. J. P. J. Chem. Soc. A 1969, 1517-1520. [103] Daemen, L. L.; Bulaevskii, L. N.; Maley, M. P.; Coulter, J. Y. Phys. Rev. Lett. 1993, 70, 1167-1170. [104] Zeldov, E.; Majer, D.; Konczykowski, M.; Geshkenbein, V. B.; Vinokur, V. M.; Shtrikman, H. Nature 1995, 375, 373-376. [105] Grigorenko, A.; Bending, S.; Tamegai, T.; Ooi, S.; Henini, M. Nature 2001, 414, 728731. [106] Chen, G.; Goddard III, W. A. Science 1988, 239, 899-902. [107] Prinz, G. A. Science 1998, 282, 1660-1663. [108] Coronado, E.; Galán-Mascarós, J. R.; Gomez-García, C. J.; Laukhin, V. Nature 2000, 408, 447-449. [109] Ohno, H.; Chiba, D.; Matsukura, F.; Omiya, T.; Abe, E.; Dietl, T.; Ohno, Y.; Ohtani, K. Nature 2000, 408, 944-946.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

76

Soon-Jae Kwon

[110] Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; von Molnár, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Science 2001, 294, 1488-1495. [111] Ganichev, S. D.; Ivchenko, E. L.; V. V. Bel'kov,; Tarasenko, S. A.; Sollinger, M.; Weiss, D.; Wegscheider, W.; Prettl, W. Nature 2002, 417, 153-156. [112] Moodera, J. S.; Meservey, R.; Hao, X. Phys. Rev. Lett. 1993, 70, 853-856. [113] Rieger, A. L.; Rieger, P. H. J. Phys. Chem. 1984, 88, 5845-5851. [114] Poizat, O.; Giannotti, S.; Sourisseau, C. J. Chem. Soc. Perkin Trans II 1987, 829-834. [115] Kaneko, M.; Motoyoshi, J.; Yamada, A. Nature 1980, 285, 468-470. [116] Bose, A.; He, P.; Liu, C.; Ellman, B. D.; Twieg, R. J.; Huang, S. D. J. Am. Chem. Soc. 2002, 124, 4-5. [117] Nakahara, A.; Wang, J. H. J. Phys. Chem.1963, 67, 496-498. [118] Kosower, E. M.; Cotter, J. L. J. Am. Chem. Soc. 1964, 86, 5524-5527. [119] Grätzel, M. Acc. Chem. Res. 1981, 14, 376-384. [120] Prout, C. K.; Murray-Rust, P. J. Chem. Soc. A 1969, 1520-1525. [121] Seehra, M. S.; Castner Jr., T. G. Phys. Rev. B 1970, 1, 2289-2303. [122] Mabbs, F. E.; Collison, D. Electron Paramagnetic Resonance of d Transition Metal Compounds; Elsevier: New York, NY, 1992; p274, p1167, p1181. [123] Eremin, M. V.; Sigmund, E. Solid State Commun. 1994, 90, 795-797. [124] Likodimos, V.; Guskos, N.; Gamari-Seale, H.; Koufoudakis, A.; Wabia, M.; Typek, J.; Fuks, H. Phys. Rev. B, 1996, 54, 12342-12352. [125] Ranjit, K. T.; Kevan, L. J. Phy. Chem. B 2002, 106, 1104-1109. [126] Evans, A. G.; Evans, J. C.; Baker, M. W. J. Chem. Soc., Perkin Trans. 2 1977, 17871789. [127] Monk, P. M. S.; Fairweather, R. D.; Ingram, M. D.; Duffy, J. A. J. Chem. Soc., Perkin Trans. 2 1992, 2039-2041. [128] Woodward, F. M.; Albrecht, A. S.; Wynn, C. M.; Landee, C. P.; and Turnbull, M. M. Phys. Rev. B 2002, 65, 144412. [129] Jacobs, I. S.; Bray, J. W.; Hart, H. R.; Interrante Jr., L. V.; Kasper, J. S.; Watkins, G. D.; Prober, D. E.; Bonner, J. C. Phys. Rev. B 1976, 14, 3036-3051. [130] Huizinga, S.; Kommandeur, J.; Sawatzky, G. A.; Thole, B. T.; Kopinga, K.; de Jonge, W. J. M.; Roos, J. Phys. Rev. B 1979, 19, 4723-4732. [131] Norton, D. P.; Lowndes, D. H.; Pennycook, S. J.; Budai, J. D. Phys. Rev. Lett. 1991, 67, 1358-1361. [132] Haupt, S. G.; Riley, D. R.; Jones, C. T.; Zhao, J.; McDevitt, J. T. J. Am. Chem. Soc. 1993, 115, 1196-1198. [133] McDevitt, J. T.; Jones, C. E.; Haupt, S. G.; Zhao, J.; Lo, R. K. Synth.. Met. 1997 85, 1319-1322.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

In: Magnesium Diboride(MgB) 2 Superconductor Research ISBN 978-1-60456-566-9 c 2009 Nova Science Publishers, Inc. Editors: S. Suzuki and K. Fukuda

Chapter 3

S URVEYING THE VORTEX M ATTER P HASE D IAGRAM FOR P RISTINE M G B 2, AND ATOMIC S UBSTITUTED M G 1−xA Lx B 2 AND M G B 2−xC x S INGLE C RYSTALS D. Stamopoulos and M. Pissas Institute of Materials Science, NCSR “Demokritos”, 153-10, Aghia Paraskevi, Athens, Greece

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Abstract The recent discovery that the MgB 2 compound is a superconductor with remarkably high critical temperature, Tc = 39.2 K has renewed the interest of the scientific community on superconductivity worldwide. This relatively high critical temperature classifies MgB 2 as an intermediate-Tc superconductor opening new possibilities for its efficient utilization in various practical applications such as the design and construction of superconducting high-field magnets. In this chapter we study in detail the properties of vortex matter phase diagram for MgB2 single crystals by means of local Hall and global SQUID magnetometry. Starting from the case of pristine MgB 2 we extensively survey how the vortex matter phase diagram is modified upon substitution of Al for Mg, and C for B, that is for the case of Mg1−xAlx B2 and MgB2−xCx single crystals, respectively. The peak effect is observed in all cases of pristine, Al and C substituted MgB 2. Referring to the local Hall ac-susceptibility measurements the dynamic behavior of the peak effect is systematically studied upon the variation of the excitation field’s characteristics. These data enable us to discuss the possible existence of various vortex phases on the H-T phase diagram such as the Bragg glass, the vortex glass and the vortex liquid. The influence of both thermal and quenched disorder on the vortex matter phase diagram is studied on the basis of relevant theoretical propositions. In this context, parameters that provide important information for the phenomenology of vortex systems, such as the anisotropy γ, the upper-critical fields H ab,c c2 (T) that determine the ultimate transition to the normal state, and the concept of two-band superconductivity are discussed for the pristine and atomic substituted MgB 2. Except for the importance for basic physics, surveying the vortex matter phase diagram is important for practical applications; since these vortex phases have extremely different dynamic transport response, their relative participation on the phase diagram

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

78

D. Stamopoulos and M. Pissas determines the limitations for utilizing pristine, and atomic substituted MgB 2 in practical application.

1.

Introduction

In low-Tc superconductors, the superconducting transition is efficiently described by meanfield theory. The negligible influence of thermal fluctuations and the 3D nature of low- Tc superconductors result in a superconducting-normal transition of second-order. On the contrary, the small coherence lengths, the high transition temperatures, and the quasi-2D nature of high-T c superconductors greatly enlarge the temperature region in which fluctuations of the order parameter are important.[1] The parameter which measures the influence of fluctuations on the vortex matter phase diagram is the so-called Ginzburg number,[1] describing the ratio between the thermal and the condensation energy at Tc and zero temperature, respectively, for a coherence volume. The Ginzburg number is defined[1] by the equation:

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

1 Gi = 2



k B Tc 3 (0) 2 Hc (0)ξab

2

,

where Hc (0) is the thermodynamic critical field,  = λab /λc = ξc /ξab is the anisotropy parameter of the superconductor, λab (ξab ) and λc (ξc ) are the London penetration depths (coherence lengths) on the ab plane and along the c-axis, respectively. In type-II low-Tc superconductors the Ginzburg number is very low, with consequence the transition into the normal state (with increasing field) to be of second order, described by a superconducting order parameter which vanishes continuously at the upper-critical field line, Hc2 (T ). In this case, the phase diagram of a low-Tc superconductor comprises from the Meissner and the vortex lattice phases. On the other hand, in the high- Tc superconductors the Ginzburg number is several orders of magnitude higher. This difference enhances the role of thermal fluctuations leading to melting of the vortex lattice well below Hc2 (T ), thus separating the vortex phase in a solid and a liquid state.[1, 2, 3, 4, 5, 6, 7, 8] Regarding the melting transition, an interesting question is still open. What really happens in a superconductor with intermediate Ginzburg number value? In addition, if the superconductor is subjected to random point-disorder the phase diagram is drastically modified. The important parameter of the problem is now an appropriate ratio between the reduced coherence length D ≡ ξab /Lc and the Ginzburg number, defined by ν = (2π)1/2D3 /Gi1/2.[8] This parameter characterizes the relative strength of pinning 2 1/3 of any type. The length Lc = (4 ε20/nfpin ) is the single vortex collective pinning length (n and fpin are the number and the force strength of the pinning centers), ε0 = (Φ0/4πλ)2 is the line tension of vortices and Φ0 the flux quantum. Due to the influence of pinning introduced by random point-disorder, the vortex lattice looses its long range order under an order-disorder transition and is transformed to a new vortex state that is called vortex glass. Regarding the order-disorder transition, an interesting question refers to its impact on the vortex matter phase diagram of a superconductor with intermediate Ginzburg number. Taking into account the conditions that are briefly discussed above, currently it is widely accepted that, in the presence of random point-disorder (quenched disorder) and thermal fluctuations (thermal disorder), the vortex matter phase diagram consists of three generic

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Surveying the Vortex Matter Phase Diagram. . .

79

phases: the high-temperature vortex liquid, the high-field amorphous vortex glass, and the low-field, low-temperature Bragg glass. These phases are governed by the three basic energies: the energy of thermal fluctuations, the energy of pinning, and the elastic energy. The transition lines are determined by matching any two of the basic energies.[2, 3, 4, 5, 6, 7, 8] Although these topics have been extensively studied for low- Tc and high-T c superconductors, today a detailed study for the case of intermediate- Tc superconductors is still missing. The recent discovery[9] that MgB2 compound is a superconductor with an intermediate transition temperature Tc ∼ 39 K (in comparison with low-Tc and high-T c superconductors) has generated extensive scientific research (for a review see Ref.[10]). Thus, MgB 2 is an ideal candidate for studying the topics discussed right above. Measurements in single crystals[11, 12, 13, 14, 15, 18, 16, 17] and polycrystalline samples [19, 20, 21, 22, 23] have revealed that MgB2 is an anisotropic type-II superconductor, with a temperature dependent ab /H c . In addition, MgB is a phonon-mediated superconductor with anisotropy γ = Hc2 2 c2 multiple gaps[24] and strong electron-phonon coupling. The Fermi surface of MgB 2 consists of a two-dimensional cylindrical sheet parallel to c-axis, derived from σ-antibonding states of the boron pxy and from a three-dimensional band coming from π-bonding and antibonding states of the boron pz orbitals. Furthermore, the calculated superconducting gap sizes for the two distinct Fermi surfaces are different with ∆σ ≈ 7.1 meV, and ∆π ≈ 2.2 meV. Superconductivity in the π-band is induced by the σ-band, either by interband scattering or Cooper pair tunnelling. [25] Consequently, the σ-band is responsible for superconductivity in MgB 2 and thus determines the macroscopic parameters Tc and Hc2 . The small Hc2 for the π-band leads to a strong vortex core overlapping already at very low magnetic the known material parameters of MgB 2 : Tc 39 K,  ∼ 5−1 , p fields. Using c ≈ 104 A ˚ and Hc = 2.8 kOe an estimation of Ginzburg number ξab (0) = Φ0 /2πHc2 −5 is Gi ≈ 10 , that is four orders of magnitude smaller than that of YBa 2 Cu3O7−δ but five orders of magnitude larger than that of Nb,[26] ( Gi(Nb) = 10−10). The intermediate value of Ginzburg number of MgB 2 gives us a unique opportunity to further test several issues concerning the existing theoretical models of the vortex matter phase diagram in the presence of weak point disorder. [1, 2, 3, 4, 5, 6, 7, 8] The elucidation of the superconductivity mechanism, as well as the vortex matter properties, usually include atomic substitution studies. Atomic substitutions may influence the properties of a superconductor relevant with the critical current, thus making it appropriate for practical applications, by increasing the Hc2 (T ) line and/or the critical current that the superconductor can sustain without exhibiting losses. Additionally, they may also help in the clarification of the superconductivity mechanism. In MgB 2 , atomic substitutions change the impurity scattering rates, the electron-phonon interaction and the electron density. The existence of σ and π bands results in intraband (σ and π) and interband scattering. One of the fundamental differences expected between a multi-band superconductor and a conventional s-wave one-band superconductor, as far as the substitution effects are concerned, is that nonmagnetic impurities may act as Cooper pair breakers, due to the interband scattering which mixes the Cooper pairs in the two different bands.[27, 29, 28] Consequently, in a two-band superconductor the atomic substitutions could lead to reduction of Tc both by increasing the interband scattering and/or from the effect of electron doping on the electronic structure (modification of the density of states and electron phonon-interaction). Until now, carbon[30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41] and aluminium[48,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

80

D. Stamopoulos and M. Pissas

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

49, 45, 44, 43, 42, 46, 47, 50] substitutions have been studied in appreciable detail. Since carbon substitutes boron, it is expected that it induces large interband scattering.[29] On the other hand, aluminium atoms substitute Mg, producing out-of-plane distortions of the boron atoms in neighboring planes which in turn mix the in-plane px,y and out-of-plane pz orbitals, which can increases the σ − π scattering (interband scattering).[28] Both substitutions produce a similar decrease in Tc , but the influence on the Hc2 (T) is different. Carbon substitution increases Hc2 (T) substantially, while Al mainly causes the opposite. Single-crystal and powder-sample studies have shown that the substitution of Mg for Al in MgB2 produces single phase materials only for x < 0.15 and 0.5 < x < 1. In the intermediate concentration regime (0.15 < x < 0.5) the samples show tendency for phase separation. For x ∼ 0.5 a superstructure is thermodynamically more stable with unit cell doubled along the c-axis which arises from the ordering of the Mg and Al.[51] The gradual decreasing of Tc upon substitution of Mg for Al and of B for C, has been attributed mainly to the density-of-states decreasing at the Fermi level induced by electron doping and reduced lattice volume rather than increasing of interband scattering. The topics discussed right above are studied in great detail in this chapter for the case of pristine MgB 2 and atomic substituted Mg 1−x AlxB2 and MgB2−x Cx single crystals. The structure of the present chapter is as follows: Section II briefly reviews the employed experimental techniques. Section III presents the experimental results and the respective theoretical propositions for pristine MgB 2 single crystals. Section IV refers to the aluminium substituted Mg 1−x Alx B2 samples presenting results for three different single crystals having aluminium content x = 0.013, 0.101 and 0.141. Section V focuses on carbon substituted MgB2−x Cx single crystals with x = 0.04 and 0.10. Finally, Section VI summarizes our observations.

2.

Experimental Techniques

The local ac-susceptibility measurements were obtained by means of a GaAsIn Hall sensor (active area of 50 × 50 µm2 ) with dc and ac magnetic fields applied parallel to its surface. By placing the crystal right above the active area of the microR 1/f scopic Hall sensor the real µ0 = (f /H0) 0 Bz (t) sin(2πf t)dt and imaginary µ00 = R 1/f (f /H0) 0 Bz (t) cos(2πf t)dt parts of the fundamental ac-permeability were measured with a double ac-method. H0 and f are the amplitude and the frequency of the excitation magnetic ac-field (Hac =Ho sin(2πf t)), respectively and Bz (t) is the ac-magnetic induction at the crystal’s surface. The local real and imaginary parts of ac-susceptibility were deduced from local ac-permeability using the relations: χ0 = µ0 − 1 and χ00 = µ00 , respectively. Essentially, the ac-Hall voltage was modulated by a low frequency ( f = 3 Hz) ac-magnetic field superimposed on a large dc-magnetic field. A bridge circuit was employed in order to subtract the large Hall voltage offset produced by the dc-field. The dc-magnetic field was produced by means of a 100 kOe superconducting magnet hosted in an OXFORD cryostat. The particular experimental technique permits the measurement of small single crystals with dimensions of the order of the active area of the Hall sensor. Global dc-magnetization measurements were carried out using a Superconducting Quantum Interference Device (SQUID) magnetometer [Quantum Design].

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

81

Figure 1. Photo of the pristine MgB 2 single crystal studied in the present chapter. The crystal is inclined by φ ≈ 700 in respect to the applied magnetic field. The active area of the Hall sensor is also schematically shown. The dimensions of the single crystal are 250 × 250 × 40 µm3 .

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

3.

Pristine Single Crystals

In this section of the present chapter, the experimentally determined vortex matter phase diagram of MgB2 is compared with the available theoretical models based on the Lindemann criterion and the results of collective pinning theory, where the order-disorder transition line is estimated by taking into account both the pinning disorder and the thermal fluctuations. Our results show that the vortex matter phase diagram of MgB 2 can be interpreted consistently only if one take into account the role of thermal fluctuations. This conclusion implies the generic validity of existing theoretical models for the vortex matter phase diagram in the presence of weak point-disorder.

3.1.

Growth of Pristine MgB2 Single Crystals

MgB2 single crystals have been grown under high pressure in the quasiternary Mg-MgB 2 BN system at a pressure of 4-6 GPa and temperature 1400−1700 o C for 5−60 mins, in a BN container, using a cubic-anvil press (TRY Engineering).[52] The present experiments were performed on a small (250 × 250 × 40 µm3 ) MgB2 single crystal. Besides the superior sample quality, one of the most important aspects of our measurements is the sample’s microscopic size, restricting to a minimum any residual inhomogeneities. This particular single crystal is presented in Fig.1

3.2.

Experimental Data for Pristine MgB 2 Single Crystals

Figure 2(a) shows the real and imaginary parts of local ac-susceptibility at T = 15.3 K as a function of dc-magnetic field for Hkc (the angle between the applied dc-magnetic field H and the crystal’s c-axis is φ = 00 ). Initially, −4πχ0 = 1, a fact which means that the flux front has not still reached the Hall sensor (the Hall sensor is at the center of the crystal). This

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

82

D. Stamopoulos and M. Pissas 0.02

(a)

1.0

/

χ ', χ '' (arb. units)

-4πχ

Hfp

0.90 0.85

0.6

0.80 0.0 0.5 1.0 1.5 2.0

φ =0

0.4

H (kOe)

o

/

T=15.3 K Ho=17 Oe f=3 Hz

0.2

-4πχ (H)

15

Hdc (kOe)

20

35 kOe

0.01

0.000

0.00 ο

c axis

25

0

10 kOe -0.01

Ho=17 Oe f=3 Hz

H

Hirr

χ (H) 10

0.002 -0.02

-0.004 φ=70

Hon(T)

0.0 5

χ (T)

-0.002

Hp(T)

//

0

Hdc=60 kOe

//

0.95

(b)

Tirr(H)~Tc2(H)

Ton(H)

0.00

1.00

/

//

-4πχ'=(B -Ho)/Ho, χ''= B /Ho

1.05

0.8

Tp(H)

/

χ (T)

5

10

15

20

25

30

35

-0.02 40

T (K)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 2. (a) Local ac-susceptibility as a function of dc field at T = 15.3 K. The angle between the dc and ac magnetic fields with the c-axis is φ = 00 . The inset shows the detail of the measurement in the region where the critical current starts to decrease. (b) Local ac-susceptibility as a function of temperature under Hdc = 60, 35 and 10 kOe and Ho = 17 Oe which are inclined at an angle φ ≈ 700 in respect to the c-axis of the crystal. occurs up to the first-peak field, Hf p (see inset). For fields H > Hf p(15.3K) ≈ 0.5 kOe, −4πχ0 initially decreases exponentially and subsequently as a power law (fitting curves are not shown). This behavior is expected in the small and large bundle regimes, where the critical current decreases exponentially and as a power law, respectively.[1] Finally, for c , −4πχ0 and χ00 display narrow peaks as a consequence of a peak in the fields near Hc2 critical current density. This is the well known peak effect and is accompanied by an onset point H on , the peak itself H p, and its end-point, which coincides with the irreversibility point H irr (and also with the upper-critical field point H c2 ). The peak effect is also present when the magnetic field is not parallel to the c-axis as Fig.2(b) shows. In this particular case the angle between the magnetic field and the crystal’s c-axis is φ ≈ 700. As in the case of φ = 0 (see Fig.2(a)) the peak effect occurs only when H > Hi (φ). It is remarkable that the temperature where the peak effect begins to develop is independent of φ. In Ref. [53] the reported global ac-susceptibility data indicated that the peak effect is present both for Hkc and Hkab, confirming that the underlying mechanism is a feature for all directions of H. For H < Hi (φ) the peak effect was not observed. Figures 3(a) and (b) show representative measurements of local ac-susceptibility for φ = 0 and φ = 700 when H < Hi (φ), respectively. These measurements do not display any feature associated with the peak effect. In this case the local ac-susceptibility is interpreted assuming a monotonic variation of Jc (H, T ). Global magnetization measurements on the same crystal[54] show that the onset of the diamagnetic signal of the global and the local measurements coincide with each other. Consequently, the irreversibility point can be accurately identified as the respective upper-critical field Hc2. From this set of measurements one can determine the Hc2 (φ) from the onset of the diamagnetic susceptibility.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

83

0.000

0.0

Hdc=2.5 kOe φ (H ,c )~0

0

Hirr ~ Hc2

Ho=17 Oe f=3 Hz 6.8 Oe

-0.5

3.4 Oe

-1.0 15

χ ', χ '' (arb. units)

χ '=4π M'/Ho, χ ''=4π M''/Ho

0.5

Hdc=10 kOe φ (H ,c )~70

-0.005

0

Hirr~Hc2

Ho=17 Oe f=3 Hz

-0.010

8.5 Oe

(a) 20

25

T (K)

30

35

(b) -0.015 15

20

25

30

35

T (K)

Figure 3. (a) Temperature dependence of the real χ0 and imaginary χ00 at fixed dc-magnetic field 2.5 kOe. The angle between the external dc and ac magnetic fields with the c-axis of the crystal is φ = 00 . (b) Temperature dependence of χ0 and χ00 at fixed dc-magnetic field 10 kOe. The angle between the external dc and ac magnetic fields with the c-axis of the crystal is φ ≈ 700.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

3.2.1. Vortex Matter Phase Diagram for Pristine MgB 2 Single Crystals Figure 4 shows the vortex matter phase diagram for φ = 00 and 700 as it is estimated from the local measurements (see also Refs.[55]). In Fig. 4 included are the points where the screening current starts to increase when one measures during heating from zero temperature (or increases the dc field). Referring to the case φ = 00, as illustrated in Fig. 4, for T > Tc /2, the Hirr-line (or Hc2 (T)-line) displays a positive curvature, while for T < Tc /2 it displays a negative curvature and approaches zero temperature with nearly zero slope at Hirr(0) ' 29 kOe. This particular temperature variation is not compatible with what is expected from the mean field theory which results in the following temperac 2 ture variation Hc2 (T ) = Φ0 /2πξab (T ) ∝ (1 − (T /Tc)2). Such unusual temperature variation arise from nonlocal effects which in sufficiently clean materials becomes observable when the transport mean free path becomes comparable to the superconducting coherence length.[56] The experimental points can be reproduced very well using the empirical formula Hirr(T ) = 29[1 − (T /Tc)2]1.45. This behavior is more pronounced when φ increases towards φ = 900. The positive curvature, part of Hc2 (φ ≈ 700) is now more obvious in comparison with the φ = 00 case. The regime at which the peak effect occurs [the filled (open) circles in Fig. 4 represent the (T, H) points H p (T) (Hon (T)) where the maximum (onset) of the peak effect is observed] occupies a small fraction of the mixed state, located slightly below the Hirr(T ) line. In the regime between 10 and 15 kOe the peak effect is transformed to a very narrow diamagnetic step and finally, for lower fields the transition becomes gradual. The point, where the peak effect is terminated is denoted by (Ti, Hi) (see Fig. 4). Similar phase diagrams have been observed by Angst et al., [57] Lyard et al., [53] and Welp et al.[18] using torque magnetometry, global susceptibility and resistivity measurements, respectively.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

84

D. Stamopoulos and M. Pissas 70 60

H (kOe)

50

φ (H ,c )~70

40

Hp(T) φ (H ,c )~0

30

0

c

Hirr≈ Hc2 Hon(T)

20

c

10 0

0

Bragg glass

Hsv 0

(Ti,Hi)~ (24 K,15 kOe) 10

20

30

40

T (K)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 4. Experimental vortex matter phase diagram of MgB 2 compound as determined from local ac-susceptibility measurements for ϕ(H, c) ≈ 00 (H k c-axis) and ϕ(H, c) ≈ 700. Presented are: the onset of peak effect line H on (T) (open circles), the peak effect line Hp (T) (solid circles), and the irreversibility line H irr (T) (open squares). The solid line through (T, H irr)-points is a plot of the empirical formula Hirr(T ) = 29[1 − (T /Tc)2]1.45. The dashed line is a solution of Eq.3 with cL = 0.25 and ξ(0)/Lc (0) = 0.085. The thick line is a plot of Hsv = 2π(ξ/Lc )2Hc2 which defines the single-vortex pinning regime. Triangles represent the field where the flux reaches the location of the sensor for φ = 0. At the point (Ti, Hi) ' (24 K, 15 kOe) the peak effect is terminated. 3.2.2. Comparison with the Theoretical Predictions In this section using the theoretical predictions concerning the vortex matter phase diagram we will make an effort to understand this phase diagram as well as to point out the differences between MgB2 and both low-Tc and high-T c superconductors. Currently it is accepted that in the presence of random point-disorder the vortex matter appears in three phases depending on the strength of disorder. These vortex matter phases are termed Bragg glass, vortex glass, and liquid.[2, 1] The Bragg glass has no dislocations, thus if either thermal fluctuations or static disorder increase, the Bragg glass should be transformed to a phase containing defects. The increasing of the magnetic field increases the density of vortices. In addition, the specific form of the coupling of the disorder with the density of vortex lattice, leads to an effective increasing of disorder energy. Hence as the magnetic field increases the system gains energy if the Bragg glass is transformed to an amorphous arrangement of vortices. As is discussed in the ”Introduction”, this transition is called orderdisorder transition. The order-disorder transition has been studied in a number of articles [2, 3, 4, 5, 6, 7, 8] when it takes place inside the single-vortex pinning regime where the Larkin pinning length Lc is less than L0 = a (determines the size of elastic screening of local distortions). However, in the case of MgB 2 , as we see bellow, the order-disorder transition occurs inside the small or large-bundle regime. As basis for our discussion we

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

85

used the results from the work of Mikitik and Brandt[8] where the phase transition lines are estimated using the Lindemann criterion and the appropriate correlation function in the small-bundle regime. Central role in such a consideration plays the mean-squared relative displacement of two vortices (correlation function) separated by a distance r, defined by BT,dis (R, L) ≡ h[u(R, L) − u(0, 0)]2i,

(1)

where h· · · i denotes the thermal disorder (T) and quenched disorder (dis) average, respectively. From B one defines two length scales Rc and Ra in the xy plane (and similarly Lc and La along z) such that B(Rc , 0)dis ∼ max(ξ 2, hu2iT ) and B(Ra )T,dis ∼ a2, respectively. Rc is the Larkin-Ovchinikov pinning length[58] and Ra is the scale at which one enters the asymptotic regime[2] with a logarithmic growth of the displacements. The locus of (T, H) points where the order-disorder occurs, could be estimated from the condition: B(Ra = a)T,dis = c2L a2 , where cL is the phenomenological Lindemann constant and a ≈ (Φ0/H)1/2 is the spacing between vortices. Let us start our analysis disregarding the influence of thermal fluctuations. The specific form of the correlator depends on the pinning regime, which is determined by the relation of Larkin pinning length Lc with the length L0 = a (at the length L0 the condition B(a, 0) = B(0, L0) holds[1]). When Lc < L0 the vortex lattice is inside the single-vortex pinning regime. At this regime the order-disorder line is defined by

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

hdis = 2πc2L(ξ/cL Lc )−α ,

(2)

2 where hdis = Hdis /Hc2, Hc2 = Φ0 /2πξab the upper-critical field and α ≈ 3. We must note that, in order the condition Hdis < Hsv = Φ0 2 /L2c to hold self-consistently, it is necessary cL < ξ/Lc also to hold. On the other hand, when Lc > L0 or T > T1 (where ξ(T1)/Lc (T1) = cL ) correlators appropriate for the small-bundle and large bundle regimes must be used. The order-disorder transition in the small-bundle regime is given[8] solving the equation:

hdis(1 − hdis )3 = 2πc2L(ξ/cL Lc )6(1 − hsv )3 ,

(3)

where hsv = Hsv /Hc2 = 2π(ξ/Lc)2 . Considering that the onset points (To, Ho) of the peak effect coincide with the order-disorder transition, in order the experimentally observed data points to be reproduced we must assume the following: (a) D = ξ(0)/Lc (0) < cL , (b) a δ` pinning mechanism and (c) ξ(T )/ξ(0) = λ(T )/λ(0) = (1 − T 2 /Tc2)−1/2. With the above assumptions the basic parameter Dg(T ) ≡ ξ(T )/Lc (T ) which determines the hdis varies with temperature as g(T ) = (1 − (T /Tc)2 )1/2. As Mikitik and Brandt[8] have demonstrated the case of δTc pinning does not lead the Hdis-line to converge towards the Hc2 -line. This conclusion holds irrespectively of the value of the ratio D/cL. For this reason we examine only the case of δ` pinning. When D/cL > 1, at low temperature, Hdis is described by Eq. 2 which is an increasing function of temperature. As temperature increases, at T1 the ξ(T1)/Lc (T1) will equal cL , making Eq. 3 valid in the interval T1 ≤ T < Tc . At this regime Eq. 3 is a decreasing function of temperature. One can consider the crossover point T1 as a maximum of Hdis -line. Since our experimental data are not compatible with such a behavior, the Hdis -line is entirely located outside the single-vortex

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

86

D. Stamopoulos and M. Pissas

pinning regime, and is described by Eq. 3 at any T ≤ Tc . In order the numerically estimated Hdis(T ) to pass through the onset points of the peak effect, we must set ξ(0)/Lc (0) = 0.085 for cL = 0.25 (see dotted line in Fig. 4). The agreement between experimental points and theoretically calculated ones is not worthless. However, there is a serious drawback, while the second peak disappears for H < Hi , the theoretical curve persists up to zero field. Let us see how the incorporation of thermal fluctuations can take into account this inconsistency. Thermal fluctuations hu2iT , lead to melting of the vortex lattice essentially below mean-field Hc2 line. In addition, they lead to a smoothing of the pinning potential, thus renormalizing the Larkin length. If one neglects the contribution associated with the compression modulus[59] c11 a simplified formula for the thermal fluctuations hu2 iT is hui2T

2

≈ξ t



1/2 Gi h−1/2f (h), Hc2 (t)/Hc2(0)

(4)

where h = H/Hc2 (t), t = T /Tc , f (h) = (2βA )/(1−h))((1+(1+c)2)1/2 −1)/(c(1+c))), c = 0.5(βA(1 − h))1/2 and βA = 1.16. The melting line (for hm > hsv ) is determined by the Lindemann criterion, hu2 iT = 2 2 cL a , using Eq. 4 for hu2 iT t



Gi hc2 (t)

1/2

2 h1/2 m f (hm ) − 2πcL = 0,

(5)

where hm = Hm /Hc2. After the appropriate modifications of the correlator BT,dis the boundary defining the single-vortex pinning regime is given now from the solutions of the equation:

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

1/2 h1/2 D(t) + t(Gi/hc2 (t))1/2f (hsv (t)) = 0. sv (t) − (2π)

(6)

The order-disorder line (for hdis > hsv , which is our case) can be found solving the equation " #4   Gi 1/2 f (hdis ) 3 hdis (1 − hdis ) 1 + t hc2 (hdis )1/2   D(t) 6 −2πc2L [1 − hsv (t)]3 = 0. (7) cL Using the above system of equations we examined which combination of parameters can reproduce the experimentally constructed phase diagram of Fig. 4. Based on the previous conclusions that (a) the order-disorder line is located in the bundle-vortex pinning regime, (b) a δ` pinning mechanism operates in our sample and using a value Gi = 10−5 for the Ginzburg number (see ”Introduction”) we can reproduce very well the phase diagram of Fig. 4. The theoretically calculated phase diagram is shown in Fig. 5. We must note that the selection of the particular Ginzburg number is not fortuitous but comes from the known material parameters of MgB 2 . We used the irreversibility line (deduced from the real part onset of local magnetic moment) as an approximate estimation of the temperc ature variation of Hc2 (T )-line. In addition, attempting to identify the order-disorder line (Eq. 7) with the onset of the peak in the screening current a value for D = 0.11 is needed.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

87

30

TC = 38.3 K CL = 0.25 D= 0.11 -5 Gi=10

Hm

HUSV

Hc2

25

Hdis

15

C

Hc2 (kOe)

20

10

(Ti,Hi)~ (24 K,12.5 kOe)

5

HSV

0 0

5

10

15

20

25

30

35

40

T (K)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 5. Theoretical vortex matter phase diagram relevant to MgB 2 compound taking into account the thermal fluctuations. With thick line plotted is the crossover line which separates the single-vortex and the bundle-vortex pinning regimes. The dotted and dashed lines, c correspond to the order-disorder, and Hc2 (T ) transitions, respectively. These lines have been calculated supposing cL = 0.25, D = ξab (0)/Lc(0) = 0.11 and Gi = 10−5. The dashed-dotted line corresponds to the peak effect line, while the thin solid line corresponds to the melting line.

This value is slightly larger than the one used in the case where the thermal fluctuations are ignored. As we previously promised only the theoretical model predicts the intersection of the order-disorder line with the irreversibility line at point Ti (see the appropriate arrow in Fig. 5). The simulation also revealed that in order to reproduce the experimentally determined irreversibility line (we supposed that it coincided with the melting one) the same c functional form for the Hc2 (T)-line is necessary. For example, if we suppose a form of c 2 Hc2 (T ) = 29(1 − (T /Tc) ) it is impossible to find a melting line which reproduces the experimental data. It should be noted that the assignment of the irreversibility line with the melting line c is reasonable. In this case we simply suppose that the Hc2 (T)-line has the same functional form as the Hirr(T) one. When δ`-pinning mechanism and thermal fluctuations are accounted for, the theoretical model predicts that Hdis (T) intersects the Hm (T), at Ti < Tc . The experimental results indeed confirm this prediction, where the onset-line of the peak effect is terminated at the irreversibility line at H ≈ 10 kOe. The parameter which controls Ti is ν = (2π)1/2D3/Gi1/2.[8] An estimation of ν using the parameters used in our simulation is ν ≈ 6.6. This intermediate value justifies the observed value of Ti ≈ 24 K. Essentially, as the pinning strength goes to zero Ti tends to zero temperature excluding completely the order-disorder transition leaving the vortex lattice in the Bragg glass state. In the opposite limit, (large disorder strength, ν  1) Ti tends to Tc . This behavior is observed in the data of Welp et al., [18] presumably due to larger disorder of the crystal used

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

88

D. Stamopoulos and M. Pissas

in that work. Finally we should stress the remarkable agreement between the termination point of the peak effect as this is experimentally obtained (Tiex , Hiex) ' (24 K, 15 kOe) and theoretically simulated (Tith , Hith) ' (24 K, 12.5 kOe).

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

3.2.3. Peak Effect and Thermomagnetic History Effects for Pristine MgB 2 Single Crystals Let us now discuss the peak effect since several questions still remain open for its occurrence in intermediate-Tc superconductors. Figure 6 shows the real (χ0 ) and imaginary (χ00 ) fundamental ac-susceptibility at fixed temperature 14.3 K as a function of dc-magnetic field. The measurements are obtained during increasing and subsequently decreasing the dc field, as denoted by the arrows. We see that the ascending branches are above the descending ones, so that clear hysteresis exists. Similar measurements have been collected in temperature scans for fixed dc-magnetic field as Fig. 7 shows. For Hdc > 13.5 kOe the measurements display a local minimum in the χ0 at an ac-field independent dc magnetic field Hp (temperature Tp) in dc-field (temperature) scans. The corresponding χ00 curves, in the region where the local minimum in χ0 curves appears, show a single peak (for large Ho ), or two (for intermediate Ho ). In order the measurements of Fig. 6 and Fig. 7 to be understood quantitatively one has to compare the effective current density Jac ∼ cHac4πd (d is the crystal thickness) with the critical current Jc (H, T ) that the superconductor can sustain without exhibiting losses. If at some temperature Jc (H, T ) ≈ Jac holds, the ac field is completely screened by the critical current. This is the case of measurements presented in Fig. 3. On the other hand, when Jac > Jc (H, T ) the critical current is not sufficient to screen the ac field at the position of the sensor. In this case the observed χ0 can be considered as a fingerprint of the Jc (T, H). For all the measurements presented in Figs. 6 and 7 Jac > Jc (H, T ) holds. The particular structure of the critical current deduced from local ac-susceptibility measurements can be interpreted if one supposes a critical current surface Jc (H, T ), which has a ’ridge’ across the Hp -line (the peak effect). As Fig.6 shows, this surface is multi-valued in the region Hon − Hp, where the critical current depends on the measuring path. The local ac-susceptibility, at fixed temperature, as function of the dc field, roughly measures the slope of the forward and reverse branches of the local dc-magnetization hysteresis loop at the particular dc field. Hence, the hysteresis in local ac-susceptibility measurements (at the particular field regimes) means that the ascending and descending branches of the magnetization loop are determined from different critical currents. In addition, in both Figs. 6 and 7 we see that the hysteretic behavior reduces as the amplitude of ac-field increases, as has been observed in HgBa 2 CuO4+δ .[60] The observed thermomagnetic history dependence of the ac-susceptibility is not compatible with the conventional critical-state model. This model treats the critical current, Jc as a single valued function of magnetic induction B and temperature T , while our measurements indicate that Jc depends on the measuring path in the regime T < Tp . In low-Tc superconductors, the peak effect mostly occurs very close to the normal phase boundary, unlike to what holds for the cuprate superconductors where the respective effect, usually termed ”fishtail effect”, occurs far below the upper-critical field line. Further-

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . . χ

4

//

89

T=14.3 K

χ ', χ '' (arb. units)

2

Hon

0

17 Hp 8.1 5.1

-2

Hirr~Hc2

3.4

-4

H o=1.7 Oe -6

χ

-8 f=3 Hz 21.0

21.5

22.0

/

22.5

23.0

Hdc (kOe)

Figure 6. Real (χ0 ) and imaginary (χ00 ) local fundamental ac-susceptibility as a function of the dc-magnetic field at T = 14.3 K. Shown are measurements for amplitude of the acmagnetic field Ho = 1.7, 3.4, 5.1, 8.5 and 17 Oe. The arrows show which part of the curve was taken during ascending or descending of the dc magnetic field. These measurements are obtained for Hdc||Hac||c-axis.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

more, in addition to the ”fishtail effect”, a conventional peak effect is often observed in YBa2 Cu3 O7 very close to the melting transition[61] implying that there are two types of peak effects, one associated with a disorder induced transformation and the other with the thermally induced melting transition (see below). The explanation for the peak effect in terms of vortex lattice properties was first suggested by Pippard.[62] Pippard’s idea was that near Hc2 (T) the energy to shear a vortex lattice elastically gets zero more rapidly than the pinning energy. This allows the lattice to become more distorted near Hc2 (T) by adjusting to the underlying pinning landscape. As a result the critical current increases. Subsequently, Larkin and Ovchinnikov[58] interpreted the peak effect based on the hypothesis that the elastic moduli of the vortex lattice suddenly soft while going from local to nonlocal elasticity. Larkin and Ovchinikov motivated by Brandt’s discovery,[63] that the lattice of vortices is much softer for short wavelengths of compressional and tilt distortions than it is for uniform compression or tilt. The characteristic length of elastic nonlocality occurs when the wavelength of the distortions becomes comparable with the Ginzburg Landau penetration length λ0 = λ/(1 − b)1/2, here b = B/Bc2 . When the length scale Rc defined by h[u(Rc) − u(0)]2i = ξ 2 satisfies the equation Rc  λ0, then the spatial dispersion of elastic moduli is unimportant and the critical current decreases monotonically in this regime. With further increasing of the magnetic field the regime ξ < Rc ≤ λ0 is realized. In this regime the c44 is dispersive leading to an exponentially increase of critical current with the magnetic field.[58, 63] This behavior stops when the correlation radius Rc becomes of the order of the vortex lattice parameter a. In this regime the critical current falls as Jc ∼ (1−b). In the framework of the methodology used in the present chapter, the Larkin-Ovchinikov proposition for the Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

90

D. Stamopoulos and M. Pissas 0.5

χ ', χ '' (arb. units)

Hdc=23 kOe

0.0

5.7 Oe

Tirr ~ Tc2

-0.5 3.4 Oe

-1.0

Ho=1.7 Oe

Ton

Tp

f=3 Hz 6

7

8

9

10

11

12

13

14

15

T (K)

Figure 7. Real (χ0 ) and imaginary (χ00 ) local fundamental susceptibility as a function of temperature for Hdc = 23 kOe. Shown are measurements for amplitude of the ac-magnetic field Ho = 1.7, 3.4 and 5.7 Oe. The arrows show which part of the curve was taken during cooling or heating. These measurements are obtained for Hdc||Hac||c-axis. peak effect phase boundary line is expressed via the equation

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

B(a, 0)T,dis = ξ 2 + hu2 iT .

(8)

Using the appropriate expressions for correlator[8] and hu2 iT (Eq. 4) the equation which determines the location of the peak effect becomes: (1−h)(h1/2 +t(Gi/hc2(t))1/2f (h))2 − 2πD(t)2(1 − hsv ) = 0, and has two real solutions. One between hdis and hm and a second above the melting line. The first one may be related with the points (T, H) where the peak’s maximum occurs. We include this solution in Fig.5. It is interesting that, this line is terminated at the melting transition, something which resembles our experimental data, where the peak-effect line is terminated at (Ti , Hi) ≈ (24 K, 12.5 kOe) (see Fig.5). This theoretically simulated point fits nicely to the experimentally obtained one (Ti, Hi) ≈ (24 K, 15 kOe) (see Fig.4). We must note that the parameters used to simulate the other boundary lines give an intersection point located below the experimentally observed, besides the fact that there is a qualitative agreement. Recently, the onset of the peak effect, H on has been associated with the proliferation of dislocations in the vortex lattice and therefore marks the transition of the Bragg glass phase to an amorphous one, most probably of first order.[2, 3, 4, 5, 6, 7, 60, 67, 70] In the Bragg glass phase, the vortex lattice is collectively pinned so it has a small critical current (JcB ) but very high barriers leading to negligible voltage bellow JcB . On the other hand, in the high-field phase, where dislocations are present, or in the liquid phase, it is easier to pin small parts leading to higher critical currents JcD , but the pinning is not collective, hence a much more linear response is expected for J > JcD . This behavior leads the E − J characteristics to cross at the melting of the Bragg glass and to an apparent increase of the critical current close the melting and thus to a peak effect in screening current measured at constant electric-field level. It is worth noticing that an order-disorder transition can

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Surveying the Vortex Matter Phase Diagram. . .

91

also occur close to Hc1 (T) because the change of elastic constants of vortices is drastic there (e.g. exponential reduction of the shear modulus) leading to a reentrance[7] of the amorphous phase near Hc1 (T)-line. Based on this we can explain the large value of the screening current near Hc1 (T)-line. However, we do not observe any sudden decreasing of the screening current there. Finally, we would like to discuss the hysteretic behavior observed in the region H ≤ Hp (T). Pippard’s and Larkin’s-Ovchinnikov’s models attributed the peak effect to changes of the elastic constants of the vortex lattice, as Hc2 (T) is approached. In this case, there is not a phase transition. The presence however, of history effects, is favorable for a disorderdriven phase transition in the vicinity of the onset point Hon. In addition, the hysteretic behavior occurs when H ≤ Hp (T) and the critical current of the ascending branch (cooling), is larger than that of the descending one (heating). As we discussed above, at fixed temperature, as field increases the effective disorder also increases leading to a disorder induced transition in the mixed state of the superconductor from a Bragg glass to a highly disordered phase. In the former, elasticity survives and the vortex lattice maintains of quasilong range translation order. In the disordered phase, topological defects as dislocations, become energetically favorable so that the long-range order is lost. The presence of topological disorder has as consequence the increasing of the critical current density. During an isothermal magnetization loop when the field increases beyond Ho dislocations appear. The topological disorder exhibits metastable behavior due to trapping of dislocations in local minima of the free energy. The density of topological defects does not vary reversibly with field and one should expect a path-dependent critical current in the particular regime. The observation of the peak effect, with negligible thermomagnetic history effects, for large amplitude of the ac-field, may be related with the unblocking of the vortices from their pinned metastable configuration. The ac-field triggers a transition into the stable state of low pinning which does not change on subsequent larger ac-field measurements. Furthermore, as the field (temperature) is adequately reduced in comparison with Ho (To ) the residual topological disorder is practically eliminated and thus the two branches of the measurements of Fig.6 and Fig. 7 below Hon (Ton ) coincide. Similar behavior with MgB 2 has been observed in 2H-NbSe 2 (Ref. [64]), Nb (Ref. [65]), YBa2 Cu3O7 (Ref. [66, 67, 68, 69, 70]) and HgBa2 CuO4 (Ref. [60]) single crystals where the peak effect separates two regimes with radically different behavior: one below the peak where thermomagnetic history effects are prominent and one above where these effects disappear completely and the vortex lattice is transformed to a completely amorphous state.

4.

Aluminium Substituted Single Crystals

This section of the present chapter surveys the influence of aluminium substitution on the vortex matter properties of MgB 2 single crystals.[50] We observed that: (a) similarly to pristine MgB2 , the peak effect is present in all the studied Mg 1−x AlxB2 single crystals, (b) in comparison to pristine MgB 2 , the anisotropy of Hc2 decreases for low aluminium c content, (c) the c-axis upper-critical field Hc2 (T ) exhibits a nonmonotonic dependence on the aluminium content, and (d) in some of the studied crystals we observed double-peak structures (or even multiple-peak ones) in the critical current which maybe an indication for inhomogeneous aluminium distribution (phase separation).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

92

D. Stamopoulos and M. Pissas

Figure 8. Photo of a representative aluminium substituted Mg 1−x AlxB2 single crystal studied in the present chapter. The particular single crystal has aluminium content x = 0.101 and dimensions 900 × 500 × 15 µm3 .

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

4.1.

Growth of Mg1−x AlxB2 Single Crystals

Aluminium substituted MgB 2 crystals were grown in Z¨urich using a high-temperature pressure method.[71] The amount of aluminium content was determined by energy dispersive x-ray at different areas of the crystals’ surface. The average aluminium content ( x) was found lower than in the precursor and depends on the precursor composition and the growth temperature.[71] Local ac-susceptibility and global magnetization were carried out on three Mg1−x Alx B2 single crystals with average aluminium content x = 0.013 ± 0.006 (600×400×15 µm3 ), 0.101±0.010 (900×500×15 µm3 ) and 0.141±0.004 (780×440×15 µm3 ). A representative Mg1−x Alx B2 single crystal with aluminium content x = 0.101 is shown in Fig.8.

4.2.

Experimental Data for Mg 1−x Alx B2 Single Crystals

Mg0.987Al0.013B2 single crystal: Let us start the presentation of our data for a single crystal having low aluminium content x = 0.013. Figure 9 shows the temperature variation of the real (χ0 ) and imaginary (χ00 ) parts of the local ac-susceptibility, measured in an ac-field having amplitude Ho = 17 Oe and several dc-magnetic fields. For low dc-fields, (see curve with Hdc = 10 kOe) χ0 reduces monotonically for T < Tc2, whereas the corresponding χ00 forms a peak, whose location depends on the amplitude of the ac-field and the temperature variation of the critical current density Jc (H, T ), (Hac ∼ 4πJc (H, Tpeak)d, here d is the thickness of the crystal). From the measurements of Fig. 9 we can conclude that the x = 0.013 crystal have lower critical current, in comparison with the pristine one (see section III and Refs.[55, 37]). The particular temperature variation of χ0 and χ00 is typical for a type-II superconductor with a critical current increasing as temperature decreases (monotonic behavior). For Hdc = 26 kOe, the χ0 clearly displays a non-monotonic temperature variation. Specifically, just below to Tc2 a negative peak appears. Obviously, this peak is related with the so-called peak effect in the critical current density Jc as is observed in the pristine MgB 2 single crystals (see section III and Refs.[55, 57]). It is interesting to

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

93

0.2

χ /Η ο and χ /Ho (arb. units)

x=0.013 Ho=17 Oe, f=3 Hz

26 KOe

0.0 0.1

21.5 kOe

0.0

0.2

/

//

-0.1

20 kOe 0.0 0.5

χ

Tc2(H)

//

-0.2

0.0

χ

/

Hdc=10 kOe

-0.5

5

10

15

20 25 T (K)

30

35

40

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 9. Temperature variation of the real (χ0 ) and imaginary (χ00 ) fundamental local acsusceptibility measured in the indicated magnetic dc fields of the Mg 1−x AlxB2 (x = 0.013) single crystal, for Hdc||Hac ||c-axis.

be noted that the dip of χ0 at the peak-effect temperature is only a small fraction of the full, diamagnetic signal. This behavior is different from the one observed in carbon doped single crystals as we will show in the next section. Figure 10 shows the dependance, of the local ac-susceptibility on the amplitude of the applied ac-field, for the same single crystal having x = 0.013 when a dc-field Hdc = 21.5 kOe is applied. We clearly see that for a low ac-field amplitude Ho = 1.7 Oe two distinct peaks evolve just below Tc (H). The arrows denote the temperature location of the lower and upper parts of the peak effect ( TLSP, TUSP ), respectively. The onset and the location of the dip are independent of Ho. As the ac-field becomes smaller the dip at the peak temperature becomes comparable with the diamagnetic screening χ0 at T = 0 K. The latter behavior implies that the critical current at the peak field increases as the temperature is lowered. Mg0.899Al0.101B2 single crystal: Next we show results for a single crystal of higher aluminium content. Figure 11 shows the temperature variation of χ0 and χ00 , measured in several dc-magnetic fields of the x = 0.101 crystal. As for the x = 0.013 one, the ac-susceptibility data, in the field range H > 10 kOe show a complicated behavior arising c from multiple peaks in the critical current that occur right below the Hc2 -line. In this crystal (see measurements for Hdc = 21 kOe), except for the two local minima [lower second peak (LSP) and upper second peak (USP)] on the χ0 (T ) curve, denoted as TLSP and TUSP , one can see a rather weak but distinct feature occurring between them. This complicated behavior is observed for H > 10 kOe, whereas for lower dc-fields is transformed to a broad shoulder.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

94

D. Stamopoulos and M. Pissas

//

Tc2(H)

x=0.013

0.0 17 Oe

TUSP

-0.5

χ

TLSP

/

/

//

χ and χ (arb. units)

χ

-1.0 5

Ho=1.7 Oe f=3 Hz 10

Hdc=21.5 kOe 15

20

25

T(K)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 10. Temperature variation of the local ac-susceptibility measured in the indicated ac magnetic fields and Hdc = 21.5 kOe of the Mg1−x AlxB2 (x = 0.013) single crystal for Hdc||Hac||c-axis. Mg0.859Al0.0.141B2 single crystal: Finally, Fig. 12 shows representative local acsusceptibility measurements for a single crystal with even higher aluminium content x = 0.141. This sample has lower Tc = 27.6 K in comparison with the other crystals. Basically, this crystal displays similar behavior with the other samples as far the ac-susceptibility measurements are concerned. For Hdc > 15 kOe the χ0 right below the diamagnetic onset displays non-monotonic behavior which can be accounted for by the peak effect as in the pristine, the x = 0.013 and the x = 0.101 substituted single crystals. Remarkably, the particular crystal shows only one dip in the χ0 implying that only one peak value of the critical current occurs. Furthermore, comparing the value of χ0 at the peak’s maximum and the extrapolated at T = 0, we conclude that the critical current of the particular crystal is significantly lower than the one of the crystals with x = 0, 0.013 and 0.101. 4.2.1. Vortex Matter Phase Diagram for Mg 1−x AlxB2 Single Crystals Figure 13 summarizes the experimental results in the form of vortex-matter phase diagrams, for the Mg1−x AlxB2 crystals with 0.013 [panel (a)], x = 0.101 [panel (b)] and x = 0.141 [panel (c)]. The open, solid and semi-solid circles correspond to the onset of the LSP (Hon), the LSP (HLSP ), the USP (HUSP ), and the second peak (HSP ) lines for crystals x = 0.013, 0.101 and 0.141, respectively. Similarly with pristine MgB 2 (see section III above, and Ref.[55]) and carbon substituted MgB 2−x Cx (see section V below, and Ref.[37]) all these lines for the Mg 1−x AlxB2 crystals with x = 0.013, 0.101 and 0.141 converge by c (T )-line at (T ∗ , H ∗) indicated with a solid circle in Figs. 13(a) and intersecting the Hc2 13(c). For the crystal with x = 0.101 it is difficult to define this specific point. In adc (T ) and H ab (T )-lines as dition, Fig. 13 illustrates the temperature variation of the Hc2 c2

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

95

0.2

x=0.101 0.1

0.2 0.1 0.0 -0.1

χ

//

χ

/

/

0.0

Tc2(21 kOe)

Ho=5.8 Oe -0.1 f=3 Hz

21 kOe

TUSP

TLSP

0.1 0.0

20 kOe

//

χ and χ (arb. units)

21.5 kOe

0.1

-0.1 17.5 kOe

0.0 -0.1

10 kOe

0.05

Hdc=5 kOe

0.00 -0.05

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

0

5

10

15 T (K)

20

25

30

Figure 11. Temperature variation of the real (χ0 ) and imaginary (χ00) fundamental local acsusceptibility measured in the indicated magnetic dc fields of the Mg 1−x AlxB2 (x = 0.101) single crystal, for Hdc||Hac ||c-axis. measured by means of local ac-susceptibility and bulk magnetization measurements. The c upper critical field Hc2 (T ) for x = 0.013 and 0.101 crystals follows a nearly conventional ab (T ) displays a pronounced positive curvature near T . temperature variation, while Hc2 C The positive curvature is related with the two-band superconductivity of MgB 2 and generally it is expected to be most pronounced in clean materials where electronic microscopic details affect the bulk properties such as the upper critical fields. In dirty materials impurity scattering smooths out these electronic details, producing linear temperature variation c (T ) and H ab (T ) can be of the upper-critical fields. The experimental points for both Hc2 c2 least squares fitted by using the empirical formula Hc2(T ) = Hc2 (0)(1 − (T /TC)n )ν for all samples. In the context of Ginsburg-Landau theory, for anisotropic type-II superconab,c ductors, both Hc2 are linear near Tc , e.g. Hc2 (T ) ∝ (Tc − T ). This particular temperaab/H c . ture variation produces a temperature independent anisotropy parameter, γ = Hc2 c2 In the two band superconductor the situation is radically different, where positive curvature terms (e.g. Hc2 ∝ (Tc − T )n , n ≥ 2) are present. These terms essentially induce the temperature variation of γ. In our case we decided to use the empirical relation Hc2(T ) = Hc2 (0)(1 − (T /Tc)n )ν , in order to reproduce the positive (negative) curvature

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

96

D. Stamopoulos and M. Pissas

x=0.141

2 0

/

20 kOe

-2 1

4 0

Tc2(H) 18 kOe

0

Ton(H)

//

χ and χ (arb. units)

Ho =17 Oe f=3 Hz

21 kOe

Tpeak(H)

-1

-4 2

10 kOe 0

2

χ

0

H=1 kOe -2

//

χ -2 5

10

/

15

20

25

T (K)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 12. Temperature variation of the real (χ0 ) and imaginary (χ00) fundamental local acsusceptibility measured in the indicated magnetic dc fields of the Mg 1−x AlxB2 (x = 0.141) single crystal, for Hdc||Hac ||c-axis.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

50

50

(a) x=0.013

Mg1-xAlxB2

(b) x=0.101

40

20

Hon H LSP *

30

20

Hc2

Hon

*

(T ,H )~ (21 K,18 kOe)

10

ab

c

ab

Hc2

HUSP

40

ab

30

Hc2 and Hc2 (kOe)

ab

c

Hc2 and Hc2 (kOe)

97

10

HLSP H USP

c

c

Hc2

Hc2 0

0 0

5

10

15

20

25

30

35

40

0

5

10

15

20

25

30

35

40

50

(c) x=0.141

30

c

Hc2 and Hc2 (kOe)

40

20

ab

ab

Hc2

Hon HSP *

10

*

(T , H )~ (13.5 K,15 kOe) c

Hc2

0 0

5

10

15

20

25

30

35

40

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

T(K)

Figure 13. The vortex matter phase diagrams of single crystals Mg 1−x AlxB2 with 0.013 (a), x = 0.101 (b) and x = 0.141 (c). The open, solid and semi-filled circles, correspond to the onset-line (Hon), the lower second peak line (HLSP ), the upper second peak line (HUSP ) and the second peak line (HSP ) for crystals with x = 0.013, 0.101 and 0.141, respectively. The dashed lines through the Hon(T ), HLSP (T ), HUSP (T ) and HSP(T ) data serve as guide ab,c (T ), estimated to the eye. The solid (open) squares correspond to the critical fields Hc2 from SQUID (Hall) measurements.

observed near Tc (T = 0), respectively. The resulted fitting parameters can be found in Ref.[50]. Figure 14 presents the anisotropy parameter γ(T) as this was calculated by using the ab c fitting equations that resulted from the fitting of the Hc2 (T ) and Hc2 (T ) experimental data. We stress that the calculated γ(T) originates from experimental data only inside the intervals [26 K, Tc = 37 K], [18 K, Tc = 31.4 K] and [8 K, Tc = 27.6 K] for the x = 0.013, 0.101 and 0.141 substituted single crystals, respectively. For lower temperatures, the estimation of ab γ(T) is based on the theoretical values of Hc2 (T ). Interestingly, γ(T) decreases with x but maintains the same temperature dependance. Similarly with pristine MgB 2 , for x = 0.013,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

98

D. Stamopoulos and M. Pissas

5

c

γ= Hc2 /Hc2

Tc=37.0 K

x=0.013

4

x=0.101

Tc=31.4 K

ab

3 2

x=0.141 1

Tc=27.6 K 0 0

10

20

30

40

T(K)

Figure 14. Estimated anisotropy of Mg 1−x AlxB2 single crystals with 0.013, x = 0.101, and x = 0.141. We observed that as the aluminium content increases the anisotropy decreases. 0.101 and 0.141 samples γ is a decreasing function of temperature. Comparing our results to those of Kim and co-workers[72] we find that our crystals with x = 0.101 and 0.141 have approximately the same Tc with the crystals x = 0.12 and 0.21, respectively of Ref. [72]. In agreement with those results our high aluminium content crystals show a decreasing of c (0). Hc2

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

4.2.2. Two-Band Superconductivity and Possible Implications on the Vortex Matter Phase Diagram In a two-band anisotropic superconductor several parameters influence the temperature dependance of the superconducting properties, making a difficult task the isolation of those being relevant with the Mg 1−x AlxB2 compound. In the clean limit [76, 75, 73, 74] the Fermi surface topology, the Fermi velocities, the matrix of the electron phonon constants λmn , the Coulomb pseudopotentials µmn (m, n = (σ, π)) and the partial density of states ab,c Nσ and Nπ determine the upper critical fields Hc2 , the anisotropy parameters (γξ , γλ) and Tc. On the other hand, it has been demonstrated[77, 78] that in the dirty limit, the temab,c and anisotropy parameters are controlled both from interband perature variation of Hc2 and intraband scattering rates, provided that λmn , Nσ and Nπ do not change upon alloying. The role of the intraband impurity scattering on the temperature variation of the anisotropy parameter γ has also been emphasized recently by Mansor and Carbotte.[74] According to their theoretical calculations, for the clean π and σ bands the anisotropy parameter is a decreasing function of temperature, changing from 5 at T = 0 to less than 3 at Tc. At intermediate values of the intraband scattering rate, a nearly temperature independent curve has been obtained and in the dirty π band case the anisotropy has been theoretically predicted to increase with temperature. The experimental results of the aluminium substituted MgB 2 could be explained by a simple clean-band model.[79, 46] The validity of this limit in the Mg 1−x Alx B2 crystals is supported by theoretical caclulations[80] and de Haas van Alphen measurements on

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Surveying the Vortex Matter Phase Diagram. . .

99

crystals from the same source.[81] In this scenario the aluminium substitution leaves the Mg1−x Alx B2 in the clean limit although the mean free path reduces by a factor of 2-3, depending on the examined band.[81] Basically, aluminium substitution results in two drastic changes in the electronic structure of MgB 2 . The first is band filling (shifting of the Fermi level which decreases the hole density of states and shrinks the cylindrical Fermi surface) and the second is increasing of the carrier scattering rate (which is related to the increase of residual resistivity). In the case of Mg 1−x AlxB2 (Ref.[71]) the resistivity at Tc increases from ρab ∼ 0.5 µΩcm for x = 0 crystal, by a factor of 5 for the crystal x = 0.141. Therefore, this reduction is expected to lead to an equal size reduction of the mean free path `. ˚ for x = 0, for crystals of the same source, ` is expected to be 200 A ˚ for Since ` = 600 A x = 0.141. Consequently, most probably Mg 1−x AlxB2 crystals belong to the border of the dirty-clean limit especially as far the π band is concerned. ab For low aluminium content we observed a significant reduction of the Hc2 and an alc most constant behavior of Hc2 . In the clean limit the critical fields of MgB 2 at low temperature are determined mainly by the σ bands.[79, 46] In this limit the upper critical field c (0) ∝ (∆ (0)/υ ab)2 , and the coherence length anisotropy are given from the relations Hc2 σ σ ab,c ab 2 ab c ab c Hc2 (0) ∝ (∆σ (0)/υσ υσ ) and γξ = υσ /υσ . Here υσ is defined as the root-meansquared wavevector dependent Fermi velocity in the ab-plane (c-axis) averaged over the σ sheets of the Fermi surface, and ∆σ (0) is the σ superconducting gap. In order to interpret the reduction of the anisotropy parameter, we can consider that υσab reduces with aluminium, c while υσc remains approximately constant. On the other hand, the constancy of the Hc2 (0) ab requires both ∆σ and υσ to decrease with aluminium. The reduction of ∆σ with aluminium content is reasonable since it is related to the respective reduction of Tc . This simple model c does not agree with the slight increasing of Hc2 , in comparison with the pristine MgB 2 for the crystal with the lower aluminium concentration ( x = 0.013). This behavior could be explained in the context of this simple model supposing that both ∆σ and υσab have lower values, in comparison to the pristine MgB 2 , but their ratio gives a value leading to a slightly c higher Hc2 (0). Next we discuss the possible influence of the aluminium substitution on the general properties of vortex matter and especially on the peak effect.[58, 63, 82] The ”disparity” between σ and π bands, suppresses the impurity interband scattering that causes pair breaking. Therefore, in order a small region of the crystal with higher x in respect to the average value, to act as a pinning center special requirements are needed (see Ref. [29, 80] and references therein). As we see below aluminium-induced defects do not act as strong pinning centers. For a defect to act as a pinning center it is necessary its size to be of the order of ˚ for x = 0.013, 0.101 ξGL . The crystals used in this work have ξGL = 26, 39 and 59 A and 0.141, respectively. At present it is puzzling why extended Al rich defects (see below) do not act as pinning centers. In a multi-band superconductor nonmagnetic impurities may act as Cooper pair breakers due to the interband scattering which mixes the Cooper pairs in the two different bands.[27] Nevertheless, this effect is extremely small in the case of MgB2 (due to the ”disparity” of the σ and π bands preserved even in heavily substituted MgB2 samples). The onset of the peak effect line practically remains unshifted and the critical current at the peak field slightly reduces, with aluminium content. If the aluminium atoms cause significant increasing of the interband scattering between σ and π bands, because of the simultaneous increasing of the size and the number of the pinning centers, then

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

100

D. Stamopoulos and M. Pissas

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

it is reasonable a noticeable downwards shifting of the onset peak-effect line, Hon from c to be expected. This shifting was not clearly the respective upper-critical field one, Hc2 observed, implying that the aluminium atoms does not induce appreciable interband scattering, which in turn would produce pinning centers. Consequently, the overall appearance of the peak effect in aluminium substituted crystals leads us to conclude that the extended defects produced by aluminium substitution do not act as pinning centers. The peak effect is most probably related to some other kind of defects, such as vacancies, stacking faults and dislocations. Finally, we discuss here the multiple nature of the peak effect observed in some single crystals. Two peaks in the critical current have also been observed in HgBa 2 CuO4+δ , [60] YBa2 Cu3 O7,[69, 67, 85, 84, 86] and Tl 2Ba2 CaCu2 O8+x [83] superconductors. If randomly distributed pinning centers exist then the complex appearance of the peak effect is unexpected. The observed behavior could be explained by assuming the existence of pinning centers with different pinning strengths, homogenously distributed or spatially separated in the bulk of the crystal. This interpretation has been used in the case of the nearly untwined YBa 2 Cu3 O7 single crystals[84] where some remaining twin planes are always present, creating planar disorder, in addition to the point-like oxygen vacancies. Nevertheless, the situation where the crystal contains two types of defects, uniformly distributed in the entire crystal volume, cannot be excluded, e.g. clustering of Al atoms, Mg, and/or Al vacancies, dislocation networks and extended defects. It has been reported[71] that in crystals having been grown with the same method as the ones studied in this work, a second phase of composition MgAlB 4 segregates as a precipitation along the c-axis of the crystal. In addition, high resolution transmission electron Z-contrast images revealed precipitations of a second phase in the form of Al rich domains with a broad distribution of sizes and shapes.[71] Most probably, all these experimental facts infer that the double peak effect arises from these inhomogeneities.

5.

Carbon Substituted Single Crystals

Several experimental studies exist which concern the influence of carbon substitution on the physical properties and the vortex matter phase diagram of MgB 2 , based on polycrystalline samples. [87, 31, 32, 33, 34, 35, 88] The aim of the present section is to systematically review the influence of carbon substitution on the vortex matter properties using carbon substituted MgB 2−x Cx single crystals.[37] In addition, a detailed study of the transition occurring at the onset of the peak effect is presented. The new findings of our study are the following: (a) similar to pristine MgB 2 single crystals, for the MgB 2−x Cx ones, the onset of the peak effect also exhibits the characteristics of a first order transition, (b) the anisotropy of Hc2 decreases with the carbon content, and (c) in comparison to pristine MgB 2 , both c Hc2 (T ) and Hab c2 (T ) increase significantly with carbon substitution.

5.1.

Growth of MgB2−x Cx Single Crystals

Single crystals were grown by a high-pressure technique [89] previously developed for the growth of pristine MgB 2 phase [52] using precursors with a nominal composition of MgB2−x Cx , with x = 0.0−0.20. The systematic changes of the lattice parameters observed Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

101

Figure 15. Photo of a representative carbon substituted MgB 2−x Cx single crystal studied in the present chapter. The particular single crystal has carbon content x = 0.1 and dimensions 350 × 350 × 100 µm3 .

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

in crystals coming from the same batch,[89, 90] prove that C-atoms successfully substitute B-atoms. The C content was analyzed by Auger spectroscopy.[89] The high quality of the studied crystals is revealed by the sharpness of the magnetic transition in low fields (∆Tc = 0.15 K and 0.4 K for x = 0.04 and 0.1, respectively) and also by the sharp resistivity transitions and the crystallographic data.[89] The dimensions of the crystals are 750 × 350 × 40 µm3 and 350 × 350 × 100 µm3 (the shorter length is along the c-axis) for x = 0.04 and 0.1, respectively. The critical temperature (Tc ) of the crystals obtained at a low dc-magnetic field is 35.6 K and 29 K for x = 0.04 and 0.1, respectively. A representative MgB2−x Cx single crystal with carbon content x = 0.1 is shown in Fig.15.

5.2.

Experimental Data for MgB 2−x Cx Single Crystals

Figure 16 shows the temperature variation of the global magnetic moment of the MgB1.96C0.04 crystal for several magnetic fields (Hdc k c) as it was measured by the SQUID magnetometer. We note that the particular single crystal is large enough so that we were able to detect the peak effect in the global SQUID isothermal magnetization measurements for relatively low magnetic fields. The magnetization curves are first measured while increasing the temperature after zero field cooling (ZFC) from above Tc . Subsequently, the sample is field cooled (FC) under the presence of the applied dc field. In a nearly parallel fashion all curves intersect the T -axis at a characteristic point which denotes the field dependent bulk upper-critical temperatures Tc2(H). In low magnetic fields 0 kOe 33 kOe clearly show a negative peak whose height and width increase as the magnetic field increases. This negative peak is motivated by the well known peak effect in the screening current, which has been also observed in pristine MgB 2 single crystals (see section III, and Ref.[55]) and aluminium substituted ones (see section IV, and Ref.[50]). Similar data were obtained using a crystal with nominal stoichiometry MgB1.9 C0.1 (data not shown). From this negative peak in the M (T ) curves we define the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

102

D. Stamopoulos and M. Pissas

2

Ton(H)

Tc2(H)

Tep(H)

0

45

40 35

-4

31

20 Hdc=10 kOe 28.6 T (K)

-5

m (10 emu)

-2

-6

Tp(H)

-10

-4

-8

m (10 emu)

0

10 20 30 40

0 -1 -2

H dc=5 Oe

-3

Tc

-12 5

10

15

20

25

30

35

T(K)

Figure 16. Temperature variation of the global magnetic moment of MgB 1.96C0.04 single crystal for various dc magnetic fields. The inset shows a measurement under H dc = 5 Oe for the estimation of the critical temperature. In all cases Hdc k c-axis.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

temperatures where the peak effect starts as Ton(H), takes its minimum value as Tp(H) and finally ends as Tep(H). It is interesting to note that in the interval Tp(H) < T < Tc2 (H), the magnetization is nearly reversible, while for T < Tp (H) the magnetic moment presents hysteretic behavior which increases as the magnetic field increases (for instance, see the curve obtained for H dc = 45 kOe). Due to the small size of our crystal the SQUID magnetometer cannot detect the peak effect for Hdc < 33 kOe. We can achieve higher accuracy using local ac-susceptibility measurements where the filling factor is 100%. We must emphasize here that our local ac-susceptibility measurements enabled us to detect the peak effect at much lower fields compared to the SQUID measurements. Figure 17 shows the real χ0 and imaginary χ00 parts of the local fundamental ac-susceptibility, as a function of temperature, measured under several dc-magnetic fields 10 kOe ≤ Hdc ≤ 42.5 kOe for an ac-field with amplitude Ho = 8.8 Oe. The measurements have been obtained in the ZFC and FC modes. When small or moderate dc-fields are applied (H dc < 40 kOe) the ZFC and FC curves practically coincide except for a narrow region near the onset of the peak effect. At higher magnetic fields (Hdc > 40 kOe) pronounced hysteresis is observed in the whole regime below the peak effect (for more details see Fig.20 below). Except for the hysteresis observed near the onset points Ton another interesting feature is observed at the points Tep where the peak effect ends. Although at low magnetic fields both χ0 and χ00 show a smooth evolution near their end points, at intermediate fields they exhibit a sharp step ( ∆T < 100 mK) which is progressively transformed to the peak effect as the applied field is further increased. This behavior is clearly depicted in Figs. 18 (a)-(b) where we plot a detail of χ0 and χ00 near their diamagnetic onset. The sharp step finally disappears when the applied dc-field is decreased below a threshold value (≈ 10 kOe).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

0.04

MgB1.96C0.04

0.00

Ho=8.8 Oe f=3 Hz

42.5

-0.04 0.03

χ ', χ '' (arb. units)

103

0.00

35

0.03 -0.03 0.00 0.03 -0.03 0.00 0.02 -0.03 0.00

31

χ

-0.02

22

//

χ

/

Hdc=10 kOe

-0.04 5

10

15

20

25

30

35

T (K)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 17. Real (χ0 ) and imaginary (χ00 ) local fundamental ac-susceptibility as a function of temperature for Hac = 8.8 Oe and Hdc = 10 − 42.5 kOe. In all cases H k c-axis. For Hdc > 20 kOe the peak effect is always observed. These measurements refer to the case where Hdc ||Hac||c-axis.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

104

D. Stamopoulos and M. Pissas

(a)

χ ', χ '' (arb. units)

0.010

χ '' 0.005

14 kOe

Hdc=17 kOe 0.000

-0.005 20 0.003

MgB1.96C0.04 Ho=123 Oe f=3 Hz

χ' 21

22

23

24

25

26

27

28

χ ', χ '' (arb. units)

(b) 0.002

5 kOe 0.001

χ ''

4 kOe

Hdc=3 kOe

0.000 -0.001 -0.002 -0.003 31

Ho=12. 4 Oe f=3 Hz

χ' 32

33

34

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

T (K)

Figure 18. (a) Detailed local ac-susceptibility for magnetic fields where the peak effect is transformed to a very narrow step. (b) Local ac-susceptibility for dc magnetic fields where the peak effect is completely absent. These measurements refer to the case where Hdc||Hac ||c-axis. 5.2.1. Peak Effect and Thermomagnetic History Effects for the MgB 2−x Cx Single Crystals Our results show that the peak effect is also present in carbon doped MgB 2 single crystals. It is interesting to carry out a detailed study concerning the peak effect in order to understand which of the possible theoretical models is the true underlying mechanism for the observed effect in carbon doped MgB 2 . Since at present, theoretical models for the mixed state of a two-band superconductor are not available, our experimental results may stimulate further theoretical studies. The first interesting issue is the hysteretic behavior observed at the peak effect. To investigate its nature we performed measurements with different experimental protocols. In Fig. 19 we present measurements in a constant magnetic field Hdc = 40 kOe (the inset illustrates the paths traced during the measurements). After cooling the sample in zero field to 4.2 K the first run starts (at point 0) by raising the field to Hdc = 40 kOe (path 0 → 1). As we see the resulted vortex state has almost zero screening current. Raising

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

χ ', χ '' (arb. units)

Surveying the Vortex Matter Phase Diagram. . .

(a)

0.02

MgB1.96C0.04 Hdc=40 kOe

Tep

0.00

4 2

1

-0.02

H

3 5

-0.04

c

Hc2 5 3 1

Ho=5.7 Oe f=3 Hz

Tp

4 2

0

T

-0.06

χ ', χ '' (arb. units)

105

0.02 (b) 2

0.00 1

H

0 c

3

-0.02

Hc2 1 3

-0.04

2

T -0.06 0

5

10

15

20

25

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

T (K) Figure 19. (a) History dependance of the real and imaginary local ac-susceptibility for a MgB1.96 C0.04 single crystal. The measurements were performed under an ac field of amplitude Ho = 5.7 Oe that is superimposed on a dc magnetic field Hdc = 40 kOe. Firstly, the sample was zero field cooled at 4.2 K and subsequently the dc field is applied. The measurements were successively made following the paths indicated by the arrows in the inset. (b) In this protocol of measurement the sample was field cooled under a magnetic c (4.2 K) down to 4.2 K and subsequently the field was reduced to 40 kOe. field H > Hc2 The data were collected according to the paths indicated by the arrows in the inset. These measurements refer to the case where Hdc||Hac ||c-axis. the temperature (path 1 → 2) we observe the peak effect which indicates a vortex state of high screening efficiency. Interestingly, above the end point Tep of the peak effect the screening current drops again to zero. When the upper-critical temperature Tc2(40kOe) has been exceeded we start lowering the temperature following the reverse path ( 2 → 3). We observe that for T < Tp the obtained curve is well below the virgin curve ( 1 → 2). This indicates that the vortex state produced by FC possesses a higher screening current compared to the ZFC one. When we again increase the temperature (path 3 → 4) the curve lies between the two former lines in the temperature regime T < Tp. In the final decreasing temperature scan (path 4 → 5) the resulted data retraced the path obtained for path 2 → 3. The main result from these measurements is that all the curves coincide above the peak effect point TP indicating that history effects are not present in the regime T > Tp .

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

106

D. Stamopoulos and M. Pissas χ ''

0.5

χ ', χ '' (arb. unts)

0.0 -0.5

10.54 Oe

χ'

-1.0

0.0

Ho=17.6 Oe f=3 Hz

MgB1.96C0.04 Hdc=40 kOe

-0.1 0.2 0.1 0.0 -0.1 -0.2

Tp Ton 5

6

7

123 Oe

Tkink 8

9

Tep

10 11 12 13 14 15

T(K)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 20. Temperature dependance of the hysteretic local ac-susceptibility for Hdc = 40 kOe and for various amplitudes of the ac-field. These measurements refer to the case where Hdc||Hac ||c-axis. Trying to explain these experimental data, we assume that three vortex states occupy the studied regime of the phase diagram. First, a state that can be obtained only when we cool the superconductor under zero magnetic field (virgin curve). This state has the lowest screening capability indicating that it is probably related to the so-called Bragg glass.[82] The second state is that obtained when cooling the sample from above Tc in the presence of a magnetic field (paths 2 → 3 and 4 → 5). This state has a higher screening efficiency indicating that a large part of the disordered glass state survives even when the Bragg glass regime is entered. Finally, the third state exists above the end point Tep of the peak effect where the screening capability of vortex matter is zero although we are still well below the upper-critical field as that determined by global dc magnetic moment measurements. In a different experimental protocol of measurements which is schematically presented in the c (4.2 K) and we subsequently inset of Fig. 19(b), we first applied a magnetic field H > Hc2 decreased the temperature to T = 4.2 K. We then lowered the magnetic field to H = 40 kOe (path 0 → 1) and we started measuring while increasing the temperature (path 1 → 2). We may easily see that the results presented in the lower panel of Fig.19 are completely compatible to the ones described above. Recently, Stamopoulos and Pissas, and Valenzuela and Bekeris performed detailed acsusceptibility measurements in HgBa 2 CuO4+δ and YBa2 Cu3O7 single crystals, and showed that the hysteresis occurring in the ZFC and FC ac-susceptibility curves depends strongly on the applied driving force.[60, 67, 70] A high driving force exerted on vortices reveals a different behavior than that observed when a small perturbation is applied. To investigate this effect in carbon substituted MgB 2 we observed the influence of the amplitude of the applied ac-field on the hysteretic response. In Fig. 20 we show representative results. We see that the detected hysteresis progressively reduces as we apply higher ac-fields. For high enough ac-fields the hysteresis is confined only in the regime between the onset of the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

107

χ ' (arb. units)

0.00

MgB1.96C0.04 Hdc=40 kOe

B

-0.02

Ton

C

A

/

-0.04

Tkink -0.06

C

Ho=123 Oe f=3 Hz

D

-0.08

7.5

7.8

8.1

8.4

8.7

9.0

9.3

T (K)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 21. Real part of the local ac-susceptibility at the region of the peak effect onset for MgB1.96C0.04 sample. The data were collected by cooling and subsequent heating, initially, following the path D →A→D. Then we lowered the target temperature so that the path D→B→D was traced. All measurements were collected under a dc field H = 40 kOe. Open circles refer to the time dependance of the χ0 signal for 0 sec< t < 2000 sec as it relaxes from point C to C’. These measurements refer to the case where Hdc||Hac||c-axis. peak and a new characteristic point Tkink at which both in-phase and out-of-phase signals present a kink.[91, 92, 93] As may be easily seen from these data a high enough ac-field suppresses the FC disordered glass state, which is supercooled from the high temperature regime. Eventually for high enough ac-drives, the vortex glass is ”annealed” into the Bragg glass state which is expected to be the equilibrium state in the regime T < Ton.[60, 67, 70] Relaxation measurements of the ac-susceptibility performed in the regime of the peak effect support this explanation. Relevant data are presented in Fig.21. It should be noted that the ZFC ac-susceptibility curves do not show significant relaxation since point C / in Fig. 21 does not drift with time. On the other hand, the FC branch exhibits strong relaxation since point C drifts to point C / in less than 30 min (open circles). These results indicate that the zero field cooled vortex phase is probably an equilibrium state, while, due to its strong time dependence, the field cooled one is a metastable state. Furthermore, if the observed hysteresis is directly related to a true phase transition, one would expect that hysteretic minor loops should also be present, due to the finite latent heat and the different relaxation rates of the two vicinal vortex phases (namely the Bragg glass and vortex glass). [60, 67, 94, 95, 96] To this end, by starting from a temperature above the peak point we performed minor loops by progressively lowering the minimum value of the applied temperature. We clearly see that an hysteretic minor loop is present having exactly the same shape as the outer complete loop (sequence of points: D→A→D). More specifically, after reversing the temperature sweep (where point A is reached) the increasing branch of the minor loop follows a distinct path without retracing the curve of the decreasing branch. This behavior is related to a first-order transition.[60, 67, 94, 95, 96] We interpret the observed behavior by assuming that at the minor loop (sequence of points: D→A →D) a partial transition is accomplished where a small fraction of the vortex glass is transformed to the Bragg glass.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

108

D. Stamopoulos and M. Pissas

c Table 1. MgB2−x Cx single crystals: Least square estimated parameters for Hc2 (T ) n ν using the empirical formula Hc2(T ) = Hc2 (0)(1 − (T /Tc) ) . Numbers in parentheses are statistical errors referring to the last significant digit. x 0.04 0.10 Tc 35.6(0.2) 29.0(0.2) c Hc2 64(2) 78.5(2) νc 1.30(1) 1.35(2) 2.0(0) 2.0(0) nc

Eventually, the whole vortex glass undergoes complete transformation into the Bragg glass when the temperature almost reaches the onset point Ton (sequence of points: D→B→D). These results clearly prove the coexistence of two vicinal vortex phases (namely the vortex glass and the Bragg glass) in the finite temperature interval Ton < T < Tkink (or Ton < T < Tp) around the transition regime . The same behavior has been also detected at the order-disorder transition of vortex matter in HgBa 2 CuO4+δ ,[60] YBa2 Cu3O7 ,[69, 67] and Bi2 Sr2 CaCu2 O8+δ [97] single crystals.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

5.2.2. Vortex Matter Phase Diagram for MgB 2−x Cx Single Crystals Figures 22 (a)-(c) show the phase diagram of vortex matter as it is constructed by means of local ac-susceptibility and global dc-magnetic measurements for MgB 2−x Cx , for x = 0, 0.04 and 0.10. We note that the vortex matter phase diagram of pristine MgB 2 is reproduced for the sake of direct comparison. Notice that in all three cases the same scale is used in the (H,T) parameters. The hatched regimes concern the region of the phase diagram where the peak effect occurs. The lines Hon(T ), Hp(T ) and Hep(T ) correspond to the onset, the peak-point and the end-point of the peak effect, respectively. We see that these lines intersect the Hc2 (T ) line at a characteristic point (T ∗ , H ∗) where the peak effect terminates. The characteristic intersection temperature T ∗ ∼ 26 K does not depend on carbon content, while the characteristic intersection field H ∗ depends on carbon content in a non-monotonic way. In the presented phase diagrams we also include the points where the diamagnetic moment evolves during cooling in the global dc-magnetization measurements, c (T ) and H ab(T ), both for Hdc||c-axis and Hdc⊥c-axis. These points correspond to Hc2 c2 c respectively. We have least squares fitted the experimental points for Hc2 (T ) by using the empirical formula Hc2(T ) = Hc2(0)(1 − (T /Tc)n )ν for all samples. The fitted parameters are summarized in Table 1. ab c Also, from these experimental data the anisotropy parameter γ = Hc2 /Hc2 was deduced. Figure 23 shows the temperature variation of γ for the three crystals studied. In the regime studied in this chapter the anisotropy curves of carbon doped crystals are well below the corresponding curve of pristine MgB 2 and does not depend on the carbon content. This finding is in contrast to the aluminium substituted single crystals where we observed that the anisotropy progressively decreases as the aluminium content increases. Finally, referring to the peak effect, we observe that it extends to a progressively higher region of the phase diagram as carbon doping increases (hatched region in Figs. 22 (a)c (T ) line (c)). In the pristine crystal the peak effect appears in a narrow regime near the Hc2

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . . 80

(a) MgB2

70 60 50

H(kOe)

109

ab

Hc2 (T)

40

c

Hep(T)≈ Hc2(T)

30

*

*

(T , H )~ (26.5 K,12.5 kOe)

20

Hp(T)

10

Hon(T)

0 0

5

10

15

20

25

30

35

40

80

(b)

Hep(T)

70

MgB1.96C0.04

H (kOe)

60 50

ab

Hc2 (T)

c

Hc2(T)

40

Hp(T)

30

Hon(T) (T3,H3)

20 10 *

0

5

10

80 70

(26 K, 17 kOe)

15

20

25

Hp

40

35

40

(c)

c

MgB1.9C0.1

Hc2(T)

50

30

Hep(T)

60

H(kOe)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

*

(T ,H )~

0

ab

Hc2 (T) Hon(T)

30 20 10

*

*

(T ,H )~

(25 K, 15 kOe)

0 0

5

10

15

20

25

30

35

40

T(K)

Figure 22. The vortex matter phase diagram of MgB 2 (a), MgB1.96C0.04 (b) and MgB1.9 C0.1 (c). The semi-filled, solid and open circles, open and solid squares correspond to the onset line of the peak effect Hon , the peak effect line Hp , the end-point line of the peak effect c (T ) and H ab(T ) lines. Hep , Hc2 c2 c (T )). This regime extends as carbon content in(the Hep(T ) practically coincides with Hc2 c creases and the Hep(T ) is located well below the Hc2 (T ) line. Although the critical current below the Hon(T ) line does not increase significantly, in comparison to the pristine com-

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

110

D. Stamopoulos and M. Pissas 8 7

MgB2-xCx

c

5

ab

γ =Hc2 /Hc2

6

4

x=0

3 2

x=0.04 x=0.1

1 0 20

22

24

26

28

30

32

34

36

38

40

T (K)

Figure 23. Estimated anisotropy of MgB 2−x Cx single crystals with 0, x = 0.04, and x = 0.10. We observe that at low carbon content studied in this chapter, the anisotropy does not exhibit noticeable dependence. c pound, the simultaneous increase of Hc2 (T ) and the enhancement of the peak-effect region may improve the usefulness of carbon doped MgB 2 for current-carrying applications .

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

6.

Conclusion

We have surveyed the vortex matter phase diagram for pristine and atomic substituted MgB2 single crystals. Especially, Al for Mg and C for B substitutions were reviewed for three aluminium doped Mg 1−x Alx B2 (x = 0.013, 0.101 and 0.141) and two carbon doped MgB2−x Cx (x = 0.04, 0.1) single crystals. Regarding Al substitution, the Mg 1−x AlxB2 single crystals exhibit decreasing anisotropy as x increases. Also, similarly to pristine MgB 2 , all Al-substituted crystals display the peak effect, which for the lower Al content splits into multiple distinct peaks. In c comparison to pristine MgB 2 , for the Mg1−x AlxB2 single crystals the Hc2 (0) increases slightly only for the x = 0.013 crystal, while it decreases for the crystals with x = 0.101 and x = 0.141. The influence of the Al content on the electronic structure of MgB 2 was also discussed regarding (i) the band filling and (ii) the increasing of the carrier scattering rate. Regarding C substitution, the studied MgB 2−x Cx crystals exhibit lower anisotropy in comparison to pristine MgB 2 . Also, similarly to pristine MgB 2 , the MgB2−x Cx single crystals display the peak effect in the local Hall and the bulk magnetization SQUID meac surements. In comparison to pristine MgB 2 , for the MgB2−x Cx single crystals the Hc2 (0) increases, a fact that implies a decrease of the mean-free path upon C substitution. Concerning the peak effect, it has been studied in great detail for all the cases of pristine MgB2 , Al-substituted Mg 1−x Alx B2 , and C-substituted MgB 2−x Cx single crystals. Regarding the order-disorder transition ascribed to the onset point of the peak effect and the accompanying thermomagnetic history effects, we report several similarities with the highTc and low-Tc superconductors. This fact implies that the peak effect can be effectively explained with the same mechanism in all superconductors.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

111

Finally, the experimentally surveyed vortex matter phase diagram was compared with current theoretical propositions (mostly for the case of pristine MgB 2 ). It was realized that the experimentally constructed vortex matter phase diagram cannot be reproduced by theory in the case where the thermal fluctuations are ignored. Nevertheless, their influence is minor (major) in comparison with high-Tc (low-Tc) superconductors.

Acknowledgments We would like to thank S. Tajima, S. Lee, N. Zhigadlo, and J. Karpinski for providing the high-quality single crystals studied in the present chapter.

References [1] G. Blatter et al., Rev. Mod. Phys. 66, 1125 (1994); E. H. Brandt, Rep. Prog. Phys. 58, 1465 (1995);T. Nattermann and S. Scheidl, Adv. Phys. 49, 607 (2000);T. Giamarchi and S. Bhattacharya cond-mat/0111052 (2001); G. I. Menon Phys. Rev. B 65,104527 (2002). [2] T. Giamarchi, and P. Le Doussal, Phys. Rev. B 55, 6577 (1997); [3] D. Ertas, and D. R. Nelson, Physica C 272, 79 (1996). [4] M. J. P. Gingras, and D. A. Huse, Phys. Rev. B 53, 15193 (1996).

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[5] A. E. Koshelev, and V. M. Vinokur, Phys. Rev. B 57, 8026 (1998). [6] V. Vinokur, B. Khaykovich, E. Zeldov, M. Konczykowski, R. A. Doyle, and P. H. Kes, Physica C 295, 209 (1998). [7] J. Kierfield, Physica C 300, 171-183 (1998). [8] G. P. Mikitik, and E. H. Brandt, Phys. Rev. B 64, 184514 (2001). [9] J. Nagamatsu et al., Nature(London) 410, 63 (2001). [10] C. Buzea and T. Yamashita, Supercond. Sci. Technol. 14, R115 (2001). [11] A.V. Sologubenko, J. Jun, S. M. Kazakov, J. Karpinski and H.R. Ott Phys. Rev. B 65, 180505R (2002). [12] Yu Eltsev, S. Lee, K. Nakao, N. Chikumoto, S. Tajima, N. Koshizuka and M. Murakami, Phys. Rev. B 65, 140501(R) (2002). [13] A. K. Pradhan, Z. X. Shi, M. Tokunaga, T. Tamegai, Y. Takano, K. Togano, H. Kito and H. Ihara, Phys. Rev. B 64, 212509 (2001). [14] F. Manzano, A. Carrington, N. E. Hussey, S. Lee, A. Yamamoto, and S. Tajima, Phys. Rev. Lett. 88, 047002 (2002). Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

112

D. Stamopoulos and M. Pissas

[15] M. Angst, R. Puzniak, A. Wisniewski, J. Jun, S. M. Kazakov, J. Karpinski, J. Roos, and H. Keller, Phys. Rev. Lett. 88, 167004 (2002). [16] J. Karpinski, M. Angst, J. Jun, S. M. Kazakov, R. Puzniak, A. Wisniewski, J. Roos, H. Keller, A. Perucchi, L. Degiorgi, M. R. Eskildsen, P. Bordet, L. Vinnikov and A. Mironov, Supercond. Sci. Technol. 16, 221 (2003). [17] S. Lee, T. Masui, H. Mori, Y. Eltsev, A. Yamamoto and S. Tajima, S.Lee, Supercond. Sci. Technol. 16, 213 (2003). [18] U. Welp, A. Rydh, G. Karapetrov, W. K. Kwok, G. W. Crabtree, Ch. Marcenat, L. Paulius, T. Klein, J. Marcus, K. H. P. Kim, C. U. Jung, H.-S. Lee, B. Kang, and S.-I. Lee, Phys. Rev. B 67, 012505 (2003); U. Welp, A. Rydh, G. Karapetrov, W.K. Kwok, G.W. Crabtree, C. Marcenat, L.M. Paulius, L. Lyard, T. Klein, J. Marcus, S. Blanchard, P. Samuely, P. Szabo, A.G.M. Jansen, K.H.P. Kim, C.U. Jung, H.-S. Lee, B. Kang, S.-I. Lee,Physica C 385,154 (2003) [19] O. F. de Lima et al., Phys. Rev. Lett. 86,5974 (2001); [20] F. Simon et al., Phys. Rev. Lett. 87, 047002 (2001). [21] S. L. Bud’ko, et al., Phys. Rev. B 64, 180506 (2001); [22] G. Papavassiliou, et al., Phys. Rev. B 65, 012510 (2002); M. Pissas, et al., Phys. Rev. B 65, 184514 (2002).

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[23] V. Likodimos and M. Pissas, Phys. Rev. B 65, 172507 (2001). [24] Y. Wang, T. Plackowski and A. Junod, Physica (Amsterdam) 355C, 179 (2001); P. Szab´o et al., Phys. Rev. Lett. 87, 137005 (2001); X. K. Chen et al., Phys. Rev. Lett. 87, 157002 (2001); F. Giubileo et al., Phys. Rev. Lett. 87, 177008 (2001); M. R. Eskidsen et al., cond-mat/0207394; R. S. Gonnelli et al., cond-mat/0208060. [25] N. Nakai, M. Ichioka and K. Machida, J. Phys. Soc. Japan 71, L23 (2002). [26] E. M. Forgan, S. J. Levett, P. G. Kealey, R. Cubitt, C. D. Dewhurst and D. Fort, Phys. Rev. Lett. 88, 167003 (2002). [27] A. A. Golubov, I. I. Mazin, Phys. Rev. B 55, 15146 (1997). [28] S. C. Erwin and I. I. Mazin, Phys. Rev. B 68, 132505 (2003). [29] I. I. Mazin, O. K. Andersen, O. Jepsen, O. V. Dolgov, J. Kortus, A. A. Golubov, A. B. Kuzmenko, and D. van der Marel, Phys. Rev. Lett. 89, 107002 (2002). [30] K. Papagelis, J. Arvanitidis, S. Margadonna, Y. Iwasa, T. Takenobu, M. Pissas. and K. Prassides, J. Phys.: Condens. Matter 14, 7363 (2002). [31] M. Avdeev, J. D. Jogensen, R. A. Ribero, S. L. Bud’ko and P. C. Canfield, Physica C 387, 301 (2003). Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

113

[32] P. Samuely, Z. Holanova, P. Szabo, J. Kacmarcik, R. A. Ribeiro, S. L. Bud’ko and P. C. Canfield, Phys. Rev. B 68, 020505(R) (2003). [33] R. H.T.Wilke, S. L. Budko, P. C. Canfield, D. K. Finnemore, R. J. Suplinskas, S.T. Hannahs, Phys. Rev. Lett. 92, 217003 (2004). [34] H. Schmidt, K. E. Gray, D. G. Hinks, J. F. Zasadzinski, M. Avdeev, J. D. Jorgensen, and J. C. Burley, Phys. Rev. B 68, 060508(R) (2003). [35] R. Ribeiro, S. L. Bud’ko, C. Petrovic, P. C. Canfield, Physica C 384, 227 (2003) [36] R. H. T. Wilke, S.L. Bud’ko, P.C. Canfield, D.K. Finnemore, S.T. Hannahs, Physica C 432 193 (2005). [37] M. Pissas, D. Stamopoulos, S. Lee, and S. Tajima, Phys. Rev. B 70, 134503 (2004). [38] E. Ohmichi, T. Masui, S. Lee, S. Tajima, and T. Osada, J. Phys. Soc. Jpn. 73, 2065 (2004). [39] E. Ohmichi, E. Komatsu, T. Masui, S. Lee, S. Tajima, and T. Osada, Phys. Rev. 70, 174513 (2004), [40] S. M. Kazakov et al., Phys. Rev. B 71, 024533 (2005). [41] R. Puzniak, M. Angst, A. Szewczyk, J. Jun, S. M. Kazakov, and J. Karpinski, condmat/0404579.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[42] P. Postorino et al. Phys. Rev. B 65, 020507(R) (2001);B. Renker et al, Phys. Rev. Lett. 88, 067001 (2002). [43] P. Postorino, A. Congeduti, P. Dore, A. Nucara, A. Bianconi, D. Di Castro, S. De Negri, and A. Saccone Phys. Rev. B 65, 020507(R) (2001). [44] V. Likodimos, S. Koutandos, M. Pissas, G. Papavassiliou, K. Prassides Europhys. Lett. 61, 116 (2003). [45] M. Putti, M. Affronte, P. Manfrinetti, and A. Palenzona Phys. Rev. B 68, 094514 (2003). [46] M. Putti, C. Ferdeghini, M. Monni, I. Pallecchi, C. Tarantini, P. Manfrinetti, A. Palenzona, D. Daghero, R. S. Gonnelli, and V. A. Stepanov Phys. Rev. B 71, 144505 (2005). [47] M. Ortolani, D. Di Castro, P. Postorino, I. Pallecchi, M. Monni, M. Putti, and P. Dore Phys. Rev. B 71, 172508 (2005). [48] S. V. Barabash and D. Stroud, Phys. Rev. B 66, 012509 (2002). [49] O. de la Pena, A. Aguayo and R. de Coss, Phys. Rev. B, 66, 012511 (2002). [50] M. Pissas, D. Stamopoulos, N. Zhigadlo, and J. Karpinski, Phys. Rev. B 75, 184533 (2007). Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

114

D. Stamopoulos and M. Pissas

[51] S. Margadonna, K. Prassides, I. Arvanitidis, M. Pissas, G. Papavassiliou, and A. N. Fitch, Phys. Rev. B 66, 014518 (2002). [52] S. Lee, H. Mori, T. Masui, Yu. Eltsev, A. Yamamoto, S. Tajima, J. Phys. Soc. Jpn. 70, 2255 (2001). [53] L. Lyard, P. Samuely, P. Szabo, T. Klein, C. Marcenat, L. Paulius, K. H. P. Kim, C. U. Jung, H.-S. Lee, B. Kang, S. Choi, S.-I. Lee, J. Marcus, S. Blanchard, A. G. M. Jansen, U. Welp, G. Karapetrov, and W. K. Kwok, Phys. Rev. B , 66,180502 (2002);L. Lyard, P. Samuely, P. Szabo, C. Marcenat, T. Klein, K. H. P. Kim, C. U. Jung, H-S Lee, B. Kang, S. Choi, S-I Lee, L. Paulius, J. Marcus, S. Blanchard, A. G. M. Jansen, U. Welp, G. Karapetrov and W. K. Kwok, Supercond. Sci. Technol. 16, 193 (2003). [54] M. Pissas (unpublished results.) [55] M. Pissas, S. Lee, A. Yamamoto and S. Tajima, Phys. Rev. Lett. 89, 097002 (2002); L. Lyard, P. Samuely, P. Szabo, T. Klein, C. Marcenat, L. Paulius, K. H. P. Kim, C. U. Jung, H.-S. Lee, B. Kang, S. Choi, S.-I. Lee, J. Marcus, S. Blanchard, A. G. M. Jansen, U. Welp, G. Karapetrov, and W. K. Kwok, Phys. Rev. B 66, 180502(R) (2002); U. Welp, A. Rydh, G. Karapetrov, W. K. Kwok, G. W. Crabtree, Ch. Marcenat, L. Paulius, T. Klein, J. Marcus, K. H. P. Kim, C. U. Jung, H.-S. Lee, B. Kang, and S.-I. Lee , Phys. Rev. B 67,012505 (2003); M. Angst, R. Puzniak, A. Wisniewski, J. Jun, S. M. Kazakov, and J. Karpinski, Phys. Rev. B 67, 012502 (2003).

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[56] E. Helfand and N. R. Werthamer, Phys. Rev. 147, 288 (1966). [57] M. Angst, R. Puzniak, A. Wisniewski, J. Jun, S. M. Kazakov, and J. Karpinski Phys. Rev. B 67, 012502 (2003); M. Angst, R. Puzniak, A. Wisniewski, J. Roos, H. Keller, P. Miranovic, J. Jun, S.M. Kazakov, and J. Karpinski, Physica C 385,143 (2003). [58] A. I. Larkin and Yu. N. Ovchinnikov, J. Low Temp. Phys. 34, 409 (1979). [59] I.M. Babich, Yu.V. Sharlai, and G.P. Mikitik, Fiz. Nizk. Temp. 20, 227 (1994) [Low Temp. Phys. 20, 220 (1994)]. [60] D. Stamopoulos and M. Pissas, Phys. Rev. B 65, 134524 (2002); ibid, Supercond. Sci. Technol. 14, 844 (2001). [61] B. Billon, M. Charalambous, J. Chaussy, R. Koch, and R. Liang, Phys. Rev. B 55, R14753 (1997). [62] A. B. Pippard, Philos. Mag. 19, 217 (1967). [63] E. H. Brandt, J. of Low Temp. Phys. 26, 709 (1977). [64] G. Ravikumar, V. C. Sahni, P. K. Mishra, T. V. Chandrasekhar Rao, S. S. Banerjee, A. K. Grover, S. Ramakrishnan, S. Bhattacharya, M. J. Higgins, E. Yamamoto, Y. Haga, M. Hedo, Y. Inada, and Y. Onuki, Phys. Rev. B 57, R11069 (1998); S. S. Banerjee et al. cond-mat/0007451.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Surveying the Vortex Matter Phase Diagram. . .

115

[65] P. L. Gammel, U. Yaron, A. P. Ramirez, D. J. Bishop, A. M. Chang, R. Ruel, L. N. Pfeiffer, E. Bucher, G. DAnna, D. A. Huse, K. Mortensen, M. R. Eskildsen, and P. H. Kes, Phys. Rev. Lett. 80, 833 (1998). [66] S. Kokkaliaris, et al, Phys. Rev. Lett. 82.5116 (1999). [67] D. Stamopoulos, M. Pissas, and A. Bondarenko Phys. Rev. B 66, 214521 (2002). [68] W. K. Kwok, J. A. Fendrich, C. J. van der Beek and G. W. Crabtree, Phys. Rev. Lett. 73, 2614 (1994), and references therein. [69] A. A. Zhukov, S. Kokkaliaris, P. A. J. de Groot, M. J. Higgins, S. Bhattacharya, R. Gagnon and L. Taillefer , Phys. Rev. B 61, R886 (2000). [70] S. O. Valenzuela and V. Bekeris, Phys. Rev. Lett. 84, 4200 (2000); ibid. 86, 504 (2001); S. O. Valenzuela, B. Maiorov, E. Osquiguil, and V. Bekeris, Phys. Rev. B 65, 060504 (2002). [71] J. Karpinski, N. D. Zhigadlo, G. Schuck, S. M. Kazakov, B. Batlogg, K. Rogacki, R. Puzniak, J. Jun, E. M¨uller, P. W¨agli, R. Gonnelli, D. Daghero, G. A. Ummarino, V. A. Stepanov, Phys. Rev. B, 71, 174506 (2005). [72] Heon-Jung Kim, Hyan-Sook Lee, Byeongwon Kang, Woon-Ha Yim, Younghun Jo, Myung-Hwa Jung, and Sung-Ik Lee, Phys. Rev. B 73, 064520 (2006). [73] M. E. Zhitomirsky and V. -H. Dao, Phys. Rev. B 69, 054508 (2004). [74] M. Mansor, J. P. Carbotte, Phys. Rev. B 72, 024538 (2005).

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[75] T. Dahm and N. Schopohl, Phys. Rev. Lett. 91, 017001 (2003). [76] P. Miranovi´c, K. Machida and V. G. Kogan, J. Phys. Soc. Jpn. 72,221 (2003). [77] A. Gurevich, Phys. Rev. B 67, 184515 (2003). [78] A. A. Golubov and A. E. Koshelev, Phys. Rev. B 68, 104503 (2003). [79] M. Angst, S. L. Budko, R. H. T. Wilke, and P. C. Canfield, Phys. Rev. B, 71, 144512 (2005). [80] J. Kortus, O. V. Dolgov, R.K. Kremer, and A. A. Golubov, Phys. Rev. Lett. 94, 027002 (2005). [81] A. Carrington, J. D. Fletcher, J. R. Cooper, O. J. Taylor, L. Balicas, N. D. Zhigadlo, S. M. Kazakov, J. Karpinski, J. P. H. Charmant, and J. Kortus, Phys. Rev. B 72, 060507(R) (2005). [82] T. Giamarchi, and P. Le Doussal, Phys. Rev. B 55, 6577 (1997); D. Ertas, and D. R. Nelson, Physica C 272, 79 (1996);A. E. Koshelev, and V. M. Vinokur, Phys. Rev. B 57, 8026 (1998); V. Vinokur B. Khaykovich, E. Zeldov, M. Konczykowski, R. A. Doyle, and P. H. Kes, Physica C 295, 209 (1998);J. Kierfield, Physica C 300, 171-183 (1998).

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

116

D. Stamopoulos and M. Pissas

[83] M. Pissas, D. Stamopoulos, V. Psycharis,Y. C. Ma, N.L. Wang, Phys. Rev. B, 73, 174524 (2006). [84] D. Pal, S. Ramakrishnan, A. K. Grover, D. Dasgupta and Bimal K. Sarma, Phys. Rev. B 63, 132505 (2001); L. Miu, Phys. Rev. B 65, 096501 (2002);D. Pal, S. Ramakrishnan, and A. K. Grover, Phys. Rev. B 65, 096502 (2002). [85] A. I. Rykov Studies of high temperature superconductors , Nova Science Publishers inc., edited by Anant Narlikar, Vol. 31, p. 149. [86] T. Nishizaki, K. Shibata, T. Sasaki, and N. Kobayashi, Physica C 341-348, 957 (2000). [87] T. Takenobu, T. Ito, D. -H. Chi, K. Prassides, Y. Iwasa, Phys. Rev. B 64, 134513 (2001); I. Maurin, S. Margadonna, K. Prassides, T.Takenobu, T.Ito, D.H. Chid, Y.Iwasa, A.Fitch Physica B 318, 392 (2002); K Papagelis, J Arvanitidis, S. Margadonna, Y. Iwasa, T. Takenobu, M Pissas. and K. Prassides, J. Phys.: Condens. Matter 14, 7363 (2002). [88] Z. Holanova, P. Szabo, P. Samuely, R. H. T. Wilke, S. L. Bud’ko, P. C. Canfield, cond-mat/0404096. [89] S. Lee, T. Masui, A. Yamamoto, H. Uchiyama, and S. Tajima, Physica C 397,7 (2003).

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[90] S. Lee, T. Masui, A. Yamamoto, H. Uchiyama, and S. Tajima, Physica C in press (2004). [91] S. B. Roy, Y. Radzyner, D. Giller, Y. Wolfus, A. Shaulov, P. Chaddah, Y. Yeshurun, Physica C 390, 56 (2003),and references therein. [92] M. Pissas, E. Moraitakis, G. Kallias and A. Bondarenko, Physica C 341-348, 1331 (2000);M. Pissas, E. Moraitakis, G. Kallias, A. Bondarenko, Phys. Rev. B 62, 1446 (2000). [93] M. Chandran, R. T. Scalettar, and G. T. Zim´anyi, Phys. Rev. B 67, 052507 (2003). [94] W. Jiang, N. C. Yeh, D. S. Reed, U. Kriplani, and F. Holtzberg, Phys. Rev. Lett. 74, 1438 (1995). [95] V. B. Geshkenbein, L. B. Ioffe, and A. I. Larkin, Phys. Rev. B 48, 9917 (1993). [96] G. W. Crabtree, W. K. Kwok, U. Welp, J. A. Fendrich, and B. W. Veal, J. Low Temp. Phys. 105, 1073 (1996). [97] C. J. van der Beek, S. Colson, M. V. Indenbom, and M. Konczykowski, Phys. Rev. Lett. 84, 4196 (2000). [98] S. R. Park, S. M. Choi, D. C. Dender, J. W. Lynn, and X. S. Ling, Phys. Rev. Lett. 91, 167003 (2003). Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

In: Magnesium Diboride (MgB2) Superconductor Research ISBN: 978-1-60456-566-9 Editors: S. Suzuki and K. Fukuda © 2009 Nova Science Publishers, Inc.

Chapter 4

NANOCRYSTALLINE MICROSTRUCTURE OF MECHANICALLY ALLOYED MGB2 SUPERCONDUCTOR PRECURSOR POWDER FOR BULK AND TAPE FABRICATION AND IMPLICATIONS ON THE SUPERCONDUCTIVITY

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

W. Häßler, O. Perner, C. Fischer, K. Nenkov, C. Rodig, M. Schubert, M. Herrmann, L. Schultz, B. Holzapfel and I. F. W. Dresden Institute for Metallic Materials, P.O. Box: 270016, D-01171 Dresden, Germany and Dresden University of Technology, Department of Physics, Institute for Physics of Solids, D-01062 Dresden

J. Eckert Technische Universität Darmstadt, FB 11 Material- und Geowissenschaften, FG Physikalische Metallkunde, Petersenstraße 23, D-64287 Darmstadt, Germany TU Darmstadt, Germany

Abstract In order to enhance the reactivity of the starting substances and, therefore, to reduce the processing temperature for the MgB2 formation process as well as to improve the flux pinning abilities of the resulting material, the ambient temperature preparation technique of mechanical alloying was successfully applied starting with the elemental magnesium and boron powders. Processing in highly purified argon atmosphere hinders the contamination with oxygen and leads to grain refinement down to several nanometers. The high reactivity of the milled powders causes the formation of MgB2 at reduced temperatures. The result is a partially reacted precursor powder with clean particle surfaces and no oxide entry during processing. The milled powder mixture was hot pressed for a short time resulting in highly densified nanocrystalline single-phase bulk material with composition close to the stoichiometric ratio of MgB2, which exhibits good grain connectivity and low oxide content. The high density of

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

118

W. Häßler, O. Perner, C. Fischer et al. grain boundaries which act as pinning centers enhances the upper critical field Hc2 and the irreversibility field Hirr as well as the critical current density Jc and the pinning force per unit volume Fp remarkably. Depending on the preparation parameters the critical temperature Tc is reduced to 30 - 35 K due to residual strain in the material and impurities stemming from the milling tools. Furthermore, monofilamentary Fe- as well as Cu-cladded and multifilamentary tapes with Fe sheath have been prepared by the PIT method using the mechanically alloyed partially reacted powder mixtures consisting of the constituents Mg, B and MgB2 as precursor. With this precursor the tapes can be annealed at relatively low temperatures of 773 – 873 K. Despite reduced Tc values of 30 - 35 K, maximum critical current densities Jc of 30 kA/cm2 and 9 kA/cm2 in external magnetic fields of 7.5 T and 10 T, respectively, are achieved at 4.2 K. The irreversibility fields Hirr of these tapes are 9.5 T and 4.2 T at 10 K and 20 K, respectively. Investigation of the microstructure by optical microscopy, SEM/WDX and XRD reveals that the high Jc values are mainly due to the remarkably small grain size of the MgB2 phase and defects, in particular precipitates of magnesium oxide. The properties of tapes with iron sheath are compared to those with Cu-sheath.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Introduction The potential of the superconducting compound MgB2 for technical applications in the temperature range between 20 and 30 K was already mentioned [1] just after its discovery [2]. Since then research started to prepare optimized samples concerning the critical temperature Tc, the critical current density Jc, the upper critical field Hc2 as well as the irreversibility field Hirr [3]. Soon two important properties were recognized to be crucial for potential application of MgB2 [4]. First, despite the lack of weak-link behaviour at the grain boundaries, it is decisive to obtain a sufficient connection between the grains to facilitate the penetration of the superconducting current through the grain network [5]. Because of this, optimized densification is a very important factor for the preparation of bulk samples from powders. The other crucial factor is the capability of the microstructure of MgB2 to allow for an effective flux pinning [6]. The creation of pinning centers was achieved by irradiation [7], composition variation [8] and addition of different compounds [5, 9]. Although some improvements were obtained so far, all these methods show disadvantages especially due to a high temperature sintering process that is required for densification into bulk specimens. Hence, there is still a strong need for further optimization of all preparation parameters in order to obtain MgB2 superconductors with improved properties. The Mg – B phase diagram [10] shows that MgB2 is a line compound. Any deviation from its exact stoichiometric composition, which cannot be compensated by formation of point defects or interstitials, is expected to lead to introduction of secondary phases. In the case of initial Mg excess this results in extra Mg in the material and in the case of Mg deficit there is the possibility of formation of MgB4 and MgB7 compounds [11]. Thus, to receive a maximum amount of MgB2 superconducting phase fraction it is crucial to control the exact stoichiometry. Many preparation methods established for MgB2 include a thermal treatment step where the compound is annealed at elevated temperatures up to 1500 K for several hours [3, 12]. Due to the high Mg vapour pressure it is very difficult to maintain a constant Mg – to – B ratio even in sealed crucibles and for Mg surplus. Due to all these difficulties, which have to be overcome, mechanical alloying as a powder metallurgy processing technique seems to be an appropriate tool to prepare MgB2 powders [13 - 15]. The possibility of the easy creation of a nanocrystalline microstructure by this

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Nanocrystalline Microstructure of Mechanically Alloyed MgB2…

119

technique [16] can provide a high density of magnetic flux pinning grain boundaries thus increasing the critical current density Jc. Furthermore, the fine-grained powder is well suited for wire and tape fabrication [17] because of the ease to highly densify the material and, therefore, to avoid a weak connection between the MgB2 grains. In this investigation it will be shown that mechanical alloying provides a variety of microstructure improving properties making this technique very promising for MgB2 powder preparation for powder-in-tube prepared filamentary wires and tapes.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Experimental The process of mechanical alloying consists of cold-welding, fracturing and rewelding of the starting powder particles [14], as it is schematically illustrated in Fig. 1. This leads to a grain size reduction of the Mg and B particles and a simultaneous formation of MgB2 [15]. Due to the high reactivity of the nanocrystalline powder the mechanical alloying is done in a purified Ar-atmosphere to avoid oxidation. In order to achieve an effective milling of the powder tungsten carbide (WC) milling tools, i.e. milling vials and balls, were used. WC has a density of 15.6 g/cm3 and, hence, a high powder – to – ball mass ratio of 1 : 36 can be achieved. This leads to a higher impact on the powder particles meaning a higher milling intensity and, hence, to a faster formation [18] of MgB2. The rotational speed of the planetary ball mill was kept constant for the present investigations. As starting materials we used amorphous boron (99.9 % purity, 1µm grain size, Mateck, Alfa Aesar) and fine-grained magnesium (99.8 % purity, 250 µm maximum particle size, Goodfellow) powders in the stoichiometric ratio of MgB2. Mechanical alloying was realized in a high-energy Retsch PM 400 ball mill for different milling times between 20 and 100 hours and constant milling intensity at ambient temperature. The mechanically alloyed powder was hot compacted in order to prepare bulk samples. In a vacuum chamber an uniaxial pressure of 640 MPa was applied at a temperature of 973 K for 10 min on powder with an amount of about 300 mg, which led to the formation of discs with a diameter of 10 mm and a thickness of about 1 mm. The tapes were prepared using the well known powder-in-tube (PIT) technique [19]. After filling the precursor into the metal tube (Cu or Fe) the composite was deformed by wire drawing and rolling to a monofilamentary tape of about 0.35 mm thickness and 3.5 mm width. For the preparation of multifilamentary tapes, 19 monofilamentary wires were bundled in a outer sheath tube and rolled again to a tape. It has to be mentioned that during forming work hardening of the sheath material takes place. Therefore annealing steps at about 720K for pure Fe to reduce work hardening are necessary. Before heat treatment pieces of 35 mm length were sealed in Ar filled quartz tubes or were wrapped in a getter foil. The embedded tapes were heat-treated at temperatures between 770 K and 970 K for 3-10 h aiming to complete the formation of MgB2. Tc measurements were carried out resistively. The transport critical currents (Ic) were determined by the standard four probe method using 1 µV/cm as criterion. The measurements were carried out at 4.2 K in fields up to 15 T applied parallel to the main plane of the tapes. Jc was related to the MgB2 core area determined on the lateral cross-section of the tapes. Typical values of the filling factor (ratio of core area to overall area of the cross-section) were in the range of 0.31–0.37. The upper critical field Hc2 and the irreversibility field Hirr were

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

120

W. Häßler, O. Perner, C. Fischer et al.

determined from resistance-vs.-temperature transition curves using the criteria 90% of the normal state resistance and zero resistance, respectively.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 1. Schematic illustration depicting the mechanism of mechanical alloying. Fracturing and coldwelding of the powder particles takes place because of the collisions of the WC balls.

Chemical analysis of the mechanically alloyed MgB2 powder was carried out by inductively coupled plasma - optical emission spectroscopy (ICP-OES). For this, the material was first dissolved and subsequently analysed in a plasma by optical spectroscopy. Phase analysis was performed using a Philips X’Pert PW 3040 X-ray diffractometer with Co Kα radiation. Rietveld refinement [20] of the obtained X-ray diffraction patterns using MgB2, Mg, MgO and WC peaks allowed to determine the lattice parameters, the grain size and the internal lattice strain. The thermal behaviour of the mechanically alloyed powders was investigated using differential scanning calorimetry (DSC) employing a Netzsch DSC 404 calorimeter. The powders were heated with a constant heating rate of 20 K/min up to 973 K under flowing argon gas while the heat flow was measured. Microstructure investigations were made using a scanning electron microscope LEO 1530 equipped with a field emission gun at 15 kV and a transmission electron microscope JEOL 2000 FX operated at 200 kV. Transport measurements of the pressed samples were carried out with the four-point method in a Physical Property Measurement System (PPMS) at external magnetic fields up to 9 T. The critical current temperature Tc was determined in the heating-up resistance curve at 90% of the normal-state resistance at 40 K and the transition width ΔTc was obtained between 10% and 90% of the normal-state resistance. The upper critical field Hc2 and the irreversibility field Hirr were determined at different applied fields from the heating-up transition curves at 90 % of the normal-state resistance and zero resistance, respectively. The critical current density Jc was calculated using the Bean model [21] from magnetization curves measured in a vibrating sample magnetometer (VSM) at temperatures between 7.5 K and 20 K.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Nanocrystalline Microstructure of Mechanically Alloyed MgB2…

121

Results Mechanically Alloyed Powders

(110)

(002)

(101)

(100)

Inductively coupled plasma - optical emission spectroscopy (ICP-OES) reveals a stoichiometric Mg : B ratio for the as-milled powder. As impurities we find 1.3 wt% O and a total of 0.8 wt% of W, C and Co as debris from the milling tools for the 50 h milled powder.

Intensity (a.u.)

Mg WC 20 h

50 h

100 h

30

40

50

60

70

80

90

2θ (degree)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 2. X-ray diffraction pattern of mechanically alloyed Mg and B powders in dependence on the milling time. Peaks of Mg and WC are marked by symbols, MgB2 peaks are indicated with their indices.

X-ray diffractometry (Fig. 2) revealed that the partially reacted powder consists of MgB2 and residual unreacted Mg besides a small amount of WC stemming from the milling tools. The B powder is not detectable by this characterization method due to its amorphous structure. Rietveld refinement [20] of the resulting X-ray patterns reveals that after mechanical alloying the phase fraction of MgB2 reaches 48 wt% for the 50 h milled powder besides an impurity content of MgO and few WC wear debris. This clearly shows that any contact of the highly reactive mechanically alloyed powder with air and introduction of oxide impurities has to be avoided as far as possible because MgO already forms during the heat treatment at a rather low temperature. Rietveld refinement also reveals that the phase fraction of MgB2 of the whole powder sample depends strongly on the milling time. Whereas we obtain only small MgB2 peaks for the 20 h milled powder, MgB2 becomes the main phase after 100 h of milling. After mechanical alloying the phase fraction of MgB2 is only 31 wt% for the 20 h milled powder but already reaches 55 wt% for the 100 h mechanically alloyed material. Detailed information on the lattice parameters, grain size and internal strain was also received by Rietveld refinement of the X-ray diffraction patterns. Whereas the lattice parameter c shows the behaviour of the layer distances in MgB2 unit cell, the lattice parameter a describes the atom distances in the hexagonal Mg and B layers [22]. For the powders subjected for different milling times the lattice parameter c decreases slowly with increasing

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

122

W. Häßler, O. Perner, C. Fischer et al.

milling time. In contrast, a increases slowly to a maximum value. A possible reason for this effect can be a lattice deformation due to atoms that are located on interstitial sites. But even after 100 h of mechanical alloying a and c are in the vicinity of the literature values of a=0.3085 nm and c=0.3523 nm [22], respectively. The coherent scattering length that can be regarded as minimal bound for the grain size and the internal strain of the lattice can be determined using the models of Scherrer [23] as well as of Stokes and Wilson [24], respectively. With increasing milling time the Mg grain size decreases whereas the size of the MgB2 grains increases from 4 nm for 20 h mechanically alloyed powder to about 10 nm after 100 h of milling. During mechanical alloying fracturing, cold-welding and grain size reduction depending on the brittleness and ductility of the powders, respectively, take place. The Mg grain size is reduced from 250 µm in the beginning to only a few nanometers after 50 h of milling. This causes a higher reactivity of the material because of the creation of clean and uncontaminated surfaces and an increased surface area – to – volume ratio. As a result of the milling process we obtain an increased formation rate of MgB2 from the starting elements Mg and B compared to untreated powder. The effect that MgB2 is very brittle leads to the desired grain size reduction. Accordingly, two parallel processes occur: the increase of the MgB2 phase fraction in the powder as well as the growth of the MgB2 grains and a continuous grain fracturing. Additionally, we find an increase of the defect density inside the MgB2 lattice. For longer milling times an enrichment and doping of impurities stemming from the milling tools and a possible decomposition of metastable phases can occur and, therefore, may deteriorate the advantageous superconducting properties of MgB2 (Fig. 2)

20 K / min

Heat flow (a.u.)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

exothermal

100 h 50 h 20 h

0,5 mW / mg

700

750

800

850

900

Temperature (K)

Figure 3. Differential scanning calorimetry plots of mechanically alloyed powders in dependence on the milling time.

The thermal behaviour of the as-milled powders was investigated by DSC analysis (Fig. 3). The partially reacted powders show an exothermic MgB2 formation reaction, which starts well below 800 K and is completed at 900 K. This allows to compact the powder samples at the relatively low temperature of 973 K compared to conventional sintering of MgB2 [3],

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Nanocrystalline Microstructure of Mechanically Alloyed MgB2…

123

which is advantageous to maintain a constant Mg : B ratio and to receive afterwards a fully reacted MgB2 compound without residual Mg and B. The series of powder samples with different milling time shows a strong reaction peak for the 20 h milled powder and a rather small peak for the 100 h powder sample. The enthalpy of the peaks clearly shows the strong relationship between milling time and the degree of MgB2 formation. The peak height decreases and the maximum of the peak moves to lower temperatures with increasing milling time. This result corresponds to the findings of the XRD measurements meaning that as-milled powder with a lower MgB2 fraction contains a higher fraction of residual Mg and B, which reacts during the heat treatment in the DSC, thus showing a higher MgB2 formation peak and vice versa. The shift of the peak maximum can be explained by smaller grain sizes of Mg and B with increasing time and, therefore, a higher reactivity leading to a lower starting temperature for the MgB2 formation.

100 nm

(a)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

MgB2

(b) Figure 4. Microstructure of the mechanically alloyed powder as observed by SEM investigation and of the hot pressed bulk samples by TEM.

Microstructure investigations of the as-milled powder by scanning electron microscopy (SEM) (Fig. 4a) reveal homogeneous particles with a size in the range of 1 to 10 µm, which consist of nanocrystallites with a size of less than 100 nm.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

124

W. Häßler, O. Perner, C. Fischer et al.

Hot Pressed Bulk Samples Chemical analysis after short-time hot pressing reveals no change of the stoichiometric Mg:B ratio. Obviously, no Mg loss during the heat treatment takes place, which is due to the low temperature of 973 K and the short annealing time of 10 min. Only the oxygen fraction increased due to an unavoidable short air contact step during the heat treatment to about 4 wt%. The influence of milling time on the phase composition of the hot pressed powders was also investigated by ICP-OES. The stoichiometric Mg : B ratio of the powders does not change with increasing milling time revealing that there is no preferential sticking to the milling tools. Additionally, we find that there is no Mg loss during the heat treatment. In contrast, the impurity content increases with increasing milling time from 20 to 100 h from 0.3 wt% to 1.7 wt% for W, 0.2 wt% to 1.1 wt% for C and 0.06 wt% to 0.12 wt% for Co. The oxygen content lies in the range of 2-4 wt% for all the powders irrespective of the milling time showing no clear trend. After hot pressing a nanocrystalline microstructure with inclusions of WC debris stemming from the milling tools was found (Fig. 4b). The material is highly densified reaching about 85 – 95% of the theoretical density of MgB2 of 2.62 g/cm2. The density of the hot pressed bulk sample of the 50 h milled powder reaches about 84% of the theoretical density of MgB2.

1,0

R / R(Tc)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

0,8

100 h Tc onset = 30.4 K ΔTc = 2.1 K

20 h Tc onset = 33.5 K ΔTc = 1.5 K

0,6

50 h Tc onset = 34.5 K

0,4

ΔTc = 0.9 K

0,2 0,0 24

26

28

30 32 34 Temperature (K)

36

38

40

Figure 5. Transport measurements of the superconducting transition in MgB2 bulk samples in dependence on the milling time.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Nanocrystalline Microstructure of Mechanically Alloyed MgB2…

125

The lattice parameter a approaches the literature value and c is slightly higher than predicted possibly due to occupation of interstitial sites. This will have an influence on the superconducting properties of MgB2, which is expected to be determined by the boron layer structure [3]. After hot pressing for 10 min at 973 K with 640 MPa the microstructure remains nanocrystalline with a grain size of about 25 nm upon hot pressing. The internal strain drops to about half of the value of the as-milled MgB2 powder but is still rather large. Hence, a short heat treatment does not destroy the desired nanocrystalline microstructure and annihilates some of the lattice defects introduced during the mechanical alloying process. This effect can be used to improve the superconducting properties because it is supposed that structural defects like grain boundaries are acting as pinning centres in MgB2. Transition curves for the samples milled for different milling times are shown in Fig. 5. The critical transition temperature Tc first increases with increasing milling time and reaches a maximum at 34.5 K for the 50 h milled and subsequently hot pressed powder. For longer milling times, Tc drops remarkably. The maximum Tc for this series of samples lies well below the usually measured value of 39 K for conventionally prepared material [2] revealing a strong relationship between mechanical alloying and superconducting properties , in terms of the phase fraction of MgB2, the grain size, the internal strain as well as impurities. The width of the transition is smallest for the powder sample milled for 50 h exhibiting ΔTc = 0.9 K. The critical current density Jc shown in Fig. 6a exhibits a similar dependence on milling time as it was measured for the critical temperature Tc. This suggests that for both properties Tc and Jc the same mechanisms determining the superconducting properties are relevant. For the lower temperature of 7.5 K, there is a wide range before Jc drops below 105 A/cm2. For the 50 h milled sample, this is the case for an applied field of 6.4 T. For 20 K, the pinning is strongly reduced. The reasons for this behaviour are related to grain size effects, lattice deformation as well as the impurity content of the bulk samples. Compared to other MgB2 bulk samples prepared by different techniques [6, 25, 26] our results are comparable to optimized sintered samples and thin films revealing an enhanced flux pinning at higher temperatures and in higher external magnetic fields, respectively. In Fig. 6b Hc2 is plotted as a function of T, revealing an almost linear temperature dependence for different samples. Near Tc a positive curvature is detectable [15]. The MgB2 bulk sample prepared from 50 h milled powder possesses the highest upper critical field for a given temperature. Shorter as well as longer milling times decrease Hc2 considerably. The behaviour of Hirr for the same bulk samples is also plotted in Fig. 6b showing the same temperature dependence as Hc2. Again, the 50 h milled bulk sample displays the best field dependence, which is comparable to thin films [6]. The comparison of Hc2 and Hirr in dependence of preparation parameters and temperature gives some information about the flux pinning capability of the mechanically alloyed nanocrystalline material. The ratio of about 0.7 that is found for the 50 h milled sample for higher external magnetic fields is comparable with the data reported for thin film samples [6]. This high ratio compared to a ratio of ~ 0.5 of untextured bulk samples [27] can be explained by the large number of grain boundaries due to the nanocrystalline microstructure, which causes an improved flux pinning behaviour.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

126

W. Häßler, O. Perner, C. Fischer et al. 6

20 h

50 h

2

Critical current density Jc (A/cm )

10

10

5

10

4

10

3

10

2

7.5 K 20 K

0

1

2

50 h

20 h

100 h

3

4

5

100 h

6

7

8

Magnetic field μ0H (T)

(a)

8

Hc2

μ0H

20 h 50 h 100 h

(T) 6

Magnetic field

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

4 irr

H

20 h 50 h 100 h

2

0 5

10

15

20

25

30

35

Temperature (K) (b) Figure 6. Critical current density Jc obtained from magnetization measurements at 7.5 and 20 K of MgB2 bulk samples in dependence on the milling time. Upper critical field Hc2 and irreversibility field Hirr determined by transport measurements of MgB2 bulk samples in dependence on the milling time.

Tapes Several research groups have dealt with the development of a low-cost MgB2 conductor using the "powder-in-tube" (PIT) technique [28-34], a review can be found in [35]. There are two

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Nanocrystalline Microstructure of Mechanically Alloyed MgB2…

127

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

methods reported in the literature. One (ex-situ PIT technique) involves direct filling of metallic tubes with commercial MgB2 powder and then drawing and rolling into tapes followed by sintering at relative high temperatures (1070-1270 K). An alternative approach (in-situ PIT technique) is characterized by filling the metallic tubes with elemental Mg and B powders and subsequent deformation and heat treatment, during which the elements react to form MgB2 at lower temperatures (870-970 K). This reduces undesirable interactions between the precursor constituents and the sheath material. Both methods facilitate the preparation of tapes with high Jc values, e.g., of 10 kA/cm2 at 7.5 T and 4.2 K [36] and 9 kA/cm2 at 8 T and 4.2 K [37] for tapes prepared by ex-situ PIT or in-situ PIT technique, respectively, using an undoped precursor. Dou et al., [37] achieved record values of about 40 kA/cm2 at 5 K in an external field of 8 T by doping the precursor with nanometer-sized SiC particles. In this paper, a special kind of the in-situ process characterized by the use of a partially reacted precursor powder is reported. As explained in the previous chapter, partial reaction of Mg with B is induced by mechanical alloying of Mg+2B powder mixtures resulting in a precursor powder, which consists of the constituents Mg, B and MgB2 with nanocrystalline grain size (about 40–100 nm).

(a)

(b)

(c) Figure 7. Metallographical cross-section of (a) monofilametary tape with Cu-sheath; (b) monofilametary tape with Fe-sheath; (c) multifilametary tape with Fe-sheath (19 filaments), annealed at 870K for 3h in Ar.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

128

W. Häßler, O. Perner, C. Fischer et al.

Fig. 7 shows the metallographical cross-sections of a monofilamentary tape with Cusheath (a), another with Fe-sheath (b) and of a 19-filamentary tape with Fe-sheath (c). It can be seen that the tape with Fe-sheath has a denser filament structure and the reaction layer at the interface to the metal sheath is thinner in comparison to tapes with Cu-sheath (Fig. 7a, b). The main phase of the reaction layer is MgCu2 resp. FeB2. The better densification during tape forming is caused by the higher mechanical strangth of Fe in comparison to Cu. Additionally to the reaction layer at Cu-cladded tapes a high Cu diffusivity into the filament was detected by SEM/WDX studies [38]. XRD-measurements on annealed monofilamentary tapes were carried out to investigate the phase composition. Already during the annealing steps during forming at 720K the amount of MgB2 increases from about 30wt% (after mechanical alloying) to about 50wt%. The reaction of the residual Mg and B takes place during the final annealing of the tape. As secondary phases higher borides (2…4%), MgO (2…4%) and WC (about 1%) were found. The optimal annealing temperature as well as the amount of higher borides and MgO at constant annealing conditions depends on the quality of the used boron [39]. 70 60

Resistivity (µΩ)

50 40 0T 2T 4T 6T

30 20 10

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

0 10

15

20

25

30

35

40

Temperature (K)

Figure 8. Resistive transition curves R(T,B) of a Fe-sheathed tape (annealed at 870K for 3h in Ar).

The transition curves R(T,B) of a monofilamentary Fe-sheathed tape as a function of applied magnetic field is shown in Fig. 8. The Tc values of these tapes are about 2 K lower than those of hot pressed pellets suggesting that the distortion of the MgB2 lattice due to the high energy milling of the precursor powder and the mechanical treatment of the tapes can not be completely healed out at 770 K. It should be emphasized that the Tc values of the tapes shown in Figure 8 are generally lower than those of tapes prepared by using commercial Mg2B or MgB2 powder with micrometer-sized grains [35]. This is not due to a deviation from the ideal stoichiometry of the superconducting compound. It is more likely that the depression of Tc is caused by the substitution of the above mentioned contaminations for Mg and B in MgB2, respectively. Another reason might be the precipitation of nanometer-sized particles at grain boundaries, which may act as "weak links". These arguments are supported by recent investigations on thin MgB2 films and bulk materials, which suggest that oxygen might change Tc by incorporation into the MgB2 lattice [40] or by formation of precipitates along the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Nanocrystalline Microstructure of Mechanically Alloyed MgB2…

129

grain boundaries, which then act as superconducting weak links [41]. However, it has to be mentioned that in spite of lowering Tc oxygen can enhance Jc [40, 41]. This may also be a consequence of flux pinning caused by MgO precipitates observed within the MgB2 grains [41]. Moreover, C can substitute B in MgB2 thus strongly lowering Tc [42]. Furthermore it should be mentioned that the critical temperatures varies in dependence on the used quality of the boron powder in the range of 30…35 K for the same annealing conditions, which is discussed in more detail in [39]. The reason can be seen probably in the different carbon and oxygen content of different boron powders. The critical fields were calculated from the R(T,B)-curves (Fig. 8). Typical values for tapes with mechanically alloyed precursor are at 20 K BC2=6.2 T and Birr=5.5 T, the extrapolated values for 4.2 K are 14 T resp. 13 T.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

2

Critical current density Jc (kA/cm )

4.2 K 100 Fe

Cu 10

1

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14

Magnetic field µ0H (T) Figure 9. Critical current densities of Cu- and Fe-sheathed tapes in dependence on the magnetic field at 4.2K. The different tapes were annealed at different temperatures between 770K and 870K for 3h.

Fig. 9 shows the field dependence of Jc at 4.2 K for tapes with Cu- and Fe-sheath. The reason for the low critical currents in Cu-sheathed tapes can be found in the strong Cudiffusion into the filament during annealing. The values of the tapes with Fe-sheath that were annealed for 3 h at 870 K exceed the highest ones so far reported for undoped samples. This can be attributed to the very fine-grained nanocrystalline microstructure of the superconducting phase. The size of the recognizable primary grains is of the same order of magnitude (< 100 nm) as the grains of the mechanically alloyed precursor used as starting material [15, 17]. However, the primary grains of the tapes are partially sintered together forming larger grains and dense areas. In Fig. 10 the Jc(B)-curves of Fe-sheathed tapes at 4.2 K and 20 K are compared. A critical current density of 30 kA/cm2 was measured in a magnetic field of 7.5 T at 4.2 K. At 20 K a critical current density of about the same value

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

130

W. Häßler, O. Perner, C. Fischer et al.

(28 kA/cm²) was found in lower field of 3 T. The Jc values at 20 K are important because a future application of MgB2 tapes will be in the vicinity of this temperature.

2

Critical current density Jc (kA/cm )

100

4.2K

20K 10

1

2

4

6

8

10

12

Magnetic field µ0H(T)

Figure 10. Critical current densities of different Fe-sheathed tapes annealed at 870K for 3h in dependence on the magnetic field at 4.2K and at 20K.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Conclusion The mechanically alloyed powder consists of a powder mixture of MgB2, Mg and B with a small amount of MgO and WC impurities. This gives a favourable composition for further processing by PIT where the ductility of Mg allows an easy deformation of the formed wire and the nanocrystalline powder can be highly densified by rolling. As a disadvantage the powder mixture contains some impurities, which in fact can deteriorate the superconducting properties. Altogether, mechanically alloyed nanocrystalline Mg+2B powder mixtures are appropriate precursors for manufacturing of MgB2 conductors by the PIT method. Fesheathed tapes prepared by using such precursors reveal Jc values at 4.2 K in external magnetic fields of 6-10 T (e.g., 30 kA/cm2 at 7.5 T ) exceeding those of all other so far reported values for undoped MgB2 tapes. The very fine-grained nanocrystalline microstructure of the superconducting phase seems to be responsible for these excellent Jc values of undoped tapes. Higher Jc values were so far only published for MgB2 wires doped with nanocrystalline SiC. Although the critical temperatures of the present tapes are lower than the best values published for ex-situ or in-situ PIT processed conductors, the Hirr values of our tapes are comparable at 20K with those published so far.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Nanocrystalline Microstructure of Mechanically Alloyed MgB2…

131

Acknowledgments The authors would like to thank C. Mickel for TEM investigations, W.Gruner for chemical analysis and both for useful discussions. We want to acknowledge further U. Fiedler, K. Berger , C.Goetzel and K. Schroeder for technical assistance.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

References [1] Larbalestier, D.; Gurevich, A.; Feldmann, D. M.; Polyanskii, A. Nature 2001, 414, 368-377 [2] Nagamatsu, J.; Nakagawa, N.; Muranaka, T.; Zenitani, Y.; Akimitsu, J. Nature 2001, 410, 63-64 [3] Buzea, C.; Yamashita, T. Supercond Sci Tech 2001, 14, R115-R146 [4] Larbalestier, D. C.; Cooley, L. D.; Rikel, M. O.; Polyanskii, A.A.; Jiang, J.; Patnaik, S.; Cai, X. Y.; Feldmann, D. M.; Gurevich, A.; Squitieri, A.A.; Naus, M. T.; Eom, C. B.; Hellstrom, E. E.; Cava, R. J.; Regan, K. A.; Rogado, N.; Hayward, M. A.; He, T.; Slusky, J. S.; Khalifah, P.; Inumare, K., Haas, M. Nature 2001, 410, 186-189 [5] Serquis, A.; Liao, X. Z.; Zhu, Y. T.; Coulter, J. Y.; Huang, J. Y.; Willis, J. O.; Peterson, D. E.; Mueller, F. M.; Moreno, N. O.; Thompson, J. D.; Nesterenko, V. F.; Indrakanti, S. S. J Appl Phys 2002, 92, No. 1, 351-356 [6] Eom, C. B.; Lee, M. K.; Choi, J. H.; Belenky, L. J.; Song, X.; Cooley, L. D.; Naus, M. T.; Patnaik, S.; Jiang, J.; Rikel, M.; Polyanskii, A.; Gurevich, A.; Cai, X. Y.; Bu, S. D.; Babcock, S. E.; Hellstrom, E. E.; Larbalestier, D. C.; Rogado, N.; Regan, K. A.; Hayward, M. A.; He, T.; Slusky, J. S.; Inumaru, K.; Haas, M. K.; Cava, R. J. Nature 2001, 411, 558-560 [7] Bugoslavsky, Y.; Cohen, L. F.; Perkins, G. K.; Polichetti, M.; Tate, T. J.; Gwilliam, R.; Caplin, A. D. Nature 2001, 411, 561-563 [8] Brutti, S.; Ciccioloi, A.; Balducci, G.; Gigli, G.; Manfrinetti, P.; Palenzona, A. Appl Phys Lett 2002, 80, No. 16, 2892-2894 [9] Dou, S. X.; Pan, A. V. ; Zhou, S. ; Ionescu, M. ; Liu, H. K. ; Munroe, P. R. Supercond Sci Technol 2002, 15, 1587- 1591 [10] Massalski T. (Ed.) Binary Alloy Phase Diagrams, second ed.; ASM International, Materials Park, OH, 1990 [11] Hinks, D. G.; Jorgensen, J. D.; Zheng, H.; Short, S. Physica C 2002, 382, 166-176 [12] Handstein, A.; Hinz, D.; Fuchs, G.; Müller, K.-H.; Nenkov, K.; Gutfleisch, O.; Narozhnyi, V. N.; Schultz, L. J Alloys and Comp 2001, 329, 285-289 [13] Eckert, J.; Holzer, J. C.; Krill III, C. E.; Johnson, W. L. J Appl Phys 1993, 73 No 6, 2794-2802 [14] Schultz, L.; Eckert, J. Topics in Applied Physics; Springer-Verlag Berlin, Heidelberg, 1994; Vol. 72, 69-118 [15] Gümbel, A.; Eckert, J.; Fuchs, G.; Nenkov, K.; Müller, K.-H.; Schultz, L. Appl Phys Lett 2002, 80, No. 15, 2725-2727 [16] Gümbel, A.; Perner, O.; Eckert, J.; Fuchs, G.; Nenkov, K.; Müller, K.-H.; Schultz, L. IEEE Transactions on applied superconductivity 2003, Vol. 13, No. 2, 3064-3067

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

132

W. Häßler, O. Perner, C. Fischer et al.

[17] Eckert, J.; Perner, O.; Fuchs, G.; Nenkov, K.; Müller, K.-H.; Häßler, W.; Fischer, C.; Holzapfel, B.; Schultz, L.in: Advances in Solid State Physics; Ed. Kramer, B.; Springer Verlag, Berlin, 2003; Vol. 43, pp 703 [18] Eckert, J.; Schultz, L.; Hellstern, E.; Urban, K. J Appl Phys 1988, 64 No 6, 3224-3228 [19] Flükiger, R.; Grasso, G. in: Handbook of Applied Superconductivity; Ed. Seeger, B.; IOP Publ. Bristol 1998, Vol. 1, 466 [20] Young, R. A. (Ed), The Rietveld Method, Oxford University Press, Oxford, 4 1993 [21] Bean, C. P. Rev of Modern Physics 1964, 31-39 [22] Pearsons Handbook of Crystallographic Data for Intermetallic Phases, Edition, Ed. Villars, P.; Calvert, L. D.; ASM International 1991; Vol. 2, 2 [23] Scherrer, P. Gött Nachr 2 1918, 98 [24] Stokes, A. R.; Wilson, A. J. C. Proc Phys Soc (London) 1944, 56, 174 [25] Finnemore, D. K.; Ostenson, J. E.; Bud’ko, S. L.; Lapertot, G.; Canfield, P. C. Phys Rev Lett 2001, 86, 2420-2422 [26] Braccini, V.; Coopley, L. D.; Patnaik, S.; Larbalestier, D. C.; Manfrinetti, P.; Palenzona, A.; Siri, A. S. Appl Phys Lett 2002, 81, No. 24, 4577-4579 [27] Fuchs, G.; Müller, K.-H.; Handstein, A.; Nenkov, K.; Narozhnyi, V. N.; Eckert, D.; Wolf, M.; Schultz, L. Sol State Commun 2001, 118, 497-501 [28] Glowacki, B.A.; Majoros, M.; Vickers, M.E.; Zeimetz, B. Physica C 2002, 372-376, 1254-1257 [29] Suo, H.L.; Beneduce, C.; Su, X.D.; Flükiger, R. Supercond Sci Technol 2002, 15, 1058-1062 [30] Goldacker, W.; Schlachter, S.I.; Zimmer, S.; Reiner, H. Supercond Sci Technol 2001, 14, 787-793 [31] Grasso, G.; Malagoli, A.; Modica, M.; Tuminao, A.; Ferdeghini, C.; Siri, A.; Vignola, C.; Martini, L.; Previtali, V.; Volpini, G.; Supercond Sci Technol 2003, 16, 271-275 [32] Feng, Y.; Zhao, Y.; Pradhan, A.K.; Zhou, L.; Zhang, P.X.; Liu, X.H.; Ji, P.; Du, S.J.; Liu, C.F.; Wu, Y.; Koshizuka, N. Supercond Sci Technol 2002, 15, 12-15 [33] Kovac, P.; Husek, I.; Melisek, T. Supercond Sci Technol 2002, 15, 1340-1344 [34] Fischer, C.; Rodig, C.; Häßler, W.; Perner, O.; Eckert, J.; Nenkov, K.; Fuchs, G.; Wendrock, H.; Holzapfel, B.; Schultz, L. Appl Phys Lett 2003, 83, No. 9, 1803-1805 [35] Flükiger, R.; Suo, H.L.; Musolino, N.; Beneduce, C.; Toulemonde, P.; Lezza, P. Physica C 2003, 385, 286-305 [36] Fujii, H.; Kumakura, H.; Togana, K. J Mater Res 2002, 17, 2339-2345 [37] Dou, S.X.; Soltanian, S.; Horvat, J.; Wang, X.L.; Zhou, S.; Ionescu, M.; Liu, H.K.; Munroe, P.G.; Tomsic, M. Appl Phys Lett 2002, 81, 3419-3421 [38] Fischer, C.; Häßler, W.; Rodig, C.; Perner, O.; Behr, G.; Schubert, M.; Nenkov, K.; Eckert, J.; Holzapfel, B.; Schultz, L. Physica C 2004, 406, 121-130 [39] Häßler, W.; Herrmann, M.; Perner, O. to be publ. [40] Patnaik, S.; Cooley, L.D.; Gurevich, A.; Polyanski, A.A.; Jiang, J.; Cai, X.Y.; Sqitieri, A.A.; Naus, M.T.; Lee, M.K.; Choi, J.H.; Belenki, L.; Bu, S.D.; Letteri, J.; Song, X.; Schlom, D.G.; Bacock, S.E.; Eom, C.B.; Hellstrom, E.E.; Larbalestier, D.C. Supercond Sci Technol 2001, 14, 315-319 [41] Liao, X.Z. ; Serquis, A.; Zhu, Y.T.; Huang, J.Y.; Civale, L.; Peterson, D.E.; Mueller, F.M.; Xu, H.F. J Appl Phys 2003, 93, 6208-6214 [42] Ribeiro, R.A.; Budko, S.L.; Petrovic, C.; Canfield, P.C. Physica C 2003, 385, 16-23

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

In: Magnesium Diboride (MgB) 2 Superconductor Research ISBN 978-1-60456-566-9 c 2009 Nova Science Publishers, Inc. Editors: S. Suzuki and K. Fukuda

Chapter 5

T HERMAL T RANSIENTS IN M G B 2 C ONDUCTORS Antti Stenvall and Risto Mikkonen ∗ Institute of Electromagnetics Tampere University of Technology FINLAND

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Abstract The high critical temperature of MgB 2 (39 K) offers increased range of operation temperature when compared to LTS materials. When operation temperature is raised from the liquid helium temperature (4.2 K) to the vicinity of 20 K the increased specific heat makes the operation of a superconductor much more stable. At 20 K hydrogen is the only possible liquid coolant. However, the use of hydrogen requires special care, especially if overpressure occurs in a cryostat and fast evacuation to air is required. Thus, cryocooler operation is preferred around 20 K due to its safety and simplicity. For an end user, cryocoolers require very little knowledge about cryogenics. Therefore, the wide commercialization prospects of MgB 2 are mainly related to conduction cooled applications operating in the vicinity of 20 K. In addition, at least so far the properties and price of NbTi at 4.2 K are transcendent when compared to MgB 2. During thermal disturbances, the cooling power of a cryocooler is negligible. Therefore, adiabatic stability considerations play an import role for system designs which utilize MgB2 superconductor and conduction cooling. In this chapter we first consider the computation of the critical current for an MgB 2 coil which includes conductor with ferromagnetic matrix. Then magnet stability under thermal transients is studied with a quench analysis algorithm. For conductor stability considerations, a numerical model to compute minimum propagation zones and normal zone propagation velocities for adiabatic MgB 2 conductors is presented and verified with the measurement results.

1.

Critical Current for Coils With Ferromagnetic Matrix

Computation of the magnetic flux density B distribution forms a basis for a coil design. After that, the field in the possible working volume, energy and coil current carrying capacity can be estimated. Regardless of the n-value of the used conductor, it is important to know how B is distributed in the coil. When magnetic flux density distribution can be ∗

E-mail address: [email protected]

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

134

Antti Stenvall and Risto Mikkonen

computed in a coil it is well known how to estimate the current carrying capacity of LTS or HTS windings. For LTS materials, with high n-values, the maximum magnetic flux density in the coil and the short sample critical current characteristic give the upper limit for the attainable coil current. However, magnets are designed to operate below this. Some small magnets are designed to operate between 10% - 30% below the coil critical current, but in large magnets such as ATLAS, this safety margin can be even 67% [1]. These kind of criteria are not sufficient for HTS magnets due to low n-values, which lead to significant heat generation also at sub-critical currents. Therefore, so called thermal runaway current has to be found instead [2]. This current depends on cooling conditions, coil dimensions, material properties and temperature T . It defines the maximum current which can not be continuously exceeded without eventually quenching the magnet. Generally, a magnet can be operated with higher currents for a while without a thermal runaway. Finally, safety margin is more preferably computed from the thermal runaway current, not from the coil critical current. For both of these methods, it is essential to know how to compute the magnetic flux density distribution in the coil volume. When a coil consists of conductor including ferromagnetic matrix, its magnetization has to be taken into account in coil critical current and magnetic field distribution computations [3]. Numerical methods has to be used in these computations. Because of complex coil structure, in which there are several turns each including multiple filaments, it is not possible to model the actual structure of the coil with e.g. finite element method even in solenoids, in which a 2D approach can be taken. Thus, the coil cross-section needs homogenization. In this homogenization, the engineering permeability is given to a homogeneous coil instead of the permeability µ of each constituent separately. Depending on the conductor structure, the homogenized coil material can be anisotropic. Meanwhile, the coil cross-section is replaced with homogeneous material, the actual magnetic flux density, which is directed to individual conductors, can not be found directly from the compted B distribution in the coil volume. However, it is essential to know the magnetic flux density which is applied to each conductor in order to solve the coil critical current or to compute the thermal runaway current by using measured short sample critical current, Ic, data. Consequently, a correspondence between the applied magnetic field of a short sample measurement and magnetic flux density distribution in the homogenized unit cell has to be found because of the notably effect of magnetization. Then, we can compute the relation between the applied B and average value of magnetic flux density in the homogenized bulk. After this Ic can be determined everywhere in the coil cross-section from the computed B distribution for homogenized coil with engineering permeability. In case of an actual coil, the current and the magnetic flux is not distributed evenly to filaments even within one conductor [4], but to straightforward the analysis without doing major mistake the presented approach is taken. Let us first begin with the homogenization of the conductor cross-section for the modelling of a coil cross-section. Here, we concentrate on a commercial tape by Columbus Superconductors. The tape consists of 14 MgB 2 filaments embedded in a nickel matrix with a copper core. An iron diffusion barrier locates between copper and nickel. The tape, dimensions and boundary conditions for the next presented engineering permeability problem is presented in figure 1. Unit cell filling factor for the tape was 50%. Because the tape aspect ratio is not 1,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Thermal Transients in MgB2 Conductors

135

Az=Bapp∆x/2

Az=−Bapp∆x/2

∆y=1.14 mm

0.65 mm

3.6 mm ∆x=4.09 mm ∇Az⋅n=0

∇Az⋅n=0 z MgB2 (4.5%, 14 filaments) Copper (7.5%) Iron (4.1%) Nickel (33.9%) Epoxy (50%)

y x

Figure 1. Investigated tape configuration and unit cell, including dimensions and boundary conditions for solving engineering permeability in y-direction. the engineering permeability µeng is anisotropic. For the engineering permeability in xdirection µxeng an applied magnetic flux density Bapp is directed in x-direction through the tape. Then, the standard magnetostatic formulation

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

∇×

1 ∇ × A = J, µ

(1)

where µ is the permeability, A is the magnetic vector potential as B = ∇ × A and J is the current density, is solved in the unit cell. From the obtained results µxeng (Bapp ) is computed as R Bx ds x µeng (Bapp ) = RS , (2) S Hx ds where S is the cross-section of the unit cell and Bx and Hx are the magnetic flux density and magnetic field intensity x-components. B and H are related according to the constitution law as B = µH. Figure 2 presents computed engineering permeabilities as a function of magnetic flux density for few values of current I. Current was equally divided between the superconducting filaments and the virgin curves of iron and nickel magnetization were expected. For the simulation of a short sample critical current measurement, we placed the homogenized unit cell in a magnetic field Bx,app. Then, we applied homogeneous current density to the unit cell cross-section that corresponded to the critical current of the tape. After this, the relation Bx,ave → Bx,app, where Bx,ave is the average magnetic flux density x component in the unit cell, was computed. This was repeated with several values of Bapp in parallel and perpendicular directions to determine the critical current as a function of Bave in the unit cell. Figure 3 presents the homogeneous unit cell carrying its critical current at 20 K and Bx,app = 1 T. As seen, due to magnetization and self-field Bx,ave is 1.17 T in the unit cell while maximum value is 1.22 T. Thus, using the Ic around 1.2 T in this case would

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

136

Antti Stenvall and Risto Mikkonen

Relative engineering permeability

8

2.6 (a)

7 6

2.2 I=0 I=50 I=100 I=200 I=300

5 4

2 1.8

3

1.6

2

1.4

1

(b)

2.4

0

1 2 Magnetic flux density [T]

3

0

1 2 Magnetic flux density [T]

3

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 2. Engineering permeability in (a) x-direction and (b) y-direction as a function of magnetic flux density for few values of current. not be appropriate, but Ic of 1 T must be used. Critical currents are presented in figure 4. Finally, these new unit cell critical current curves were used to compute the coil critical current. For the coil cross-section we replaced Bave , as pointwise values of B because, in the coil cross-section the variation of B is relatively low in the area of a single mm size conductor. Also, typically no compensation of self-field is done to individual conductors when critical current characteristic is used for determining coil critical current. However, for magnets wound of cables this approach is not justified because of large self-fields [5, pp.340-342]. It is not clear whether the modelling of MgB 2 coils should resemble LTS or HTS coils from the n-value perspective. In practice, manufacturers present conflicting n-values which can be characteristic for their conductors or arise from sample warming during the measurement [6, 7, 8]. Characterizing a conductor at low temperatures with a cryocooler differs considerably from that with a liquid coolant [8]. However, both methods for determining coil critical current (LTS and HTS like) are standard practice and, thus, well understood and widely used. Therefore, we just briefly present here the computations for an LTS like MgB 2 winding. However, if the thermal runaway current is computed for a coil which consists of ferromagnetic conductor with a low n-value this same method can be applied to compute electric fields of individual turns. For the study of coil critical current computation, we chose five solenoids with different inner radii ri , outer radii ro and heights h. Coil 1 had dimensions of a Nb 3Sn SMES magnet built at the Tampere University of Technology Institute of Electromagnetics [9]. This coil represented a relatively small coil. Coil 2 had dimensions of one of the two main coils to be built for the MgB 2 DC induction heater in European project ALUHEAT [10]. This coil represented a relatively large coil. Coils 3, 4 and 5 had rectangular, thin and thick cross-

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Thermal Transients in MgB2 Conductors

137

10

6

1.15

4 1.1

y [mm]

2 0

1.05 −2 −4

1

−6 0.95

−8 −10 −10

−5

0 x [mm]

5

Magnetic flux density x−component [T]

1.2 8

10

Figure 3. Homogeneous unit cell in critical current measurement carrying its critical current at 20 K and 1 T applied magnetic flux density. B is applied in positive x-direction and current is through surface.

3

10

Critical current [A]

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

(a)

(b)

T=15 K T=20 K T=25 K T=30 K

2

10

1

10 0.5

1 1.5 2 2.5 Magnetic flux density [T]

3 0.5

1 1.5 2 2.5 Magnetic flux density [T]

3

Figure 4. (solid lines) Ic (Bapp) and (dashed lines) Ic (Bave) characteristics for (a) parallel and (b) perpendicular applied magnetic flux at different temperatures.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

138

Antti Stenvall and Risto Mikkonen

sections, respectively. Coil 4 had large bore, whereas coils 3 and 5 had smaller bores. The filling factor of each coil was expected to be 50%. Dimensions of the coils are presented in table 1. We set the coil operation temperature to 20 K and computed the coil critical currents Ic,coil according to the presented model with finite element method. However, due to the cylindrical symmetry A had only the azimuth component Aϕ not equal to zero. Then, the stored energy E of a coil was computed as E=π

Z

rJaveAϕ da,

(3)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Coil cross−section

where Jave is the average current density on the coil cross-section. In addition to this computation routine, we applied a traditional linear method to compute the coil critical currents for each coil. Then, matrix magnetization was totally neglected and the short sample critical current curves were used as such to give the coil critical current. To compute the effect of the matrix magnetization on the stored energy, we computed E in both the modelling cases when the coils operated with Ic,coil of the non-linear model. Table 1 presents the results of the analysis. The difference in the non-linear and linear Ic,coil depended on the coil shape. However, the linear model always gave higher Ic,coil. The biggest differences were noticed with coils 1 and 2. Then, the linear model gave about 20% higher Ic,coil than non-linear model. In both the cases, the weakest spot located on the coil flange due to anisotropic critical current characteristics. The third biggest difference, 15%, was observed with thick coil 4. Then, the linear model gave Ic,coil from the axial mid-point at coil inner radius, whereas Ic,coil is defined from the coil flange. Figure 5 presents critical current contours of the both models when the coil 3 was operating at its Ic,coil. In fact, the critical current at coil inner radius was lower according to the linear model, but the flange defines Ic,coil according to the non-linear model. Thus, it can be possible to use ferromagnetic matrix also to shield the filaments and to increase the operation current, but with this conductor configuration such a behaviour was not observed in any of the coils. The shielding effects of the ferromagnetic matrix in MgB2 conductors have been studied in [11]. When Ic,coil was found from the coil inner radius, i.e. with coils 3 and 5, the difference between the linear and non-linear model was only 6% and 3%, respectively. Thus, for a

Table 1. Critical currents and stored energies for investigated coil geometries of different dimensions computed according to presented non-linear model and standard linear model. Coil

ri [mm]

ro [mm]

h [mm]

1 2 3 4 5

200 450 100 200 100

243 550 200 250 300

90 200 100 200 50

Ic,coil [A] Non-linear Linear 158 189 99 120 118 125 136 156 130 134

E(Ic,coil,non−linear) [kJ] Non-linear Linear 5.3 5 124.1 118.6 8.9 8.1 19.1 18.3 14.7 13.8

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Thermal Transients in MgB2 Conductors

160 180

90

(a) 140

(b)

200

180

100

250

80

139

0

20

0

180

25

70

200

z [mm]

0 30

300

60 50

240

250 200

210

300

350

350

300

220 230 r [mm]

220 230 r [mm]

240

350

210

400

0 200

400

180

10

250

350

20

200

30

180 160

250

40

250

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 5. Critical current contours for coil 3 cross-section when operated at its critical current computed according to (a) non-linear model (136 A) and (b) linear model (156 A).

tape conductor like this, the matrix magnetization has more damaging effect on the coil performance if the critical current is defined on the coil flange than if it is defined on the coil inner radius. That is, the perpendicular field was more damaging than the parallel. This has also been found when the shielding of saturated Bi-2223/Ag tapes with covering nickel layers has been studied [12]. Due to the matrix magnetization, it was natural that the linear model gave lower stored energies than the non-linear model at the same currents. The biggest difference was observed with coils 3 (9%) and 5 (6%). Both of these had smaller inner radii than the other coils. The smallest differences (4%) were achieved with the ALUHEAT coil 2 and the thin coil 4. For the energy computations, the linear model gave always few percents less stored energy than the non-linear model when the coils were operating at the same current. The linear model suggested higher coil critical currents than the non-linear model. When Ic,coil was determined by the coil flange, the difference was at its maximum of about 20%. On the other hand, the linear model gave very good approximate for the Ic,coil when the weakest spot located at the coil inner radius. In fact, this margin (3% and 6%) was below typical safety margins, whereas 20% was in the limit and, thus, if traditional linear modelling tools are used in this kind of a case, the coil may not reach the targeted operation parameters.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

140

2.

Antti Stenvall and Risto Mikkonen

Quench Analysis for Adiabatic Coils

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

In a coil design phase it is always important to perform a detailed quench analysis. From the analysis results, one can deduce if the coil can go through a safe quench and what kind of a quench detection and protection system would be useful for the winding. Crucial parameters in the quench analysis are the maximum voltage over the normal zone and the hot spot temperature rise. The first constricts the electrical insulation of the conductor, and the second is limited in order not to degrade the coil critical current during a quench. If these indicate that a coil can get damaged during a quench, a protection system has to be designed to prevent the possible damage, and the quench must be simulated again by taking into account the protection system. Even though an analysis of an unprotected coil suggests a safe quench, some protection scheme is typically applied for safety and to reduce heat dissipation in cryogenic environment. If the stored energy can be dissipated outside the coil e.g. in a shunt resistor or a secondary circuit, or it can be fed back to the grid, the re-cooling time of the coil and the possible consumption of liquid coolant is reduced. Thereby, the quench is made less expensive event. Performing a coil quench analysis requires running through a detailed computer algorithm. Taking numerical approach is necessary. Several general quench codes and also some specialized ones for cases such as ATLAS toroids have been presented [13, 14, 15, 16, 17, 18, 19, 20, 1, 21]. The basics of all these codes is to solve in the coil volume the heat diffusion equation ∂T ∇ · λ∇T + Q = C , (4) ∂t where λ, Q and C are the thermal conductivity, the heat generation and the volumetric specific heat, respectively. The transverse heat conduction of the winding, the modelling of quench origin and the propagating normal zone front pose especial problems. We had developed a quench model for solenoids and racetracks [21]. For this study it was extended to be capable of simulate different heat generations and structure in the quench origin. The program was implemented in Matlab and Comsol Multiphysics finite element software. The investigated coil had same dimensions and properties as the SMES coil 1 in the critical current analysis in the previous section. However, we expected an improved critical current characteristic, in which the operation current I was 200 A at 20 K while the Ic,coil was 300 A and determined by the coil flange. Then, the critical current at the coil inner radius was 317 A. For this analysis, we did not take into account the matrix magnetization in order to shorten the simulation time. The coil was equipped with a detection in which the current source was switched off and the coil was short-cirtuited when the voltage over normal zone exceeded 2 V. For the present analysis, the earlier program was further developed to study how the quench origin should be modelled in a quench analysis. First, the whole winding was homogenized and the bulk heat conductivity tensor was given for the coil. For the heat generation in the quench origin, we had two approaches: the one averaged over the tape unit cell (case I) and the one over the tape cross-section (case II). In the second approach, we modelled the actual coil structure near the quench origin (case III). In addition to the conductor where the quench was ignited, one adjacent turn and epoxy layers in between were modelled from 10 cm length. Elsewhere, homogenized properties were expected.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Thermal Transients in MgB2 Conductors

141

In each case heat generation was computed according to the power law. For the quench ignition, a heater was used to trigger the quench. That was implemented by adding a power of 5 W to the quench origin for 200 ms. The quench origin was a 2 cm long conductor in the location of maximum magnetic flux density in the coil inner radius. A detailed quench analysis requires several quench simulations in which the origin and the quench current are varied [22]. A numerical model was used to determine effective bulk transverse heat conductivities [23]. Meshing the 3D coil with care is especially important in quench analysis. It is not possible to create geometries which correspond to actual ones in a conductor or filament level even in rather small coils, because the amount of elements needed in meshing the coil volume in a FEM software is limited. Thus, some homogenization of the winding is required. Also, softwares have typically problems with 3D meshes, in which dimensions vary notably. Thus, the coil domain could be meshed only with detailed meshing parameters. It is advisable to mesh with high precision the areas of the highest interest and rapid changes in the function to be solved. In a quench analysis, the quench origin presents the area of the highest interest and the frontier of the propagating normal zone presents the area of rapid change in Q of (4). The latter causes difficulties, because the frontier moves with time in the winding. The movement along the coil circumference is the fastest due to the highest thermal conductivity. Thus, we meshed the coil very densely in the quench origin. In the actual structure of the coil, it was also necessary to take into account the low thermal conductivity and zero heat generation of the epoxy. The coil inner radius at the height of the quench origin was also meshed densely. Because we ignited the quench from the position of maximum magnetic flux density, it was necessary to model only one quarter of the coil volume. Thus, the two edges on the coil cross-section, leaving from the quench origin were meshed so that the element size grew much slower than in the other parts of the coil when receding from the quench origin. Figure 6 presents a view of the meshed coil with a visualization of critical meshing parameters. Figure 7 presents results from the three quench analyses. The coil initial temperature was homogeneous 20 K. While the quench heater was on, the temperature of the hot spot rose to 48 K (case I and case II) and 60 K (case III). If the heater operation time of 100 ms was used, the quench did not start in simulations I and II. When the 5 W heater was on for 200 ms the quench started in all the cases. Thus, 200 ms was chosen as the heater operation time. After, shutting off the heater the temperature decreases to 35 K, 39 K and 54 K in cases I, II and II, respectively. This was due to the sudden decrease in the local heat generation and the heat conduction was powerful enough to cause this decrease. The average current density in the conductor area was 85 A/mm 2 . After the local minimum of temperature, the hot spot temperature continued to increase. Because of the considerably large temperature margin it took about 3 s to detect the quench. At that time, the maximum hot spot temperature had risen to 77 K, 83 K and 93 K in cases I, II and II, respectively. Then, the current started to decay and in case III the hot spot temperature reached its maximum value 152 K at 7.0 s, while the current was 83 A. Simulation was still continued until only 1% of the total coil energy (9.6 kJ) was left, i.e., at I = 20 A. This happened at 10.3 s when the maximum hot spot temperature was 143 K. In cases I and II the maximum hot spot temperatures were 126 K and 131 K, respectively. Other characteristics except the temperature showed similar behaviour in all

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

142

Antti Stenvall and Risto Mikkonen

200

150

150

Current [A]

200

(a)

100 50

(b)

100 50

0 10

0.1

Voltage [V]

Temperature [K] Resistance [Ω]

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 6. View of mesh in quench analysis and important issues on meshing.

(c) 0.01

0.001

0

5 time [s]

10

2 1

0.1

(d)

0

5 time [s]

10

Figure 7. Results from quench analysis of (—) case I, (– · –) case II and (– –) case III.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Thermal Transients in MgB2 Conductors

143

the cases. Thus, the effect of the epoxy with a low heat conduction around the tape had considerable effect on the quench origin, and for a detailed simulation the actual coil structure needs to be modelled. During the current decay, the maximum voltage over the normal zone was a little bit less than 20 V in each case. The voltage was very low and only normal insultion is required for the coil with so low voltages. The normal zone resistance was at its maximum around 0.2 Ω in all the cases. Concerning the small stored energy, the hot spot temperature rise was quite high. However, the biggest concern is the temperature rise before the quench detection. In YBCO coils operating around 20 K the slow quench propagation has posed real problems to detect the quench before a coil gets completely broken [24]. In these cases, it can be complicated to use passive protection efficiently. However, the magnet can be protected against the quench efficiently if the quench can be detected early in the safe area. In the investigated coil, the maximum hot spot temperature at quench origin was 93 K in the detailed model. This is still acceptable value, but quite high. Typically tolerable maximum temperature during a quench is at most 300 K. If very rapid changes occur, 150 K is a better limit to restric thermal stresses.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

3.

Minimum Quench Energy and Normal Zone Propagation Velocities

After a coil quench analysis has been performed and protection designed, it is known that the coil can quench safely. Next thing is to study what kind of point disturbances, of e.g., mechanical origin, can typically occur in a coil to cause a quench. For example, a wire movement releases some energy which locally raises temperature in a coil. In accelerator magnets, beam losses cause serious energy bursts. If this local energy burst oversteps minimum quench energy (MQE) a thermal runaway occurs causing a quench. If the energy burst is smaller than MQE a temporary normal zone can exist in a coil, but it contracts, and the coil returns to operation temperature. For a given conductor it is important to know MQE at operation conditions. If it is too low, when compared to estimated disturbances, the operation current or temperature has to be lowered. It is well known that conductors with low n-values can operate at over-critical currents for a while also in almost adiabatic conditions. Therefore, the effect of n-value on MQE must be considered. Analytical methods are not possible, but instead, a numerical approach is required to simulate the dynamics of local disturbance. In this section we present a 1D model for a conductor in which an arbitrary heat pulse is fed in a short length of the adiabatic conductor to study whether a recovery or thermal runaway occurs. MQE is found on the limit. This method, in which the conductor cross-section is expected isothermal, is applicable for single conductors but not for e.g. Rutherford cables with aluminum casing. Also, in these cables the current diffusion into stabilizer can be a slow phenomenon which causes higher local heat generation than averaged current density suggests [1]. The MQE and normal zone propagation measurements were carried out with an early stage development version of Columbus Superconductors tape presented in figure 1. Since these tapes, the manufacturing process of such conductors has developed, and consequently, the critical current has improved significantly. The measured critical current for the experi-

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

144

Antti Stenvall and Risto Mikkonen

mentally investigated tape at the self-field was Ic(T ) = 953 − 26T.

(5)

and the n-value of the conductor at self-field was 15 [8]. Figure 8 presents a schematic view of the setup for measuring MQE and normal zone propagation velocity vnzp. To measure real 1D propagation, the sample was separated in the measurement area from the sample holder. Then, the heat exchange happened only by conduction along the sample and by radiation to the radiation shield. Still, it was discovered that the end cold mass of the sample heater affected results at low currents. The ends of the sample holder were electrically separated with a bakelite to be sure that the applied current flows all the time in the conductor and no current sharing between the sample holder and conductor occurs during the measurement. With this kind of setup, one must be very careful in order not to burn the conductor when quench occurs. However, with automated system this was not a problem. Current contact Cooling contact 60 mm 0.5 mm Position of voltage taps 0

3 4

15

25

35

[mm]

Heater Superconductor

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

20 mm

K

K

Sample holder Nut

Mounting hole Bakelite support Temperature sensors 150 mm

Figure 8. Schematic view of MQE and vnzp measurement system. In the measurement of MQE, a constant current was applied to the heater for a specific time in order to find if the initial normal zone causes a thermal runaway. The minimum time for heater operation which causes a quench was found to determine MQE. This measurement was modelled with a 1D FEM method. The previously presented formulation for solving 1D minimum propagation zones with FEM was further developed to correspond our measurement situation [25]. In the developed model, we applied on the heater length additional power to the conductor which corresponded to the heater power, and then we looked into the shortest operation time which caused a thermal runaway. We used the resolution of 0.1 ms for the heater operation. Then, MQE was given as the product of the heater operation time and the power. The heater power was 1 W and typical operation times were on the range of 10-200 ms.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Thermal Transients in MgB2 Conductors

145

Figure 9 presents the measured and modelled minimum quench energies at 25.5 K and 28.0 K. At low currents, computed values of MQE were lower than the measured. At 100 A and 25.5 K, measured MQE was 188 mJ, while the computed value was 139 mJ, almost 27% smaller. Corresponding values at 28 K were 136 mJ and 119 mJ. Then, the computed one was almost 13% smaller. The difference is most likely due to the cold mass of the sample holder, which received some of the energy from the heater. In computations (25.5 K and 100 A) we found out that the temperature had risen already to 29.7 K at the position of the sample holder edge when the superconductor below the heater reached its critical temperature, 32 K, at the operation current. This occurred 19 ms after the heater start-up. Thus, it is natural that sample holder had affected the measurements. This was possible, because the temperature margin of the conductor operating at 100 A was quite high (6.5 K at 25.5 K and 4 K at 28.0 K). This effect weakened when the temperature stability margin lowered with increasing current, and then the computed and measured results were in better correspondence. 200 Measured Computed

180

MQE [mJ]

160 140 120

Top=25.5 K, Ic=286 A

100

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

80 60

T =28.0 K op Ic=221 A

40 100

150

200

250

Current [A]

Figure 9. Computed and measured MQE as a function of operation current at temperatures 25.5 K and 28.0 K. The relative and absolute difference decreased when the operation current was increased. At 150 A, the relative difference was about 10% for both the cases. Modelled MQE at 25.5 K was then (16 mJ) lower than measured one whereas at 28 K the modelled one was only 7 mJ lower. At 200 A and 25.5 K the correspondence was also very good. The difference between the measured and computed MQE was 7 mJ. When temperature was risen to 28 K, the modelled MQE was 11 mJ higher than the computed one. With the operation current of 250 A, the measurements could be done only at 25.5 K because at 28 K the conductor critical current was 221 A. Then, the computed value was 4% (3 mJ) higher than the measured one. It is not fully understood why the modelled MQE values became higher than the measured ones when the current was increased. One reason could

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

146

Antti Stenvall and Risto Mikkonen

20 81 ms

V

1

Voltage [mV]

15

10 Propagation time for 10 mm

5

V2 Voltage criterion

0 0

0.05

0.1

0.15

0.2 0.25 Time [s]

0.3

0.35

0.4

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 10. Measured voltage curves V1 and V2 and schematic view of defining vnpz when operation current was 200 A at 25.5 K. be that the increased current caused some heat generation at joints which also resulted to tape temperature rise and, thus, the temperature margin decreased. At the highest currents, this effect might have been enough to affect the measurement. The effect of the contact resistance on MQE and V − I measurement of conduction cooled measurement systems need to be studied more in the future. vnzp was measured with a voltage criterion by measuring voltages between voltage taps at 4 and 25 mm (V1) and 4 and 15 mm (V2) as a function of time (figure 8). The distance between the taps located at 15 and 25 mm (i.e. 10 mm) was divided by the time difference between the surpassing of the voltage criterion Vc, 2 mV, at these taps to give vnpz. Figure 10 presents measured voltages at 200 A and 25.5 K for a propagating normal zone as a function of time and a schematic view for defining vnzp. The measurement frequency (around 100 Hz per channel) was enough to determine the vnpz, but chosen voltage criterion (2 mV) was somewhat arbitrary. However, with criteria of 4 mV and higher it was not possible to determine the vnpz to operation current of 100 A anymore because the maximum V2 was a little bit below 4 mV before switching the current off. Also, the dependence of vnpz on Vc was quite low. At 25.5 K and 200 A, the criteria of 0.2, 0.5, 1, 2 and 3 mV gave the time differences of passing Vc for voltages V1 and V2 84, 81, 80, 81 and 82 ms, respectively. These yield to the maximum difference of less than 4% (less than 0.5 cm/s) in measured vnpz. For comparison, this similar voltage criterion was applied also for our MQE model. We applied MQE to the conductor, and then computed corresponding voltage curves. V1 was computed as V1 (t) =

Z

4 mm

min 25 mm



I Aconductor

ρnorm(T ), Ec



I Ic (T (x, t))

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

n 

dx,

(6)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Thermal Transients in MgB2 Conductors

147

where Aconductor, ρnorm and Ec are the conductor cross-section area, normal state resistivity and critical electric field criterion, 1 µV/cm. V2 was correspondingly integrated between 15 mm and 4 mm. Figure 11 presents the measured and simulated voltages at 200 A and 28 K between the two voltage taps. The simulated voltages fit quite well at high values of current to the measurement data until the knee in voltages occurs. At this time the normal zone has reached the voltage tap located at 4 mm. For the measured and computed values, the times of voltage V1 passing Vc in measurements and simulations were matched. When the normal zone had propagated to the voltage tap located at 4 mm, the computed voltage rose more rapidly than the measured. This is most likely due to the cooling capacity of the cold sample holder. In the computations, the model was made very long to simulate true adiabacy near the quench origin for a short while. Therefore, this cooling effect was not taken into account. Anyhow, the measured vnpz could, in this case be simulated with good accuracy. However, at low currents, the correspondence was rather poor as seen in figure 12. Both the measured voltages V1 and V2 rise more gently than the simulated ones. The initiated minimum propagation zone required more energy than at higher currents due the higher temperature stability margin. Therefore, it can be expected that in the actual case the cooling effect of sample holder cold mass is considerable also here as it was expected to be in the corresponding MQE measurements. The value of vnpz given by the computational model was considerably higher than the actually measured at the low currents. Still, in a long 1D propagation (coil with insulation of very low heat conductivity) the result given by the simulation can be closer to the reality. Finally, the measured and computed values of vnpz at 25.5 K and 28.0 K are presented in figure 13. As already stated, the correspondence of simulated and measured voltages was not good at low currents. This is, thus, reflected to the values of vnpz. At 100 A, the computational model gave three-fold and twice the vnpz measured at 25.5 K and 28 K, respectively. The corresponding values of the measured vnpz were 2.1 cm/s and 3.8 cm/s. When the current was increased, the measured and computed vnpz became closer. At 150 A, the computed values were roughly 50% (less than 4 cm/s) higher than measured. At 200 A the absolute difference between the measured and computed values was less than 3 cm/s at 25.5 K and 28 K. This is already lower than vmpz at 100 A while the relative difference decreased to 23% and 12% for the temperatures of 25.5 K and 28 K, respectively. When the operation current was further increased to 250 A at 25.5 K the computed and measured values of vnpz were 18.3 cm/s and 20.3 cm/s. Thus, the computational model shows good correpondence with the measurements when the cold mass of the sample holder does not have effect on the measurement. This occurs near the critical current when the normal zone propagates almost equally with the rising temperature frontier. The finite element method model presented earlier for the MQE simulation proved to be applicable also for simulation of normal zone propagation velocity. However, with the presented measurement system the correspondence of the measurements and simulated MQE and vNPZ was not very good at low currents. We believe that, even though the measurement system was designed specially for adiabatic 1D measurement, the sample holder affected the measurements when stability margin was high. Thus, further study is required on the effect of sample holder on the measurements in conduction cooled environments. With high currents the correspondence of the measurement results and modelling was very good.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

148

Antti Stenvall and Risto Mikkonen 25 Measured Computed 20 Voltage [mV]

V1 15

10 V2

5

Top=28 K

0 0

0.1

0.2

0.3 Time [s]

0.4

I=200 A 0.5

0.6

Figure 11. Measured and computed voltages V1 and V2 at 28 K and 200 A.

Measured Computed

8 Voltage [mV]

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

10 V1

6 4 V2

2

Top=28 K

0 0

0.2

0.4

0.6 Time [s]

0.8

I=100 A

1

1.2

Figure 12. Measured and computed voltages V1 and V2 at 28 K and 100 A.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Thermal Transients in MgB2 Conductors

4.

149

Conclusion

3.5 25.5 K 28 K 3

2.5

2

20 vNPZ [cm/s]

Normalized vNPZ

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

We presented how the critical current for coils with a ferromagnetic matrix can be computed. This included first computing the engineering permeability for the conductor. Then short-sample measurement situation was simulated with a homogenized unit cell. Thus, the measured critical currents were made to match the maximum value of the magnetic flux density on the unit cell. This was then used to give the critical current for coil the cross-section. So, we used an LTS type method for determining the coil critical current. However, if the thermal runaway current is computed for a coil which consists of ferromagnetic conductor and low n-value this same method can be applied to compute the electric fields of individual turns. We analysed five different coil geometries. According to the results, the non-linear method always gave lower critical currents than the traditional linear method. When the critical current was determined by the coil flange the difference between Ic,coil of the models was the highest (about 20%), whereas the lowest difference (3%) was noted when the coil inner radius included the weakest spot. In fact, in one case, we found that the ferromagnetic matrix shielded the conductor in the inner radius, but then the flange determined the critical current. To study the coil behavior during fault, a 3D quench simulation for solenoids was presented and discussed. The modelling of the heat generation and the structure of the quench origin were scrutinized. In one approach, the effective material properties were used everywhere in the coil, whereas in the other approach the actual coil structure in the level of actual conductor-epoxy structure was modelled near the quench origin. The latter proved to be difficult for the commercial FEM program to mesh and initialize the geometry, but with detailed settings quench was successfully simulated. About 20 K higher maximum hot spot

10

0 100

150

200

250

1.5

1 100

150

200

250

Current [A]

Figure 13. Computed values of vnpz normalized with corresponding measured values at operation temperatures of 25.5 K and 28.0 K. Inset presents measured values of vnpz. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

150

Antti Stenvall and Risto Mikkonen

temperature rise was simulated with the detailed model of the quench origin. Also, when the quench heater operation time was shorten to half, the quench did not start with bulk models but did with the detailed one. These indicate that the low heat conductivity of insulation has notable effect on the quench ignition, and more reliable results can be achieved if the real coil structure is taken into account near the quench origin. Finally, the stability of individual MgB 2 conductors was studied computationally and experimentally. This included minimum quench energy and normal zone propagation velocity studies at the self-field and in cryocooler operated environment. For simulations, the already presented 1D finite element code was further developed to correspond the measurement situation, in which the quench was initiated with a heater. When the conductor n-value was taken into account, the presented simulations were in good agreement with the measurements at high currents. This was also the case with the normal zone propagation velocities at currents close to the critical. Far below the critical current, the cold mass of the sample holder affected on the quench ignition causing higher measured MQE than modelled, and it also slowed the quench propagation causing 2-3 time slower propagation than was simulated.

Acknowledgements The authors thank Joonas J¨ arvel¨ a for invaluable help with MQE and vnzp measurements.

References

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[1] Gavrilin, A.V., Dudarev, A.V. & ten Kate, H.H.J., (2001). Quench modeling of the ATLAS superconducting toroids. IEEE Trans. Appl. Supercond., 11, 1693-1696. [2] Lehtonen, J., Mikkonen, R. & Paasi, J., (2000). A numerical model for stability considerations in HTS magnets. Supercond. Sci. Technol., 13, 251-258. [3] Stenvall, A., Korpela, A., Mikkonen, R. & Kov´ aˇc, P., (2006). Critical current of an MgB2 coil with a ferromagnetic matrix. Supercond. Sci. Technol., 19, 32-38. [4] Uˇsa ´k, P., Pol´ ak, M., Kvitkoviˇc, J., Mozola, P., Barnes, P.N., & Levin, G.A., (2007). Current distribution in the winding of a superconducting coil. IEEE Trans. Appl. Supercond., 18, 1597-1600. [5] Fabbricatore, P. & Musenich, R. B7.4 Critical current measurements of superconducting cables by the transformer method. Published in Seeber, B., Editor, (1998). Handbook of Applied Superconductivity. Bristol: Institute of Physics Publishing . [6] Tomsic, M., Rindfleisch, M., Yue, J., McFadden, K., Doll, D., Phillips, J., Sumption, M.D., Bhatia, M., Bohnenstiehl, S. & Collings, E.W., (2007). Development of magnesium diboride (MgB 2 ) wires and magnets using in-situ strand fabrication method. Physica C, 456, 203-208. [7] Grasso, G., (2007). Current state of MgB2 wires for magnet application. Presented at 20th Magnet Technology Conference, August 27-31 2007, Philadelphia, Pennsylvania, USA. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Thermal Transients in MgB2 Conductors

151

[8] Stenvall, A., Hiltunen, I., J¨ arvel¨ a, J., Korpela, A., Lehtonen, J. & Mikkonen, R., (2008). The effect of sample holder and current ramp rate on conduction cooled V − I measurement of MgB2 . Supercond. Sci. Technol., 21, 065012 (6pp). [9] Korpela, A., Lehtonen, J., Mikkonen, R. & Per¨ al¨ a, R., (2003). Quench in a conduction-cooled Nb 3Sn SMES magnet. Supercond. Sci. Technol., 16, 1262-1267. [10] Runde, M., Stenvall, A., Magnusson, N., Grasso, G. & Mikkonen, R., (2008). MgB2 coils for a DC superconducting induction heater. J. Phys.: Conf. Ser. 97, 012159 (6pp). [11] Sivasubramaniam, K., Laskaris, E.T. & Ryan. D., (2003). Suitability of MgB2 tapes with iron sheaths for multiturn superconducting coils. IEEE Trans. Appl. Supercond., 13, 3277-3279. ˇ [12] G¨ om¨ ory, F., Souc, J., Seiler, E., Klinˇcok, B., Vojenˇciak, M., Alamgir, A.K.M., Han, Z. & Gu, C., (2007). Performance improvement of superconducting tapes due to ferromagnetic cover on edges. IEEE Trans. Appl. Supercond., 17, 3083-3086. [13] Wilson, M.N., (1983). Superconducting Magnets. Oxford: Oxford University Press. [14] Eyssa, Y.M. & Markiewicz, W.D., (1995). Quench simulation and thermal diffusion in epoxy-impregnated magnet system. IEEE Trans. Appl. Supercond., 5, 487-490.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[15] Eyssa, Y.M., Markiewicz, W.D. & Miller, J., (1997). Quench, thermal, and magnetic analysis computer code for superconducting solenoids. IEEE Trans. Appl. Supercond., 7, 159-162. [16] Yamada, R., Marscin, E., Lee, A., Wake, M. & Rey, J-M., (2003). 3-D/2-D quench simulation using ANSYS for epoxy impregnated Nb 3Sn high magnetic field magnets. IEEE Trans. Appl. Supercond., 13, 1696-1699. [17] Picaud, V., Hiebel, P. & Kauffmann, J-M., (2002). Superconducting coils quench simulation, the Wilson’s method revisited. IEEE Trans. Magn., 38, 1253-1256. [18] Tominaka, T., Mori, K. & Maki, N., (1992). Quench analysis of superconducting magnet systems. IEEE Trans. Magn., 28, 727-730. [19] Oshima, M., Thome, R.J., Mann, W.R. & Pillsbury, R.D., (1991). PQUENCH - a 3-D quench propagation code using a logical coordinate system. IEEE Trans. Magn., 27, 2096-2099. [20] Gavrilin, A.V. (1993). Computed simulation of thermal process during quench in superconducting winding solenoid. IEEE Trans. Appl. Supercond., 3, 293-296. [21] Stenvall, A., Korpela, A., Mikkonen, R. & Grasso, G., (2006). Quench analysis of MgB2 coils with a ferromagnetic matrix. Supercond. Sci. Technol., 19, 581-588. [22] Stenvall, A., Korpela, A., Lehtonen, J. & Mikkonen, R., (2008). The effect of local damage inside a winding on quench behavior in an Nb 3 Sn magnet. IEEE Trans. Appl. Supercond., 18, 1271-1274. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

152

Antti Stenvall and Risto Mikkonen

[23] Lehtonen, J., Mikkonen, R. & Paasi, J., (2000). Effective thermal conductivity in HTS coils. Cryogenics, 40, 245-249. [24] Masson, P.J., Rouault, V.R., Hoffmann, G. & Luongo, C.A., (2008). Development of quench propagation models for coated conductors. IEEE Trans. Appl. Supercond., 18, 1321-1324.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[25] Stenvall, A., Korpela, A., Lehtonen, J. & Mikkonen, R., (2008). Formulation for 1D minimum propagation zone. Physica C, 468, 968-973.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

In: Magnesium Diboride (MgB2) Superconductor Research ISBN: 978-1-60456-566-9 Editors: S. Suzuki and K. Fukuda © 2009 Nova Science Publishers, Inc.

Chapter 6

THEORIES OF PEAK EFFECT AND ANOMALOUS HALL EFFECT IN SUPERCONDUCTING MGB2 Wei Yeu Chen and Ming Ju Chou Department of Physics, Tamkang University, Tamsui 25137, Taiwan

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Abstract Magnesium diboride, MgB2 , has the highest Tc of 40 K for intermetallic compounds with anisotropic type-II superconductors. The promising potential in application has attracted numerous attentions on this novel material. In this chapter, we shall first investigate the quasiorder-disorder first-order phase transition or the peak effect and then study the anomalous Hall effect of superconducting MgB2 . It is well understood that the presence of impurities due to quenched disorder, doping or irradiation destroy the long-range order of flux line lattice, after which only short-range order, the vortex bundles, remains. If the applied magnetic field or the temperature increases, a first-order phase transition between the shortrange order and disorder in the vortex system eventually appears owing to enormous increase in the dislocations inside the short-range domains. The origin of peak effect is in this kind of first-order phase transition. The peak value of the critical current density J c , the exact peak position and its corresponding half-width for a constant temperature as well as for a constant applied magnetic field, are obtained by calculating the critical current density explicitly. All the results are in good agreement with the experiments. The anomalous Hall effect for MgB2 is also studied based upon the theory of thermally activated motion of vortex bundles over a directional-dependent energy barrier. It is shown that the directional-dependent potential barrier renormalizes the Hall and longitudinal resistivities and the Hall anomaly is induced by the competition between the Magus force and the random collective pinning force of the vortex bundle. The Hall and longitudinal resistivities as functions of temperature and applied magnetic field for the thermally activated motion of vortex bundles are obtained. The double sign reversal, or reentry phenomenon, is also investigated. These studies are essential because they might provide some important information for their future applications.

Keywords: Peak effect,; Quasiorder-disorder phase transition, Anomalous Hall effect, Collective pinning, Intermetallic compound, Random walk theorem

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

154

Wei Yeu Chen and Ming Ju Chou

1. Introduction The discovery of magnesium diboride, MgB2 compound [1] has encouraged extensive scientific research [2-5]. MgB2 has the highest critical temperature Tc of 40 K for the intermetallic compounds with a hexangonal A1B2 structure. It possesses a two-band/two-gap and possible phonon-mediated anisotropic type-II superconductors [1-45] with less anisotropy than high- Tc cuprates. Its sample-dependent anisotropic constant γ = H cab / H cc2 is in the interval 2 ≤ γ ≤ 6 . The absence of the weak link problem, fewer material complexities, longer coherence length ( ξ ~ 5 n m ), and suitability for fabrication of good Josephson junctions in MgB2 samples make it attractive for practical applications. Recently, we [6] have developed a theory for the quasiorder-disorder first-order phase transition in the vortex system and a theory of thermally activated motion of vortex bundles over a directional-dependent energy barrier [7]. Based on the framework of our theories, we investigate the peak effect and anomalous Hall effect for this fascinating MgB2 material. The

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

presence of impurities due to quenched disorder, doping or irradiation destroy the long-range order of flux line lattice, after which only short-range order, the vortex bundles, remains [6, 7, 8]. For low temperature and applied magnetic field, the transverse size of short-range order, the vortex bundle, is approximately 10 −6 m. This is the region of large vortex bundles. If the applied magnetic field increases for a fixed temperature or the temperature increases for a fixed magnetic field, a quasiorder-disorder first-order phase transition between the shortrange order and disorder in the vortex system, or the peak effect eventually occurs [6] due to the enormous increase in the dislocations inside the short-range domains. In this case, the vortex lines become a disordered amorphous vortex system. However, they are not individual single quantized vortex lines; the vortex lines still bound close together to form small vortex bundles of the dimension R ≅ 10 −8 m . This is the region of small vortex bundles of the vortex system. In this chapter, we shall determine the peak value of the critical current density J c , the exact peak position and its corresponding half-width for a constant temperature as well as for a constant applied magnetic field by calculating the critical current density explicitly. On the other hand, based on the theory of thermally activated motion of vortex bundles jumping over the directional-dependent potential barrier, we investigate the anomalous Hall effect for MgB2 . It is shown that the directional-dependent potential barrier renormalizes the Hall and longitudinal resisitivities strongly, and the Hall anomaly is induced by the competition between the Magnus force and the random collective pinning force of the vortex bundles. We also find that the domains of anomalous Hall effect includes two regions [7], namely, the region of thermally activated motion of small vortex bundles and that of the large vortex bundles, separated by the contour of the quasiorder-disorder first-order phase transition or the peak effect [6] of the vortex system. The Hall and longitudinal resistivities as functions of temperature and applied magnetic field are also calculated. This chapter is organized as follows: The theory of peak effect is presented in Sec.2. It is shown that the peak effect is induced by the quasiorder-disorder first-order phase transition of the vortex system. We calculate the volume of the short-range order of the vortex system

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2

155

during this kind of first-order phase transition by evaluating the random, thermal, and quantum averages of the displacement of the vortex lattice inside the short-range order. The peak effect is then investigated by calculating the critical current density of the vortex bundle directly. The peak value of the critical current density J c , the exact peak position and the corresponding half-width for a constant temperature as well as for a constant applied magnetic field are also obtained. In Sec.3, we develop a theory of thermally activated motion of vortex bundles jumping over a directional-dependent potential barrier. Based on this theory, we investigate the anomalous Hall effect for type-II superconductors and the condition for the appearance of this fascinating phenomenon. The Hall and longitudinal resistivities are also calculated. Sec. 4 is devoted to a conclusive remarks.

2. Theory of Peak Effect for Type-II Superconductors The critical current density usually decreases with increasing applied magnetic field for a fixed temperature or as the temperature is increased for a fixed applied magnetic field in pristine MgB2 samples. However, for doping or neutron irradiation samples, the peak effect in

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

the critical current density is observed as a function of the applied magnetic field for a constant temperature or as a function of temperature for a constant applied magnetic field [4, 5]. The presence of impurities destroys the long-range order of flux line lattice; only shortrange order, the vortex bundles, remains [6, 7, 8]. In particular, if the applied magnetic field increases for a fixed temperature or the temperature increases for a fixed magnetic field, a quasiorder-disorder first-order phase transition between the short-range order and disorder in the vortex system, or the peak effect, eventually occurs [6] due to the enormous increase in the dislocations inside the short-range domains. In this section we would like to investigate this quasiorder-disorder first-order phase transition in great details.

2.1. Mathematical Description of the Model Let us consider a type-II conventional and high- Tc superconductor. The Hamiltonian of the fluctuation for the flux line lattice (FLL) in the z − direction is given by [9, 10, 11],

H = H f + HR ,

(1)

where H f = H kin + H e represents the Hamiltonian for the free modes, with H kin the kinetic energy part [9],

H kin =

1 2ρ

∑μ Pμ ( K ) Pμ (− K ) , K

H e the elastic energy part [9, 12],

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

(2)

156

Wei Yeu Chen and Ming Ju Chou

He =

∑

1 1 C L K μ K ν S μ ( K ) Sν ( − K ) + 2 Kμν 2

∑μ (C

2 66 K ⊥

+ C 44 K z2 ) S μ ( K ) S μ (− K ) ,

(3)

K

and H R represents the random Hamiltonian, given as [9, 10, 11],

H R = ∑ f Rμ ( K ) S μ (− K ) ,

(4)

Kμ

where ( μ ,ν ) = ( x, y ) , ρ is the effective mass density of the flux line, K ⊥2 = K x2 + K y2 ,

Pμ ( K ), S μ ( K ) are the Fourier transformations of the momentum and displacement operators and C L , C11 , C 44 and C 66 are temperature- and K -dependent bulk modulus, compression modulus, tilt modulus and shear modulus, respectively. f R (K ) is the Fourier transformation of the total random pinning force f R (r ) = −∇ (VCR (r ) + VSR (r )) , with VCR (r ) the random potential energy of the collective pinning, which is the sum of the contributions of defects within a distance ξ of the vortex core position r , where ξ is the temperaturedependent coherent length and VSR (r ) the random potential energy of strong pinning. The

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

correlation functions of the total random pinning force are assumed to be the short-range correlation,

th are the thermal, quantum, and random averages, and

β (T , B) is the

temperature- and magnetic field-dependent correlation strength. The equation of motion for the operator S μ (K ) can be obtained from Eq. (1) as ••

ρ S μ ( K ) + C L ( K ⋅ S ( K )) K μ + (C 66 K ⊥2 + C 44 K z2 ) S μ ( K ) + f μ ( K ) = 0 ,

(6)

Then the solution of Eq. (6) can be obtained as

S μ ( K ) = S Rμ ( K ) + S f μ ( K ) ,

(7)

where S Rμ (K ) stands for the deformation displacement operator of the FLL due to the collective pinning of the random function f Rμ (K ) and S fμ (K ) is the displacement operator for the fluctuation of the free modes. They are given by

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2 S Rμ ( K ) = [( K ⋅ f R ( K ))

δ α ,1 K⊥

]⋅

1 C11 K ⊥2

+ C 44 K z2

+ [ f Rα ( K ) − ( K ⋅ f R ( K ))

δ α ,1 K⊥

]⋅

157

1 C 66 K ⊥2

+ C 44 K z2

,

(8) and

S fμ ( K ) =

2 ρω Kμ

(α −+Kμ + α Kμ ) ,

(9)

respectively, where μ = 1 represents the component that parallel to K ⊥ direction, while

μ = 2 perpendicular to the K ⊥ direction. It is understood that the free Hamiltonian can be diagonalized with the eigenmodes spectrum [9],

ω K1 = [

1

ρ

(C11 K ⊥2

+

1 2 2 C 44 K z )]

,

1

1

ω K 2 = [ (C 66 K ⊥2 + C 44 K z2 )] 2 , ρ

(10)

with α K+μ , α Kμ are the creation and the annihilation operators for the corresponding

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

eigenmodes.

2.2. Critical Current Density And Peak Effect For Type-II Superconducting Films In this subsection we would like first to calculate the critical current density for type-II superconducting films in thermodynamic equilibrium. By taking into account the balance of the Lorentz force and the collective pinning force, the critical current density J c can be obtained as follows:

1 β (T , B) 2 [ ] , B π R2 d 1

Jc =

(11)

where B is the applied magnet field, d is the thickness of the superconducting films, with

d > λ0 , where λ0 is the penetration depth at zero temperature, R is the transverse size of the short-range order during the quasiorder to disorder phase transition, and can be determined by the following condition,

>th = γ a02 , Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

(12)

158

where

Wei Yeu Chen and Ming Ju Chou

γ is a dimensionless constance, a 0 = (

2Φ 0

1

3B

) 2 is the lattice constant and Φ 0 stands

for the unit flux. Taking into account the fact that C11 >> C 66 , after some algebra, we obtain

>th =

π

d 2k nπ z 2 [ 1 − cos ( + K ⊥ R cosθ )] ∑ 2 ∫ d n = −∞ (2π ) d ω2 f B ( ω2 ) β (T , B) ], ×[ + n nπ π C66 K ⊥2 + C44 ( ) 2 (C66 K ⊥2 + C44 ( ) 2 ) 2 d d ∞

(13)

where f B is the Bose-Einstein distribution function, R = | R | , θ is the angle between K ⊥

2π , … . Taking the classical d d limit, and considering the non-dispersive regime of the above equation, we arrive at

and R , and the possible values of k z are given by 0, ±

π

,±

2 π k B T 1 β (T , B) R 2 ⋅ + , 2 2 d C66 C44C66 ξ 0

>th =

(14)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

where k B is the Boltzmann constant and ξ 0 is the coherent length at zero temperature. In deriving the above equation, the summation has been carried out by contour integration, and 1 the cutoff value for small k has been used. Inserting Eqs (12), and (14) into Eq. (11), we R obtain,

β (T , B)

Jc =

1

( 2 π ) d B C66 [ γ

where C 66 =

B Φ0 16 π μ 0 λ

2

,

C 44 =

B2

μ0

a02

2 π kB T 1 2 − ⋅ ] C44C66 ξ 0

, λ=

λ0 T 1− TC

, ξ=

.

ξ0 T 1− TC

(15)

,

μ 0 is the

permeability and Tc is the critical temperature of the superconductor. For a constant applied magnetic field the numerator in Eq. (15) is a decreasing function of temperature due to the reduction of condensation energy, while the denominator is also a decreasing function of temperature; therefore, there will exist a peak of the critical current density J c for constant applied magnetic field. This peak critical current density J c appears at temperature TP , when the conditions are satisfied,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2

159

∂ J c (TP , B ) ∂ 2 J c (TP , B ) | B = 0 and |B < 0 , ∂T ∂T2

(16)

and the half-width of the peak is obtained as, 1

ΔThalf − width = [

J c (TP , B ) ]2 . 2 ∂ J c (TP , B) |( |B ) | ∂T 2

(17)

However, in the case of constant temperature, if the applied magnetic field is not too close to the upper critical field BC 2 , the numerator is an increasing function of the applied magnetic field due to the increasing vortex density, while the denominator is also an increasing function of the applied magnetic field B. In this case, there will be a peak critical current density J c at some value B P of the applied field. The peak of the critical current density appears when the following criteria are satisfied:

∂ 2 J c (T , BP ) ∂ J c (T , BP ) |T = 0 and |T < 0 , ∂B ∂ B2

(18)

The corresponding half-width of the peak is given by 1

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

ΔBhalf − width

J (T , BP ) )2 . =( 2 c ∂ J c (T , BP ) |( |T ) | ∂B 2

(19)

All the above derivations are independent of the mechanism for the superconductivity. Therefore our theory is applicable for both conventional and high- Tc superconductors.

2.3. Critical Current Density And Peak Effect For Superconducting Bulk Materials In this subsection we first calculate the critical current density for three-dimensional superconducting bulk materials. By considering the balance of Lorentz force and the collective pinning force, the critical current density J c is given as, 1

Jc =

[ β (T , B)]2 B [π R L] 2

1 2

,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

(20)

160

Wei Yeu Chen and Ming Ju Chou

where R and L are the transverse and longitudinal sizes of the short-range order during the quasiorder to disorder phase transition, and they can be determined by the following phase transition condition:

>th = γ a02 .

(21)

Once again, > th are the random, thermal and quantum averages and

γ is a

dimensionless constance. After some algebra, we obtain

>th =∫

ω2 f B ( ω2 ) β (T , B) d 3k 2 [ 1 − cos ( K ⊥ ⋅ R + k z L)] ⋅ [ ] , (22) + 2 2 3 (2π ) C66 K ⊥ + C44 k z (C66 K ⊥2 + C44 k z2 ) 2

where f B is the Bose-Einstein distribution function. In deriving the above equation, we have taken into account the fact that C11 >> C 66 . Taking the classical limit, considering only the non-dispersive regime of the vortex bundle, the above equation becomes

β (T , B ) ( R + 2

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

>th =

kB T 1 ⋅ + 2 π C44C66 ξ0

a02 L2

λ2

1 )2

, (23)

2π 2C66 C44C66

where ξ 0 is the penetration depth at zero temperature, λ is the temperature dependent penetration depth and k B is the Boltzmann constant. In deriving the above equation we have performed the average over ϕ , which is the angle between the K ⊥ and R , and used the cutoff values for small k as k S = 2 ( R + 2

a 02 L2

λ

2

1 2

) and for large k as k L =

1

ξ0

, respectively.

Substituting Eq. (23) back to Eq. (20), we obtain, finally,

[ β (T , B)]2

Jc = B[

πλ a0

1 ]2

3

[ 2 π 2C66 C44C66

.

(24)

k T 1 ( γ a02 − 2 B ⋅ ) ]2 π C44C66 ξ 0

It is worthwhile to point out that, from the above equation, for the constant applied magnetic field, B , the numerator is a decreasing function of temperature, T, due to the reduction of condensation energy; however, the denominator is also a decreasing function of temperature, therefore there will exist a peak in the critical current density J c for a constant

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

161

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2

applied magnetic field B. On the other hand, considering the situation of constant temperature, if the applied magnetic field is not too close to the upper critical field BC 2 the numerator is an increasing function of the applied magnetic field owing to the increasing of vortex density. Moreover, the denominator is also an increasing function of the applied magnetic field B, hence there will exist a peak in the critical current density J c at some value

BP of the applied magnetic field. For a constant applied magnetic field, as we have pointed out above, there will be a peak in the critical current density J c at some value of temperature TP for a constant applied field B , the conditions for the peak of the critical current density J c appearing at temperature

TP are ∂ 2 J c (TP , B ) ∂ J c (TP , B ) |B < 0 , | B = 0 and ∂T ∂T2

(25)

and the half-width of the peak is given by 1

ΔThalf − width = [

J c (TP , B ) ]2 . 2 ∂ J c (TP , B) |( |B ) | ∂T 2

(26)

It is interesting to make the numerical estimates of the above results: for an applied magnetic field B = 0.639 T we have obtained the peak temperature TP = 30 K , the Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

−7

transverse size of the short-range order R = 4.194 × 10 m , the longitudinal range of the short-range

−6

order L = 1.908 × 10 m ,

the

critical

current

density

of

the

peak

A J c (TP , B) = 3 × 108 2 and the half-width of the peak for a constant applied magnetic m field ΔThalf − width = 2.5 K . From the above results, we find that the vortex bundle is indeed in the non-dispersion regime, which is consistent with our original assumption. These values are in good agreement with the experimental results for MgB2 superconducting bulk materials [4]. In obtaining the above results, the following approximate data have been employed:

TC = 38.2 K , β (TP , B) = 4.192 × 10− 2

2 N 2 ∂β (TP , B) −3 N = − 5 . 119 × 10 , , ∂T m3 K m3

2 ∂ 2 β (TP , B ) −9 −7 −3 N = − 3 . 353 × 10 , γ = 0.09 , ξ 0 = 5 × 10 m , λ0 = 1.2 × 10 m . 2 3 2 m K ∂T

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

162

Wei Yeu Chen and Ming Ju Chou

Considering the situation when the temperature of the system is kept at a constant value T ; if the applied magnetic field is not too close to BC 2 there will be a peak of the critical current density J c at some value B P of the applied field. The conditions for the peak of the critical current density J c are

∂ 2 J c (T , BP ) ∂ J c (T , BP ) |T < 0 . |T = 0 and ∂B ∂ B2

(27)

The corresponding half-width of the peak is given by 1

ΔBhalf − width = (

J c (T , BP ) )2 . 2 ∂ J c (T , BP ) |( |T ) | ∂B 2

(28)

Numerical estimation of the above results shows that when T = 30 K we obtained

BP = 0.639 T , the transverse size of the short-range order R = 4.194 × 10−7 m , the −6

longitudinal range of the short-range order L = 1.908 × 10 m , the peak of the critical current density for the constant temperature J c (T , BP ) = 3 × 10

8

A and the corresponding m2

half-width of the peak ΔBhalf − width = 0.167 T . From the above results, we show that the

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

vortex bundle is indeed in the non-dispersion regime, consistent with our original assumption. These values are exactly in agreement with the experimental results for MgB2 superconducting bulk materials [4], where the following approximate data have been used: TC = 38 . 2 K ,

N2 m3

β (T , B P ) = 4 . 192 × 10 − 2

∂ 2 β (T , B P ) N2 , = − 1 . 849 ∂ B2 m3 T 2

γ = 0.09 , ξ

0

∂ β (T , B P ) = 1 . 148 × 10 ∂B

,

= 5 × 10

− 9

m

, and

−1

N2 m3T

,

λ0 = 1.2 × 10 − 9 m .

3. Theory of Anomalous Hall Effect for Type-II Superconductors In this section we would like to discuss the anomalous Hall effect for type-II superconductors and the conditions of the appearance of this Hall anomaly for MgB2 superconducting samples. This Hall anomaly is the most confusing and controversial phenomenon for type-II superconductors in the last forty decades since it was first observed by van Beelen et al., [13] in 1967. Experimental data show that when the temperature is slightly below the critical temperature, the Hall resistivity in many type-II superconductors changes its sign as the temperature or applied magnetic field decreases. In some occasions, the observed Hall

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2

163

resistivity exhibits the double sign reversal, or the reentry phenomenon. Various theories, trying to explain this anomaly, have been proposed, such as the large thermomagnetic model [14], flux flow [15], opposing drift of quasiparticles [16], vortex and effective antivortex [17] and many others [18]. However, up to the present time, there is no satisfactory explanation for this sign reversal of the Hall resistivity. The origin of this Hall anomaly still remains unsolved. Recently, we [7] have developed a self-consistent theory for the thermally activated motion of the vortex bundles, under the steady-state condition, jumping over the directionaldependent potential barrier generated by the Magnus force, the random collective pinning force and the strong pinning force inside the vortex bundle. The directional-dependent energy barrier means that the energy barrier is different when the direction of thermally activated motion is different. Based on this theory, it is shown that the Hall anomaly is universal for type-II conventional and high- TC superconductors as well as for superconducting bulk materials and thin films, provided certain conditions are satisfied. We find that the directional-dependent potential barrier of the vortex bundles renormalizes the Hall and longitudinal resistivities, and the anomalous Hall effect is induced by the competition between the Magnus force and the random collective pinning force of the vortex bundle. Our results demonstrate that the domain of Hall anomaly includes two regions: the region of thermally activated motion of the small vortex bundles and that of the large vortex bundles separated by the contour of the quasiorder-disorder first-order phase transition or the peak effect [6] of the vortex system. For applied magnetic field (temperature) below the quasiorder-disorder first-order phase transition magnetic field B p (temperature T p ), the vortex system belongs to the region of thermally activated motion of large vortex bundles with the transverse size of the short-range order is approximately 10 −6 m. However, if the

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

applied magnetic field (temperature) increases beyond B p ( Tp ), a quasiorder-disorder firstorder phase transition between the short-range order and disorder in the vortex system, or the peak effect eventually occurs [6] due to the enormous increase in the dislocations inside the short-range domains. In this case, the vortex lines become a disordered amorphous vortex system. However, they are not individual single quantized vortex lines, the vortex lines still bounded close together to form small vortex bundles of the dimension R ≅ 10 −8 m . In this case, the region belongs to that of the thermally activated motion of small vortex bundles. Under the framework of our theory, the Hall and longitudinal resistivities as functions of temperature as well as applied magnetic field are calculated for type-II superconducting films and bulk materials.

3.1. Mathematical Model for Anomalous Hall Effect To proceed we first calculate the coherent frequency of the vortex bundle by random walk theorem. From the theory of forced oscillations, it is understood that the response function of the vortex line oscillates inside the potential barrier due to thermal agitation. By identifying the oscillation energy of the vortex line inside the potential barrier with the thermal energy, the thermal oscillation frequency of the individual vortex inside the potential barrier can be expressed as

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

164

Wei Yeu Chen and Ming Ju Chou

ν =ν T ,

(29)

1 kB , A stands for the average π A 2m amplitude of the oscillation, k B is the Boltzmann constant and m is the mass of the vortex

where the proportional constant ν is given by

ν =

line [19]. It is worthwhile to point out that the viscous damping of the vortex line is included implicitly in the average amplitude A . However, the oscillations of vortex lines inside the vortex bundle are not coherent, namely, their oscillations are at random. To obtain the coherent oscillation frequency ν C of the vortex bundle as a whole, by applying the random walk’s theorem, the frequency ν in equation (29) must be divided by the square root of N, the number of vortices inside the vortex bundle

νC =

ν N

=

ν T Φ0 R πB

,

(30)

where Φ 0 is the unit flux, R is the transverse size of the vortex bundle and B is the value of the applied magnetic field. The essential property can be comprehended by considering the problem of random walk. Let l0 be the length of each individual step, for a walk with N steps, if the walk were coherently in the same direction, the total length of N steps would be L = N l0 ; however, these steps are not coherently in the same direction, they are at random.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

With the aim of receiving the length of the random walk with N steps, the above expression must be divided by the square-root of N

L=

N l0 N

= N l0 ,

(31)

this is the desired answer for the random walk with N steps. Next we would like to evaluate the root-mean-square of the angle between the random collective pinning force and positive y-direction. Let us consider the case for p-type superconductors with current flowing in the positive x-direction and the applied magnetic field in the positive z-direction. If we assume that the mean angle between the random collective pinning force of a vortex line inside the vortex bundle and the positive y-direction measured in counterclockwise sense is θ , this temperature- and field-dependent θ can be obtained as follows: Since θ is small, we can approximately write θ ≅

| f el | | fL |

, | f el | and

| f L | are the magnitudes of the elastic force and the Lorentz force of the vortex line. Taking into account the fact that the compression modulus C11 is much larger than the shear modulus C66 [6], owing to the thermal fluctuations, the magnitude of the displacement vector

| S f ( r ) | of the vortex line inside the vortex bundle as well as its corresponding magnitude of Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2 the elastic force | f el | is proportional to

k B C66 or ( 1

B)

165

T TC − T [6, 9, 18], TC is

the critical temperature of the superconductors. The temperature- and field-dependent θ can now be expressed as

θ (T , B ) = α '

T , TC − T

1 B

(32)

α ′ is a proportional constant. The mean angle Θ (T , B) between the random collective pinning force of vortex bundle and the positive y-direction measured in counterclockwise sense, by the theory of random walk, can be written as

Θ(T , B ) = N θ (T , B ) = α

T , TC − T

(33)

with α = α ′ R π / Φ 0 . The root-mean-square value of the angle between the random collective pinning force for the vortex bundle and the positive y-direction in counterclockwise sense can now be obtained as π

Ψ

2 = [ ∫φ2 −π 2

exp(

−φ2 Θ 2 (T , B )

π

) dφ /

2 ∫ −π 2

exp (

−φ2 Θ 2 (T , B )

)

1 dφ ] 2 .

(34)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Keeping in mind the fact that Θ(T , B ) is usually very small in our theory, we obtain

Ψ ≅ Θ(T , B ) = α

T . TC − T

(35)

Finally, we evaluate the Hall and longitudinal resistivities through the calculation of directional-dependent energy barrier of the vortex bundles formed by the Magnus force, the random collective pinning force together with the strong pinning force inside the vortex bundle for the magnetic field in the z-direction B = B ez and the transport current in the xdirection J = J e x . Considering the case where the magnitude of Lorentz force JB is slightly greater than the magnitude of the random collective pinning force, after some algebra, the directional-dependent energy barrier of the vortex bundles both in the positive and negative x-direction as well as the positive and negative y-direction are obtained respectively as

U + V R ( JB

vby vT

− < Fp x > R ) ,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

(36)

166

Wei Yeu Chen and Ming Ju Chou

U − V R ( JB

vby vT

− < Fp x > R ) ,

(37)

U + V R ( JB − JB

vbx − < Fp y > R ) , vT

(38)

U − V R ( JB − JB

vbx − < Fp y > R ) , vT

(39)

where the potential barrier U is generated by the strong pinning force due to the randomly distributed strong pinning sites inside the vortex bundle, vb ( vT ) is the velocity of the vortex bundle (super current), V is the volume of the vortex bundle, once again, R represents the transverse size of the vortex bundle, the range of U is assumed to be the order of R and

< F p > R stands for the random average of the random collective pinning force per unit volume. The self-consistent equations for the velocity of the thermally activated motion of the vortex bundles jumping over the directional-dependent energy barrier are therefore obtained in components as

vbx = ν C R {exp[

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

− exp[

v −1 ( U + V R ( JB by − < Fp x > R ))] vT k BT

v −1 ( U − V R ( JB by − < Fp x > R )) ]} , vT k BT

(40)

and

vby = ν C R {exp[ − exp [

v −1 ( U + V R ( JB − JB bx − < Fp y > R ))] k BT vT

v −1 ( U − V R ( JB − JB bx − < Fp y > R ))]} , k BT vT

(41)

where ν C is the coherent oscillation frequency of the vortex bundle jumping over the directional-dependent potential barrier from one equilibrium position to another. Taking into v account the fact that bx R | sin Ψ )] k BT k BT vT R πB

ν

vbx = (

− exp[

+ V R − JB | vby | ( + |< Fp > R | sin Ψ )]} , k BT vT

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

(42)

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2

167

ν

vby = (

−U −V R T Φ0 ) R exp( ) {exp[ ( JB − |< Fp > R | cos Ψ )] k BT k BT R πB

− exp[

+V R ( JB − |< Fp > R | cos Ψ )]} , k BT

(43)

where Ψ is the root-mean-square value of the angle between the random collective pinning force of the vortex bundles and the positive y -direction measured in the counterclockwise

Ey Ex , ρ xy = together with Eq. J J (35) and keeping in mind that Ψ is usually very small, the longitudinal and Hall resistivities, can now be written respectively as follows: sense. By considering the identities E = −vb × B , ρ xx =

ρ xx =

ν BT Φ0

1

exp(

J π

ρ xy =

−ν

BT Φ0 J π

1

β C (T , B) 2 β C (T , B) 2 VR −U −VR ){exp[ ( JB − ( ) )] − exp[ ( JB − ( ) )]} , k BT k BT k BT V V

exp(

(44)

1 | vby | −U V R β C (T , B ) 2 T ){exp [ (( ) α )] − JB k BT k BT TC − T vT V

1 | vby | − V R β C (T , B ) 2 T (( ) α )]} , − exp [ − JB k BT TC − T vT V

(45)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

and

| vby |= Jρ xx / B ,

with (

β C (T , B )

(46)

1

) 2 is the magnitude of the random collective pinning force per unit volume,

V α is a proportional constant. It is clear that, from the above calculations, the directionaldependent potential barrier of the vortex bundle renormalized the Hall and longitudinal resistivities. Taking into account the fact that the arguments in the exponential functions inside the curly bracket of Eqs. (44) and (45) are very small when the Lorentz force is close to the random collective pinning force, we finally obtain the temperature- and field-dependent longitudinal and Hall resistivities as ρ xx =

ρ xy =

−ν

ν B Φ0 J πT

B Φ0

J πT

1

exp (

−U 2V R β C (T , B ) 2 ) ( ) [ JB − ( ) )] , k BT kB V

1 | vby | − U 2V R T β C (T , B ) 2 − JB exp( )( ) [( ) α ] , k BT kB TC − T vT V

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

(47)

(48)

168

Wei Yeu Chen and Ming Ju Chou

with | vby |= Jρ xx / B . Let us assume that the vortex system is initially in the region of the thermally activated motion of small vortex bundles. From our previous study [6], the value of 1

1 β C (T , B) 2 ( ) increases with decreasing applied magnetic field when the temperature of B V the system is kept at a constant value T ; if this value passes the value of | vby | T ( ) / (α ) , then ρ xy changes sign from positive to negative with decreasing vT TC − T 1

1 β C (T , B ) 2 applied magnetic field. On the other hand, the value of ( ) increases and that of B V

α

T decreases as temperature decreasing when the applied magnetic field is kept at a TC − T 1

constant B . Therefore, the term

1 β C (T , B) 2 T ( ) α B V TC − T

exists a maximum at some

| vby |

J ρ vT T , if this maximum is greater than , then xy possesses the sign temperature reversal property. From the above analysis, the sign reversal of the Hall resistivity appears when the following condition is satisfied: 1

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

| vby | 1 β C (T , B ) 2 T ( ) α >J , B V TC − T vT

(49)

provided T p ( B p ) is not too close to Tc ( Bc2 ). The sign reversal phenomenon could be therefore observed for heavily doped or highly irradiated fast neutron fluence MgB2 samples. The above results demonstrate the fact that the anomalous Hall effect is induced by the competition between the Magnus force and the random collective pinning force. It is interesting to note that ρ xy might appear the double sign reversal property, the detailed 1

1 β C (T , B) 2 ( ) increases B V with decreasing temperature (applied magnetic field); therefore, ρ xx decreases monotonically as temperature (applied magnetic field) decreases. As we have mentioned in the Introduction, when temperature (applied magnetic field) decreases below T p ( B p ) , the quasiorder-disorder discussion will be given in Sec. 3.4. Moreover, since the value of

first-order phase transition temperature (magnetic field) of the vortex system, the region crosses over to that of thermally activated motion of large vortex bundles. In this region, the potential barrier U generated by the randomly distributed strong pinning sites inside the bundle is large, in this case both the Hall and longitudinal resistivities decay to zero quickly with decreasing temperature (magnetic field). Based on the above analysis, the Hall anomaly is independent of the mechanism for the superconductors and the expression of V , the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2

169

volume for the vortex bundle. In other words, these anomalous properties are universal for type-II conventional and high- Tc superconductors as well as for superconducting bulk materials and thin films, provided the conditions given above are satisfied. More detailed calculations and discussion will be given in the following subsections.

3.2. Anomalous Hall Effect for Type-II Superconducting Bulk Materials For superconducting bulk materials, the volume V for the vortex bundle in Eqs. (47) and (48) is given as V = π R L , where R (L) is the transverse (longitudinal) size of the vortex 2

bundle. In this case, the longitudinal and Hall resistivities for type-II superconducting bulk materials therefore become

ρ xx =

ρ xy =

ν Φ0 B J π T

−ν Φ0 B J π T

1

β C (T , B) 2 − U 2π R 3 L )[ ][ JB − ( ) ] , kB k BT V

(50)

|v | − U 2 π R 3 L β C (T , B) 2 T )[ ] [( ) α − JB by ] , vT TC − T k BT kB V

(51)

exp(

1

exp(

with | vby |= Jρ xx / B . As we have indicated in Sec. 3.1, the above equations give rise to the

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

phenomenon of anomalous Hall effect, namely, the value of ρ xy changes it sign from positive to negative with decreasing applied magnetic field (temperature). We will discuss the cases for constant temperature and constant applied magnetic field separately as follows. Under the framework of our theory, when the system is initially in the region of thermally activated motion of small vortex bundles ρ xy possesses the desired anomaly properties as applied magnetic field decreases when the temperature of the system is kept at a constant value T . Moreover, from our previous study [6], it is shown that the quasiorder-disorder first-order phase transition of the vortex system occurs if the applied field decreases below B p , then the region crosses over to that of the thermally activated motion of large vortex bundles. In this region, the potential barrier U generated by the randomly distributed strong pinning sites inside the vortex bundle becomes large; hence, both the Hall and longitudinal resistivities approach to zero quickly with decreasing applied magnetic field. For constant applied magnetic field, within our theoretical framework, the Hall resistivity changes its sign from positive to negative as the temperature decreases for constant applied magnetic field. From our [6] previous study, it has been shown that the quasiorder-disorder first-order phase transition of the vortex system takes place when the temperature decreases below Tp , then the region crosses over to that of the thermally activated motion of large vortex bundles. In this region, the potential barrier U generated by the randomly distributed strong pinning sites within the vortex bundle becomes large; therefore, both the Hall and longitudinal resistivities reduce to zero quickly with decreasing temperature.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

170

Wei Yeu Chen and Ming Ju Chou

3.3. Anomalous Hall Effect for Type-II Superconducting Films Now we discuss the anomalous Hall effect for type-II superconducting films. In this case, the volume V for the vortex bundle in Eqs. (47) and (48) is given by V = π R d , where R is 2

the transverse size of the vortex bundle and d is the thickness of the film. The Hall and longitudinal resistivities therefore become

ρ xx =

ρ xy =

ν Φ0 B

(52)

|v | T β C (T , B) 2 − U 2 π R 3d )[ ] [( ) α − JB by ] , k BT kB V TC − T vT

(53)

J π T

−ν Φ 0 B J π T

1

β C (T , B) 2 − U 2π R 3d )[ ][ JB − ( ) ] , k BT kB V

exp(

1

exp (

with | vby |= Jρ xx / B . As we have discussed in Sec. 3.1, the above equations lead to the phenomenon of anomalous Hall effect for both the constant applied magnetic field and constant temperature. We will examine these cases separately as follows. Within the framework of our theory, it is shown that when the system is initially in the region of thermally activated motion of small vortex bundles the Hall resistivity ρ xy changes its sign from positive to negative as the applied magnetic field decreases when the temperature of the system is kept at a constant value T . The quasiorder-disorder first-order phase transition of the vortex system takes place [6] when the applied magnetic field decreases below B p . In this case, the region belongs to the thermally activated motion of

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

large vortex bundles. The potential barrier U generated by the randomly distributed strong pinning sites within the vortex bundle becomes large; hence both ρ xy and ρ xx reduce to zero rapidly. For constant applied magnetic field when T > T p , based on our theory, the Hall resistivity

ρ xy changes its sign from positive to negative as the temperature of the system decreases when the applied magnetic field is kept at a constant value B . The quasiorder-disorder firstorder phase transition of the vortex system takes place [6] when the temperature decreases below Tp , then the region crosses over to that of thermally activated motion of large vortex bundles. In this region, the potential barrier U generated by the randomly distributed strong pinning sites inside the vortex bundle becomes large. Therefore, both ρ xy and

ρ xx decrease

quickly to zero with deceasing temperature.

3.4. Reentry Phenomenon for Anomalous Hall Effect In this subsection we study the double sign reversal or the reentry phenomenon for the anomalous Hall effect. The crucial conditions for occurring this fascinating reentry phenomenon are

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2

171

1

| vby | 1 β C (T , B ) 2 T ( ) α >J B V TC − T vT and

TP < TR

(54)

where T p is the quasiorder-disorder first-order phase transition [6] temperature, TR is the temperature for ρ xy crossing over back from negative to positive value. It is understood that

Tp decreases with increasing (

β (T , B)

1 )2

, total random pinning force, namely, the random V collective pinning force plus the strong pinning force of the vortex system. Hence, in materials with large (

β (T , B)

1 )2

, such as YBa2Cu3O7 −δ [20], Tl 2 Ba2 Cu 2 O8 [21], heavily V doped or highly irradiated fast neutron fluence MgB2 samples, the reentry phenomenon could be observed. The quasiorder-disorder first-order phase transition of the vortex system takes place [6] when the temperature decreases below Tp and the system crosses over to the region of

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

thermally activated motion of large vortex bundles. In this case, the potential barrier U generated by the randomly distributed strong pinning sites inside the vortex bundle becomes large, hence both ρ xy and ρ xx decrease promptly to zero with decreasing temperature.

4. Conclusion Based on our recently developed theories for the quasiorder-disorder first-order phase transition in the vortex system and the thermally activated motion of vortex bundles jumping over a directional-dependent potential barrier, we have investigated the peak effect and anomalous Hall effect for MgB2 superconducting bulk materials and thin films. The peak value of the critical current density, the exact peak position and its corresponding half-width are calculated for constant applied magnetic field and constant temperature. The results are in good agreement with the experiments. Under the framework of our theory, it is shown that the directional-dependent potential barrier renormalized the Hall and longitudinal resistivities strongly, and the Hall anomaly is induced by the competition between the Magnus force and random collective pinning force. We also find that the domain of Hall anomaly includes two regions: the region of thermally activated motion of small vortex bundles and that of large vortex bundles separated by the contour of quasiorder-disorder first-order phase transition of the vortex system. The conditions for the appearance of sign reversal and double sign reversal for MgB2 samples are also discussed.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

172

Wei Yeu Chen and Ming Ju Chou

References [1] [2]

[3]

[4] [5] [6] [7] [8] [9] [10]

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

Nagamatsu, J.; Nakagawa, N.; Muranaka, T.; Zenitani, Y.; Akimitsu, J. Nature 2001, 410, 63-64. Pissas, M.; Lee, S.; Yamamoto, A.; Tajima, S. Phys. Rev. Lett. 2002, 89, 097002-1097002-4; Pissas, M.; Stamopoulos, D.; Lee, S.; Tajima, S. Phys. Rev B 2004, 70, 134503-1-134503-8; Kim, H. J.; Lee, H. S.; Kang, B.; Chowdhury, P.; Kim, K. H.; Park, M. S.; Lee, S. I. Phys. Rev. B 2005, 71, 174516-1-174516-5. Konski, P.; Sorkin, B. Supercond. Sci. Technol. 2004, 17, 1472-1476; Kortus, J. Physica C 2007, 456, 54-62; Naito, M.; Ueda, K. Supercond. Sci. Technol. 2004, 17, R1-R18; Blumberg, G.; Mialitsin, A.; Dennis, B. S.; Zhigadlo, N. D.; Karpinski, J. Physica C 2007, 456, 75-82. Zehetmayer, M.; Eisterer, M.; Muller, R.; Weigand, M.; Jun, J.; Kazakov, S. M.; Karpinski, J.; Weber, H. W. Journal of Physics: Conference Series 2006, 43, 651-654. Moore, J. D.; Perkins, G. K.; Caplin, A. D.; Jun, J.; Kazakov, S. M.; Karpinski, J.; Cohen, L. F. Phys. Rev. B 2005, 71, 224509-1-224509-5. Chen W.Y. and Chou M.J. Supercon. Sci. Tech. 2006, 19, 237-241; Chen W.Y.; Chou M.J. and Feng S. Physica C 2007, 460-462, 1236-1237. cond-mat/0710.0700. Larkin, A. I.; Ovchinnikov, Yu. N. J. Low Temp. Phys. 1979, 43, 409-428. Chen, W. Y.; Chou, M. J. Phys. Lett. A 2001, 280, 371-375; Chen, W. Y.; Chou, M. J.; Feng, S. Phys. Lett. A 2003, 316, 261-264. Chen, W. Y.; Chou, M. J. Phys. Lett. A 2000, 276, 145-148; Chen, W. Y.; Chou, M. J. Phys. Lett. A 2001, 291, 315-318; Chen, W. Y.; Chou, M. J. Supercon. Sci. Tech. 2002, 15, 1071-1073;Chen, W. Y.; Chou, M. J. Phys. Lett. A 2004, 332, 405-411. Chen, W. Y.; Chou, M. J.; Feng, S. Phys. Lett. A 2003, 310, 80-84; Chen, W. Y.; Chou, M. J.; Feng, S. Phys. Lett. A 2005, 342, 129-133. Brandt, E. H. Physica C 1992, 195, 1-27. Van Beelen, H.; Van Braam Houckgeest, J. P.; Thomas, H. M.; Stolk, C.; De Bruyn Ouboter, R. Physica. 1967, 36, 241-253. Freimuth, A.; Hohn, C.; Galffy, M. Phys. Rev. B 1991, 44, 10396-10399. Vinen, W. F.; Warren, A. C. Proc. Phys. Soc. 1967, 91, 409-421. Ferrel, R. A. Phys. Rev. Lett. 1992, 68, 2524-2527. Chen, W. Y.; Chou, M. J.; Huang Z. B. Chinese Physics 2000, 9, 680-684. Brandt, E. H. Rep. Prog. Phys. 1995, 58, 1465-1594. Coffey M.W. and Clem J.R. Phys. Rev. B 1991, 44, 6903-6908. G o b, W.; Liebich, W.; Lang, W.; Puica, I.; Sobolewski, R.; R o ssler, R.; Pedarnig, J. D.; B a uerle, D. Phys. Rev. B 2000, 62, 9780-9783. Hagen, S. J.; Lobb, C. J.; Greene, R. L.; Eddy, M. Phys. Rev. B 1991, 43, 6246-6248. Zehetmayer, M.; Eisterer, M.; Jun, J.; Kazakov, S. M.; Karpinski, J.; Birajdar, B.; Eibl, O.; Weber, H. W. Phys. Rev. B 2004, 69, 054510-1-054510-7. Abrikosov, A. A. JETP 1957, 5, 1174-1182. Anderson, P. W. Phys. Rev. Lett. 1962, 9, 309-311. Tinkham, M. Introduction to Superconductivity, McGraw-Hill, New York, 1975; Tinkham, M. Phys. Rev. Lett. 1964, 13, 804-807.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Theories of Peak Effect and Anomalous Hall Effect in Superconducting MgB2

173

[26] Campbell A.M. and Evetts J.E. Adv. Phys. 1972, 21, 199-429 (1972), and references therein. [27] Brandt, E. H. J. Low Temp. Phys. 1977, 26, 709-733, ibid. 735-753; 28, 263-289, ibid. 291-315. [28] LeBlanc, M. A. R.; Little, W. A. Proc. of the Seven Int. Conf. on Low Temperature Physics (University of Toronto Press, Toronto, 1960), p. 198. [29] Niessen, A.K.; Staas, F. A. Phys. Lett. 1965, 15, 26-28. [30] Bardeen, J.; Stephen, M.J. Phys. Rev. 1965, 140 , A1197-A1207. [31] Van Vijfeijken, A. G.; Niessen, A. K. Phys. Lett. 1965, 61, 23-24; Nozie’res, P.; Vinen, W.F. Philos. Mag. 1966, 14, 667-688. [32] Fiory, A. T. Phys. Rev. B 1973, 8, 5039-5044. [33] Kes P. H. and Tsuei C. C. Phys. Rev. B 1983, 28, 5126-5139;Wördenweber, R.; Kes, P. H.; Tsuei, C. C. Phys. Rev. B 1986, 33, 3172-3180. [34] Kwok, W. K.; Fendrich, J. A.; van der Beek, C. J.; Crabtree, G. W. Phys. Rev. Lett. 1994, 73, 2614-2617. [35] Koshelev A. E. and Vinokur V. M. Phys. Rev. B 1998, 57, 8026-8033;Mikitik G. P. and Brandt E. H. Phys. Rev. B 2001, 64, 184514-1-184514-14. [36] Galffy, M.; Zirngiebl, E. Solid State Commun. 1988, 68, 929-933. [37] Smith, A.W.; Clinton, T. W.; Tsuei, C. C.; Lobb, C. J. Phys. Rev. B 1994, 49, 1292712930; Hagen, S. J.; Smith, A.W.; Rajeswari, M.; Peng, J. L.; Li, Z. Y.; Greene, R. L.; Mao, S. N.; Xi, X. X.; Bhattacharya, S.; Li, Q.; Lobb, C. J. Phys. Rev. B 1993, 47, 1064-1068. [38] Essmann, U.; Tr a uble, H. Phys. Letters 1967, 24A, 526-527; Gammel, P.L.; Bishop, D. J.; Dolan, G. J.; Kwo, J. R.; Murray, C. A.; Schneemeyer, L. F.; Waszczak, J. V. Phys. Rev. Lett. 1987, 59, 2592-2595; Kleiner W.H.; Roth, L. M.; Autler, S. H. Phys. Rev. 1964, 133, A1226-A1227; Lasher, G. Phys. Rev. 1965, 140, A523-A528; Kramer, E. J. J. Appl. Phys. 1978, 49, 742-748. [39] Beasley, M.R.; Labusch, R.; Weber, W. W. Phys. Rev. 1969, 181, 682-700; DewHughes D. Cryogenics 1988, 28, 674-677; Yeshurun, Y.; Malozemoff, A. P. Phys. Rev. Lett. 1988, 60, 2202-2205. [40] [40] Clem J.R. J. Low Temp. Phys. 1975, 18, 427-434; Hao Z. and Clem J.R. Phys. Rev. B 1991, 43, 7622-7630. [41] Brandt E.H. J. Low Temp. Phys. 1986, 64, 375-393; Fisher M.P.A. Phys. Rev. Lett. 1989, 62, 1415-1418; Nelson D.R. and Seung H.S. Phys. Rev. B 1989, 39, 9153-9174. [42] Clem J.R. Phys. Rev. B 1991, 43, 7837-7846; Artemenko S.N. and Kruglo A.V. Phys. Lett. A 1990, 143, 485-488; Fisher K.H. Physica C 1991, 178, 161-170 (1991); Lawrence W.E. and Doniach S. Proc. 12th Internatl. Conf. of Low Temperature Physics LT 12 (E. Kanda,. Academic Press of Japan, Kyoto, 1971) p.361. [43] Reed, W. A.; Fawcett, E.; Kim, Y. B. Phys. Rev. Lett. 1965, 14, 790-792; Zavaritsky N.V.; Samoilov A.V. and Yurgens A.A. Physica C 1991, 180, 417-425; Chien, T. R.; Jing, T. W.; Ong, N. P.; Wang, Z. Z. Phys. Rev. Lett. 1991, 66, 3075-3078. [44] Moore M.A. Phys. Rev. B 1989, 39, 136-139; Brandt E.H. Phys. Rev. Lett. 1989, 63, 1106-1109; Gazman L.I. and Koshelev A.E. Phys. Rev. B 1991, 43, 2835-2843. [45] Niessen A.K.; Staas F.A. and Weijsenfeld C.H. Phys. Lett. 1967, 25A, 33-35; Weijsenfeld, C. H. Phys. Lett. 1968, 28A, 362-363.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

In: Magnesium Diboride (MgB2) Superconductor Research ISBN: 978-1-60456-566-9 Editors: S. Suzuki and K. Fukuda © 2009 Nova Science Publishers, Inc.

Chapter 7

PINNING ENHANCEMENT IN MGB2 BY ADDITION OF SOME METALLIC ELEMENTS Yoshihide Kimishima Department of Physics, Division of Physics, Electrical and Computer Engineering, Graduate School of Engineering, Yokohama National University, Tokiwadai 19-5, Hodogaya-ku, Yokohama 240-8501, Japan

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

1. Introduction Study on the pinning property is very important for the applications of high Tc superconductor MgB2 [1] at liquid hydrogen or 4He gas refrigerator temperature of about 20 K. Many authors have been tried to enhance the pinning force in the MgB2 superconductor by chemical modification using several kinds of element. The critical current density Jc at 20 K of liquid hydrogen temperature was about 104 A/cm2 for pure MgB2 at 20 K [2]. In this chapter, the magnetization curves M(H) of Mx(MgB2)1-x [M=Ag, Cu and Zn] and Mx(SiC)0.1-x(MgB2)0.9 [M=Ag, Cu, Nb and Pt] sintered under ambient pressure, and Cux(MgB2)1-x sintered under high pressure are analyzed to estimate the critical current density Jc by the extended critical state model. In the earlier papers [3-12], the author presented the analytical expressions of magnetization M and AC magnetic susceptibility χ ac by some critical state models for type-II superconductors, and indicated the importance of lower critical field Hc1 and surface equilibrium (reversible) magnetization Meq to analyze the magnetization curve and magnetic susceptibility. On the basis of Kim's idea [13], the author assumed the internal current density equals the critical current density of *

int

μ0 |Jc (x,H)|=

*

Beq ( Beq + 2 B0 )

2a[| Bint ( x, H ) | + B0 ]

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

(1)

176

Yoshihide Kimishima

for 2a × 2b orthorhombic long column. The origin of x-axis is located at the center of column. If a1 holds, the relation of Jcint ∝ 1/Bint can be obtained from this equation. Then the pinning force density fp=JcintBint to each quantum flux is independent of Bint, which is the case of Anderson-Kim's (or simplified Kim's) model [3,14]. On the other hand, if (Beq*/B0) 2Hc1, when the induction field inside the sample can be supposed as generated by an uniform density of fluxons; in this case H0 ≈ B0 = nφ 0, where φ 0 is the flux quantum and n is the vortex density. In their model, the ~ authors calculate the complex penetration depth, λ , by taking into account the effects of the fluxon motion and the very presence of vortices, which bring along normal material in their cores. In the linear approximation, H(ω) « H0, they found the following expression for ~ λ [39]: ~

λ2 + δ v2 λ = 1 − 2iλ2 / δ 2

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

~2

(2.2)

~ where δν is the complex effective skin depth arising from vortex motion; λ and δ, the London penetration depth and the normal-fluid skin depth, are given by

λ=

λ0

(1 − w )(1 − B0

δ=

BC 2 )

δ0

1 − (1 − w )(1 − B0 BC 2 )

;

(2.3)

here, λ0 is the London penetration depth at T = 0; δ0 is the normal skin depth at T = Tc; w is the fractions of normal electrons at H0 = 0, in the two-fluid model w = (T/Tc)4. ~ The penetration depth δν can be written in terms of two characteristic lengths, δf and

λc, arising from the contributions of the viscous and the restoring-pinning forces, respectively: 1 1 2i ~2 = 2 − 2

δv

λc

δf

where

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

(2.4)

280

A. Agliolo Gallitto, G. Bonsignore, S. Fricano et al.

λ2c =

B0φ 0 4πk p

(2.5)

δ 2f =

B0φ 0 2πωη

(2.6)

with kp the restoring-force coefficient and η the viscous-drag coefficient [41]. The effectiveness of the two terms in Eq. (2.4) depends on the ratio ωc = kp/η, which defines the depinning frequency. In particular, when the frequency of the em wave, ω, is much larger than ωc the contribution of the viscous-drag force predominates and the induced em current makes fluxons moving in the flux-flow regime. On the contrary, for ω « ωc the motion of fluxons is ruled by the restoring-pinning force. In order to discuss the experimental results we have to consider that in different ranges of temperatures and external magnetic fields the fluxons, under the action of the induced mw current, move in different regimes.

Results at T « Tc At low temperatures and in the range of magnetic fields here investigated, the terms λ and λ2/δ2 in Eq. (2.2) can be neglected; furthermore, it is reasonable to assume that the fluxon dynamics is governed by the restoring-pinning force. In this case λ « λc « δf and one obtains ~

λ ≈ λc (1 − iλc2 /δ 2f ) ,

(2.7)

~ πω 2η φ 0 B 4πω λ Im ( )= . c2 c2 πk 3p

(2.8)

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

and, using Eq.s (2.5) and (2.6), RS = −

So, the RS(H) curves should be described by the B1/2 law. The lines of Fig. 4 are plots of RS ( H 0 ) R0 = + α H 0 − H* , RN RN

(2.9)

where for R0/RN we have used the experimental values of the normalized residual resistance at H0 = 0, and we have used α and H* as phenomenological parameters. The best-fit curves have been obtained with H* = 280 Oe for both samples and α = 2.5×10–3 for the P#1 sample, α = 5×10–3 for the P#2 sample. The H* value is consistent with the values of Hc1 reported in the literature for the MgB2 superconductor [2]. We remark that, though the magnetic field dependence of RS agrees with that expected in the pinning limit, at so low temperatures such large values of the parameter α look unreasonable. By using the same experimental procedure, we have performed measurements of surface resistance in other superconductors. The results of the investigation carried out in

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Microwave Response of Ceramic MgB2 Samples

281

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

YBa2Cu3O7 (YBCO) have shown that up to H0 = 10 kOe no detectable field variations of RS are observed for T < 0.7 Tc. In order to explore a superconductor with transition temperature and upper critical field smaller than those of YBCO, we have investigated a sample of Ba0.6K0.4BiO3 (BKBO), Tc = 31 K; in this sample, at T = 4.2 K, we have found that a magnetic field of 10 kOe induces a variation of RS about ten times less than that observed in MgB2. The enhanced field variation of RS at low temperatures cannot be easily justified; on the other hand, it has been shown by several authors that the thermal and transport properties of MgB2 are strongly affected by the magnetic field [9-13]. The enhanced field dependence of the properties of MgB2 has been ascribed to the double-gap structure of this compound, with a larger gap, associated with the two-dimensional σ band, and a smaller gap, associated with the three-dimensional π band, which is rapidly suppressed by the applied magnetic field [1416]. We think that the enhanced field-induced variation of RS could be due to the unusual structure of vortices related to the different field dependence of the two gaps [14]. As one can see from Eq. (2.8), the value of RS depends on η and kp; it is not easy to understand how the unusual vortex structure influences such parameters; however, it is reasonable to hypothesize that it could affect both the vortex-vortex and the pinning-vortex interactions.

Results at Temperatures Close to Tc At temperatures close to Tc, where the pinning effects are weak, the fluxons should move in the flux-flow regime, in this case δv2 ∼ iδf2/2; furthermore, in Eq. (2.2) the terms λ and λ2/δ2 cannot be neglected. So, a simple expression for RS(H0) cannot be written. Assuming for the viscous-drag coefficient the expression η = φ0Bc2(T)/c2ρn, the only two parameters necessary to perform a comparison between the experimental and the expected RS(H0) curves are just the Hc2(T) values, which we have deduced from the experimental data, and the ratio λ0/δ0. It is easy to see that λ0/δ0 = (ωτ/2)1/2, where τ is the scattering time of the normal electrons. Values of τ reported in the literature for ceramic MgB2 are τ ~ 10–13 s [8]; so, for these samples at the microwave frequencies the ratio λ0/δ0 should be of the order of 10–2. The dashed line of Fig. 5 (b) shows the expected curve obtained using Eqs. (2.1) - (2.6) with λ0/δ0 = 10–2 and Hc2 = 6 kOe. As one can see, for H0 « Hc2, the experimental curve RS(H0) varies faster than the expected one; on the contrary, for H0 ∼ Hc2, the experimental curve varies more slowly than the theoretical one. We have calculated curves of RS(H0) using for λ0/δ0 values ranging from 10–1 to 10–3 and for Hc2(T) the values deduced from the experimental data, letting them vary within the experimental accuracy. The results have shown that the model, in the present form, does not account for the experimental data. However, the results can be justified quite well by taking into due account the upper-critical-field anisotropy. For superconducting materials in which the coherence length is much larger than the periodicity of the crystal lattice, such as the MgB2 compound, one can reasonably assume that the angular dependence of the critical field follows the anisotropic Ginsburg-Landau (AGL) theory: H c 2 (θ ) =

H c⊥2c

γ 2 cos 2 (θ ) + sin 2 (θ )

,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

(2.10)

A. Agliolo Gallitto, G. Bonsignore, S. Fricano et al.

282

where γ = H c⊥2c / H c 2 is the anisotropy factor and θ is the angle between the c-axis of c

crystallites and the external magnetic field. The values of Hc2 and its anisotropy factor reported in the literature for MgB2 strongly depend on the kind of sample investigated [3-7, 13]; furthermore, a temperature dependence of γ has been highlighted by several authors [3-6]. The AGL theory cannot surely justify the temperature dependence of the anisotropy factor. Nevertheless, it has been shown that data obtained by different techniques can be well justified using Eq. (2.10) in a large range of temperatures, magnetic fields and angles [3, 6, 7]. In order to quantitatively account for our experimental data we have assumed Hc2(θ) of Eq. (2.10). To take into account the effect of the Hc2 anisotropy in the field dependence of the surface resistance, we have to average the expected RS(H0, Hc2(θ)) curves over a suitable distribution of the crystallite orientations. We have assumed that our samples consist of crystallites with a random orientation of the c-axes with respect to the applied magnetic field. On this hypothesis, the distribution function of the grain orientation will be dN(θ) = 1/2 N0 sin(θ) dθ,

(2.11)

where N0 is the total number of crystallites.

The expected RS(H0) curves depend on the values of H c⊥2c (T ) , λ0/δ0 and γ. On the other

hand, the criterion used for deducing the Hc2(T) values reported in Fig. 3 allows to determine the field values at which the whole sample goes into the normal state, i.e., the values of H c⊥2c .

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Therefore, in order to fit the data, we have used for H c⊥2c (T ) the values deduced from the experimental results, letting them vary within the experimental uncertainty, and we have taken λ0/δ0 and γ as parameters. However, we have found that the expected results are little sensitive to variations of λ0/δ0 as long as it takes on values smaller than 0.1. Since higher values of this parameter are not reasonable, it cannot be determined by fitting the data, we have used λ0/δ0 = 10–2; so, the only free parameter is γ. By fitting the experimental data we have found that, in the range of temperatures investigated, γ does not depend on temperature, for both samples. The best-fit curves have been obtained using different values of γ for the two samples. In particular, we have obtained γ = 3 ± 0.1 for P#1 and γ = 5 ± 0.3 for P#2. The continuous lines of Fig. 4 are the best-fit curves of the experimental data. The values of the anisotropy factor, reported in the literature for MgB2, strongly depend on the type of sample investigated [3-7, 13]. In randomly oriented powder, it has been found γ = 6 – 9 at low temperature and γ ≈ 3 close to Tc [4, 5]. The γ-value we have obtained for P#1 agrees with those reported for powdered [4, 5] as well as for polycrystalline samples, on the contrary for P#2 we have obtained a higher value. So, although the two investigated samples have similar shape and have been investigated by the very same measurement method, we have found different values of γ. This finding corroborates the idea that the anisotropy of the upper critical field depends on the sample growth method, probably because of the different contaminating impurities.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Microwave Response of Ceramic MgB2 Samples

283

3. Harmonic Emission It has been widely shown that high-Tc superconductors are characterized by markedly nonlinear properties when exposed to intense em fields up to microwave frequencies [19, 20, 27-33, 36, 42, 43]. A suitable method for investigating the nonlinear response consists in the detection of signals at the harmonic frequencies of the driving field [27-36]. Besides the basic point of view, this issue takes on great relevance for the use of superconductors in technological applications [19, 20, 27]. Indeed, the nonlinearity is really the main limiting factor for application of superconductors in passive microwave devices; on the other hand, it can be conveniently exploited for assembling active mw devices. For this reasons, it is of great importance recognizing the mechanisms responsible for the nonlinear response and determining the conditions in which the nonlinear effects are important. In the following sections, we report and discuss results of second harmonic (SH) emission by MgB2 ceramic samples. Particular attention will be devoted to the investigation of the properties of the SH signals for applied magnetic fields lower than Hc1.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

3.1. Experimental Apparatus and Samples We have investigated the SH emission in several ceramic samples, powdered and bulk, produced by different techniques. However, since for all the samples we have obtained similar results, in this paper we report results in three different samples obtained from AlfaAesar powder. The P#α sample consists of ≈ 5 mg of the pristine powder; the second, P#c, has been obtained by further crushing the powder; the third, P#d has been obtained by dispersing the crushed powder in polystyrene, with a ratio of 1:10 in volume. The sample is located inside a bimodal rectangular cavity resonating at the two angular frequencies ω and 2ω, in a region where the magnetic fields H(ω) and H(2ω) are parallel and of maximal intensity. The fundamental frequency ω/2π is ≈ 3 GHz. The ω-mode of the cavity is fed by a pulsed oscillator, with pulse repetition rate of 200 pps and pulse width of 5 μs, giving a maximum peak power of ≈ 50 W. The sample is also exposed to static magnetic fields, H0, which can be varied from 0 to 10 kOe. The harmonic signals are detected by a superheterodyne receiver. Further details of the experimental apparatus are reported in Ref. [32]. The intensity of the SH signal has been measured as a function of the external magnetic field, the temperature and the input power. All the measurements have been performed with H(ω)||H(2ω)||H0.

3.2. Experimental Results Fig. 6 shows the SH signal intensity as a function of the temperature for the P#α sample. The SH emission is significant in the whole range of temperatures investigated and exhibits an enhanced peak at temperatures close to Tc. The kink at T ≈ 38 K is ascribable to the inhomogeneity of the sample; indeed, the same effect has been found in the temperature dependence of the ac susceptibility [44]. The inset shows the temperature dependence of the SH signal in a restrict range of temperatures around the peak, at three different values of the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

284

A. Agliolo Gallitto, G. Bonsignore, S. Fricano et al.

dc magnetic field. As one can see, on increasing H0 the peak position shifts toward lower temperatures.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 6. SH signal intensity as a function of the temperature for the P#α sample. The inset shows a detail of the temperature dependence of the SH signal, near the peak, at three different values of the dc magnetic field. Input peak power ≈ 30 dBm.

Figure 7. SH signal intensity as a function of the dc magnetic field for the P#α sample, at T = 4.2 K. Full symbols refer to the results obtained in the zero-field-cooled sample on increasing the field for the first time. Open symbols describe the field dependence of the SH signal on decreasing H0 after the first run to high fields. Input peak power ≈ 27 dBm.

In Fig. 7 we report the SH signal intensity as a function of the dc magnetic field for the P#α sample, at T = 4.2 K. Full symbols refer to the results obtained in the zero-field-cooled sample on increasing the field for the first time. As expected from symmetry considerations, the SH signal is zero at H0 = 0 (the noise level is ~ –75 dBm); on increasing the field it

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Microwave Response of Ceramic MgB2 Samples

285

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

abruptly increases, exhibits a maximum at ≈ 5 Oe, decreases monotonically up to ~ 40 Oe and then slowly increases until it reaches a value that remains roughly constant up to high fields. Open symbols describe the field dependence of the SH signal observed on decreasing H0, after the first run to high fields. The low-field structure disappears irreversibly after the sample has been exposed to fields higher than ~ 100 Oe; in this case, even at H0 = 0 the intensity of the SH signal takes on roughly the same value as the one measured at high fields. Fig. 8 shows the low-field behaviour of the SH signal, observed in the zero-field-cooled P#α sample by cycling the magnetic field in the range –Hmax ÷ +Hmax. The signal shows a hysteretic loop having a butterfly-like shape; on increasing the value of Hmax, the hysteresis is gradually more enhanced and the sharp minima, observed at low fields, move away from each other. The hysteretic loop maintains the same shape in subsequent field runs as long as the value of Hmax is not changed.

Figure 8. Low-field behaviour of the SH signal, observed in the zero-field-cooled P#α sample by cycling the magnetic field in range –Hmax ÷ +Hmax. T = 4.2 K; input peak power ≈ 30 dBm. The three curves refer to different values of Hmax.

Measurements performed at different input-power levels have shown that, for fixed values of Hmax, the amplitude of the hysteresis increases on decreasing the input power, suggesting that the power dependence of the SH signal is different for increasing and decreasing fields. Fig. 9 shows the intensity of the SH signal as a function of the input power level, at H0 = 20 Oe. Full symbols show the results obtained at H0 = 20 Oe reached at increasing fields; open symbols those obtained at H0 = 20 Oe, reached at decreasing fields after that Hmax had reached the value of 35 Oe. The distances between full and open symbols, at fixed input power levels, indicate the amplitude of the hysteresis at H0 = 20 Oe.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

286

A. Agliolo Gallitto, G. Bonsignore, S. Fricano et al.

The results reported in Figs. 6-9 refer to the P#α sample. The same measurements have been performed in the other samples, obtained from the P#α sample as described in Section 3.1. The main peculiarities of the SH signals observed in the P#c and P#d samples are the same as those obtained in the P#α sample, except for the relative intensity of the near-Tc peak and the low-T signal. This finding is shown in Fig. 10 where we report the SH signal intensity as a function of the temperature in the three different samples, at H0 = 10 Oe. For the sake of clearness, the three curves have been shifted one with respect to the other, as shown in the figure.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Figure 9. SH signal intensity as a function of the input power level in P#α. Full symbols are the results obtained at H0 = 20 Oe reached at increasing fields; open symbols are those obtained at H0 = 20 Oe, reached at decreasing fields.

Figure 10. SH signal intensity as a function of the temperature in the three different samples. H0 = 10 Oe; input peak power ≈ 30 dBm. The curves relative to P#c and P#α samples have been shifted upwards of 10 dB and 20 dB, respectively.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Microwave Response of Ceramic MgB2 Samples

287

3.3. Discussion

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

The nonlinear response of high-Tc superconductors to electromagnetic fields has been extensively investigated [27-36, 42, 43]. The nonlinear response detected at low temperatures has been ascribed to extrinsic properties of the superconductors such as impurities, weak links [29, 31, 33-36] or flux-line motion [27, 28]. On the contrary, nonlinearity at temperatures close to Tc is related to intrinsic properties of the superconducting state [30-33, 36]; in particular, it has been ascribed to modulation of the order parameter induced by the em field. Our results on MgB2 suggest that, also in this class of superconductors, different mechanisms come into play in the two ranges of temperature. In the following, we discuss the low-T and high-T behaviour of SH emission by considering models previously reported in the literature.

Low-Temperature Behaviour Harmonic generation has been thoroughly investigated in both ceramic and crystalline YBCO samples [27-35]. It has been shown that at low fields harmonic emission by high-quality crystals is noticeable only at temperatures near Tc [30, 32, 33], while in ceramic samples it is significant at low temperatures as well [29, 34]. This finding has suggested that the low-field and low-T harmonic signals are due to nonlinear processes occurring in weak links. In the presence of weak links, two nonlinear processes may come into play. Harmonic emission is expected when supercurrents are induced, by the H0 and H(ω) fields, in loops containing Josephson junctions (JJ). In this case, the harmonic emission is strictly related to the intrinsic nonlinearity of the Josephson current [29, 35]. On the other hand, intergrain dynamics of Josephson fluxons (JF) in the critical state may give rise to harmonic emission [35, 36]. The peculiarities of the low-T SH signal observed in the MgB2 samples cannot be accounted for neither in the framework of the model that assumes supercurrent loops containing JJ nor in that which deals with nonlinear dynamics of JF. Results similar to those shown in Fig. 8 have been obtained in BKBO crystals [36]; they have been justified by supposing that the above-mentioned nonlinear processes involving weak links come into play simultaneously. We have shown that the combined effect of the 2ω magnetization arising from the supercurrent loops containing JJ and that arising from the dynamics of JF can justify the peculiarities of the hysteretic behaviour of the low-field SH signal [36]. According to what discussed in Ref.[36], we suggest that also in ceramic MgB2 samples the low-T and lowfield SH signal arises from nonlinear processes due to the presence of weak links inside the samples. This hypothesis is supported by the irreversible loss of the low-field structure, observed in zero-field-cooled samples, after the samples had been exposed to high fields (see Fig. 7). Indeed, when H0 reaches values higher than Hc1, Abrikosov fluxons penetrate the grains and the JJ are decoupled by the applied field and/or the trapped flux. In this case, harmonic signals are due to intra-grain fluxon dynamics [28]. Concerning the origin of the SH emission at magnetic fields higher than Hc1, it has been shown that even harmonics can arise in superconductors in the critical state exposed to highfrequency magnetic fields [28]. In this case, because of the rigidity of the fluxon lattice the superconducting sample operates a rectification process of the ac field. Ciccarello et al. [28] have elaborated a model discussing these effects. It has been shown that a peculiarity of the SH signal of superconductors in the critical state is the presence of enhanced dips in the SH-vs-H0 curves, after the inversion of the magnetic-field-sweep direction, regardless of the

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

288

A. Agliolo Gallitto, G. Bonsignore, S. Fricano et al.

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

H0 value at which the inversion is operated. The presence of the enhanced dip of Fig. 7 at the extreme of the plot, in which the magnetic field reverses its direction, shows that also in MgB2 after the sample has been exposed to high fields SH emission is due to the intra-grain fluxon dynamics.

Near-Tc Behaviour The enhanced nonlinear emission observed at temperatures close to Tc cannot be accounted for by mechanisms related by the presence of weak links. Indeed, the Josephson-critical current decreases monotonically on increasing the temperature; on the other hand, near Tc no critical state, either for of Josephson or Abrikosov fluxons, can be reasonably hypothesized. So, a monotonic decrease of the SH-signal intensity it expected. The harmonic emission at temperatures close to Tc has been ascribed to the time variation of the order parameter induced by the em field [30-33, 36]. In particular, the features of second- and third-harmonic signals detected in high-Tc superconductors have been accounted for in the framework of the two-fluid model with the additional hypothesis that the em field, which penetrates in the surface layers of the sample, weakly perturbs the partial concentrations of the normal and condensate fluids [30, 32, 36]. According to this model, it is expected that on increasing the external magnetic field and/or the input power level the nearTc peak broadens and shifts toward lower temperatures [30, 32]. The experimental results reported in the inset of Fig. 6 agree with the expected ones, suggesting that the near-Tc peak detected in MgB2 originates from this mechanism. However, as one can see from Figs. 6 and 10, the peak is merged with the tail of the low-T signal and its characteristics could be affected by this contribution. In order to corroborate the hypothesis that the low-T and high-T SH signals originate from different mechanisms, the first one from processes involving weak links and the second one from the modulation of the order parameter, we have performed measurements in the three different samples (see Fig.10). As an effect of the grinding of sample P#α, by which sample P#c was obtained, a variation of the number of weak links is expected, with a consequent variation of the low-T SH signal intensity. On the other hand, the effective surface of P#c could be larger than that of P#α and, consequently, an increase of the high-T signal is expected. Actually, from Fig. 10 one can see that the ratio of the intensity of the near-Tc peak and the signal at T = 5 K is about 6 dB for P#α and 12 dB for P#c. The dispersion of the grains of the P#c in polystyrene, by which P#d was obtained, has been performed to reduce the number of weak links, maintaining unchanged the effective surface of the sample. A comparison between the SH-vs-T curves of the samples P#c and P#d of Fig. 10 shows, in effect, that the intensity of the near-Tc peak is the same for the two samples, while a further decrease of the low-T signal has be observed after dispersion of the powder in polystyrene. These findings confirm that the low-T and near-Tc SH signal have different origin and, in particular, they validate the hypothesis that the low-T signal arise from processes involving weak links.

4. Conclusion We have reported experimental results on the microwave response of ceramic MgB2. The response has been investigated in the linear and nonlinear regimes, by measuring the surface

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Microwave Response of Ceramic MgB2 Samples

289

impedance and the second-harmonic emission, respectively. The surface resistance and the SH signal have been investigated as function of the temperature and the external magnetic field. The field-induced variations of the surface resistance have been measured with the aim of investigating the dynamics of fluxons in different ranges of temperature. We have shown that the magnetic field strongly affects the microwave surface resistance of MgB2 even at low temperatures and relatively low values of the magnetic field, where the pinning effects should hinder the energy losses. Although the field dependence of the surface resistance at low temperatures follows the law expected in the pinning limit, it is more enhanced than in other superconductors. We have suggested that this enhanced field dependence of RS could be due to the unusual structure of vortices related to the different field dependence of the two energy gaps in MgB2. The results at temperatures close to Tc have been quantitatively justified in the framework of the Coffey and Clem model, with fluxons moving in the flux-flow regime, taking into account the anisotropy of the upper critical field. Our results have shown that, at least in the temperature range of about 3 K below Tc, the upper-critical-field anisotropy follows the AGL theory. The value of the anisotropy factor of the Alfa-Aesar-powder sample agrees with those reported in the literature for randomly oriented powder of MgB2. However, although the two investigated samples have similar shape, their anisotropy factors are different, corroborating the idea, commonly reported in the literature, that the values of the characteristic parameters of the MgB2 compound depend on the preparation method of the samples. The results of the second-harmonic emission have shown that, similar to what occurs in other high-Tc superconductors, several mechanisms are responsible for the nonlinear microwave response of MgB2; their effectiveness depends on temperature and intensity of the external magnetic field. The results obtained at low temperature have show that, although the presence of weak links in MgB2 does not noticeably affect the transport properties, it is the main source of nonlinear response at low magnetic fields and low temperatures. After exposing the sample to magnetic field higher than Hc1, the weak links are decoupled and the SH emission originates from the dynamics of fluxons in the critical state. At temperatures close to Tc, a further contribution to the harmonic emission is present; it arises from modulation of the order parameter by the microwave field and gives rise to a near-Tc peak in the temperature dependence of the SH signal intensity.

Acknowledgements The authors are very glad to thank E. H. Brandt, M. R. Trunin, I. Ciccarello, for their continuous interest and helpful suggestions, G. Lapis and G. Napoli for technical assistance, N. N. Kolesnikov and M. P. Kulakov for supplying one of the MgB2 samples.

References [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani and J. Akimitsu, Nature 410 (2001) 63. [2] C. Buzea and T. Yamashita, Supercond. Sci. Technol. 14 (2001) R115.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

290

A. Agliolo Gallitto, G. Bonsignore, S. Fricano et al.

[3] M. Angst, R. Puzniak, A. Wisniewski, J. Jun, S. M. Kazakov, J. Karpinski, J. Roof and H. Keller, Phys. Rev. Lett. 88 (2002) 167004. [4] S. L. Bud’ko and P. C. Canfield, Phys. Rev. B 65 (2002) 212501. [5] F. Simon, A. Jànossy, T. Fehér, F. Murànyi, S. Garaj, L. Forrò, C. Petrovic, S. L. Bud’ko, G. Lapertot, V. G. Kogan and P. C. Canfield, Phys. Rev. Lett. 87 (2001) 047002. [6] C. Ferdeghini, V. Braccini, M. R. Cimberle, D. Marré, P. Manfrinetti, V. Ferrando, M. Putti and A. Palenzona, Eur. Phys. J. B 30 (2002) 147. [7] O. F. De Lima, R. A. Ribeiro, M. A. Avila, C. A. Cardoso and A. A. Coelho, Phys. Rev. Lett. 86 (2001) 5974. [8] Yu. A. Nefyodov, M. R. Trunin, A. F. Shevchun, D. V. Shovkun, N. N. Kolesnikov, M. P. Kulakov, A. Agliolo Gallitto and S. Fricano, Europhys. Lett. 58 (2002) 422. [9] Dulcic, D. Paar, M. Pozek, G. V. M. Williams, S. Kramer, C. U. Jung, M. S. Park and S. I. Lee, Phys. Rev. B 66 (2002) 014505. [10] Shibata, M. Matsumoto, K. Izawa, Y. Matsuda, S. Lee and S. Tajima, Phys. Rev. B 66 (2003) 060501(R). [11] D. K. Finnemore, J. E. Ostenson, S. L. Bud’ko and P. C. Canfield, Phys. Rev. Lett. 86 (2001) 2420. [12] F. Bouquet, Y. Wang, I. Sheikin, T. Plackowski, A. Junod. S. Lee and S. Tajima, Phys. Rev. Lett. 89 (2002) 257001. [13] V. Sologubenko, J. Jun, S. M. Kazakov, J. Karpinski and H. R. Ott, Phys. Rev. B 65 (2002) 180505. [14] E. Koshelev and A. A. Golubov, Phys. Rev. Lett. 90 (2003) 177002. [15] R. S. Gonnelli, D. Daghero, G. A. Ummarino, V. A. Stepanov, J. Jun, S. M. Kazakov and J. Karpinski, Phys. Rev. Lett. 89 (2002) 247004. [16] Y. Bugoslavsky, Y. Miyoshi, G. K. Perkins, A. D. Caplin, L. F. Cohen, A. B. Pogrebnyakov and X. X. Xi, Phys. Rev. B 69 (2004) 132508. [17] Y. Bugoslavsky, G. K. Perkins, X. Qi, L. F. Cohen and A. D. Caplin, Nature 410 (2001) 563. [18] M. Hein, Proceedings of URSI-GA, Maastricht, August 2002; arXiv:cond-mat/0207226. [19] Vendik and O. Vendik, High Temperature Superconductor Devices for Microwave Signal Processing (Scalden Ltd, St. Petersburg, 1997). [20] Ibid. Microwave Superconductivity, H. Weinstock and M. Nisenoff eds., NATO Science Series, Series E: Applied Science - Vol. 375, Kluwer: Dordrecht 1999. [21] M. R. Trunin, Usp. Fiz. Nauk. 168 (1998) 931. [22] J. Owliaei, S. Shridar and J. Talvacchio, Phys. Rev. Lett. 69 (1992) 3366. [23] Agliolo Gallitto, I. Ciccarello, M. Guccione, M. Li Vigni and D. Persano Adorno, Phys. Rev. B 56 (1997) 5140. [24] M. Golosovsky, M. Tsindlekht and D. Davidov, Supercond. Sci. Technol. 9 (1996) 1. [25] H. A. Blackstead, D. B. Pulling, J. S. Orwitz and D. B. Chrisey, Phys. Rev. B 49 (1994) 15335. [26] M. Golosovky, V. Ginodman, D. Shaltiel, W. Gerhouser and P. Fisher, Phys. Rev. B 47 (1993) 9010. [27] T. B. Samoilova, Supercond. Sci. Technol. 8 (1995) 259. [28] Ciccarello, C. Fazio, M. Guccione and M. Li Vigni, Physica C 159 (1989) 769. [29] Ciccarello, M. Guccione and M. Li Vigni, Physica C 161 (1989) 39.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Microwave Response of Ceramic MgB2 Samples

291

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

[30] Ciccarello, C. Fazio, M. Guccione, M. Li Vigni and M. R. Trunin, Phys. Rev. B 49 (1994) 6280. [31] G. Hampel, B. Batlogg, K. Krishana, N. P. Ong, W. Prusselt, H. Kinder and A. C. Anderson, Appl. Phys. Lett. 71 (1997) 3904. [32] Agliolo Gallitto and M. Li Vigni, Physica C 305 (1998) 75. [33] M. R. Trunin and G. I. Leviev, J. Phys. III (France) 2 (1992) 355. [34] Q. H. Lam and C. D. Jeffries, Phys. Rev. B 39 (1989) 4772. [35] L. Ji, R. H. Sohn, G. C. Spalding, C. J. Lobb and M. Tinkham, Phys. Rev. B 40 (1989) 10936. [36] Agliolo Gallitto, M. Guccione and M. Li Vigni, Physica C 309 (1998) 8; ibid. 330 (2000) 141. [37] N. N. Kolesnikov and M. P. Kulakov, Physica C 363 (2001) 166. [38] M. W. Coffey and J. R. Clem, IEEE Trans. Mag. 27 (1991) 2136. [39] M. W. Coffey and J. R. Clem, Phys. Rev. B 45 (1992) 9872. [40] E. H. Brandt, Phys. Rev. Lett. 67 (1991) 2219. [41] J. Bardeen and M. J. Stephen, Phys. Rev. 140 (1965) A1197. [42] P. P. Nguyen, D. E. Oates, G. Dresselhhaus and M. S. Dresselhhaus, Phys. Rev. B 48 (1993) 6400; ibid. 51 (1995) 6686. [43] S. Sridhar, Appl. Phys. Lett. 65 (1994) 1054. [44] Agliolo Gallitto, G. Bonsignore and M. Li Vigni, Int. J. Mod. Phys. 17 (2003) 535.

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved. Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

INDEX

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

A Aβ, 86 absorption, 35, 48, 72, 274 absorption spectroscopy, 20 accelerator, 143 acceptor, 53 access, 191, 248 accuracy, 101, 147, 281 acetone, 36 acetonitrile, 56, 64 acid, 37, 52, 53 acidity, 52 adiabatic, ix, x, 133, 143, 147, 190, 196, 197 Ag, x, 139, 175, 179, 180, 181, 183, 185, 197, 198, 199, 200, 201, 202, 203 agents, 37 air, ix, 35, 36, 55, 62, 63, 64, 121, 124, 133 algorithm, x, 133, 140 alloys, 1, 179, 181, 185, 204 alternative, 127 aluminium, 79, 80, 91, 92, 93, 96, 97, 98, 99, 101, 108 aluminum, 143 ambient pressure, vii, x, 1, 175, 190, 197, 250 amine, 54 amorphous, xi, 10, 11, 12, 79, 84, 90, 91, 119, 121, 154, 163, 213, 230, 247, 248, 250, 253, 254, 255, 257, 266, 267, 268 amorphous phases, 250, 253 amplitude, 80, 88, 89, 90, 91, 92, 93, 101, 104, 164, 177, 285 anisotropy, viii, xi, 11, 21, 24, 35, 54, 77, 78, 79, 91, 95, 96, 98, 99, 107, 108, 109, 154, 234, 237, 239, 241, 242, 243, 273, 278, 281, 282, 289 annealing, 12, 119, 124, 128, 129, 212, 213, 234, 249, 253 annihilation, 157 anomalous, x, 5, 153, 154, 155, 162, 163, 168, 169, 170, 171, 212 antibonding, 24, 31, 32, 50, 51, 69, 70, 72, 79

antiferromagnetic, 20, 22, 24, 26, 27, 28, 30, 31, 32, 55, 71 application, vii, ix, x, 1, 2, 20, 21, 34, 78, 118, 130, 150, 153, 179, 190, 197, 248, 283 argon, ix, 117, 120 aspect ratio, 134, 239, 240, 241, 242, 243 assignment, 87 assumptions, 85 asymptotic, 85 atmosphere, ix, 11, 64, 117, 119, 179, 180, 185, 190, 197, 202, 203, 207, 213, 249, 257, 264 atomic orbitals, 3 atomic positions, 31 atoms, 2, 3, 4, 5, 13, 21, 31, 33, 35, 38, 39, 50, 53, 80, 99, 100, 122, 181

B barrier, x, 22, 24, 35, 37, 43, 44, 54, 62, 134, 153, 154, 155, 163, 165, 166, 167, 168, 169, 170, 171 barriers, 43, 90 basic research, vii, 1 basicity, 52 BCS theory, 2, 5, 23, 191 behavior, viii, 2, 3, 5, 20, 23, 24, 28, 32, 40, 46, 54, 59, 60, 63, 67, 68, 70, 71, 77, 82, 83, 85, 87, 88, 89, 90, 91, 92, 93, 94, 98, 99, 101, 102, 104, 105, 106, 149, 151, 212, 215, 225, 231, 249 behaviours, vii Beijing, 16 bending, 32 benzene, 64 bi-layer, 42, 46 binding, 7, 24, 33, 52 binding energy, 7 bismuth, viii, 19, 20, 31, 32, 50 blocks, 42, 46, 59, 62 Boltzmann constant, 158, 160, 164 bonding, 3, 4, 6, 22, 35, 40, 50, 51, 69, 79 bonds, 30, 31, 32, 51 Boron, 4, 252, 253, 269 Bose, 76, 158, 160 Bose-Einstein, 158, 160

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

294

Index

boson, 27 bosonized, 25 boundary conditions, 134 building blocks, 37 bulk materials, 128, 159, 161, 162, 163, 169, 171 burn, 144 butterfly, 285

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

C cables, 136, 143, 150 calibration, 215 candidates, 212 capacity, 13, 133, 134, 147 carbide, 119 carbon, xi, 21, 35, 38, 39, 41, 79, 80, 92, 94, 99, 100, 102, 104, 106, 108, 129, 211, 212, 213, 214, 215, 216, 220, 222, 224, 227, 228, 231 carbon atoms, 21, 35, 38, 39 carbon nanotubes, xi, 211, 212, 220, 228 carrier, vii, 19, 21, 23, 34, 54, 55, 97, 109 catalyst, 12 cation, 32, 37, 52, 57, 59, 63, 70 C-C, 215, 220 cell, 20, 21, 37, 80, 121, 134, 135, 136, 137, 140, 149, 190, 196 ceramic, xi, 2, 273, 274, 275, 281, 283, 287, 288 charge density, 20, 28, 30, 33 chemical approach, 71 chemical interaction, 37, 46, 52 chemical properties, 22, 34 chemical reactions, 186 chemical vapor deposition, 11 chloroform, 40 classical, 12, 14, 158, 160 clustering, 99 clusters, 66, 67, 68, 69, 70 CNTs, 213, 220, 228 codes, 140 coherence, 2, 13, 28, 30, 35, 42, 78, 83, 98, 154, 212, 215, 281 coil, x, 133, 134, 136, 138, 139, 140, 141, 143, 147, 149, 150, 233 collisions, 120 combined effect, 287 commercialization, ix, 133 community, viii, 77, 273 compatibility, 233 compensation, 136 competition, x, 153, 154, 163, 168, 171 compilation, 8 components, 20, 51, 54, 57, 67, 135, 166, 274 composition, ix, xi, 8, 9, 55, 63, 92, 99, 100, 117, 118, 124, 128, 130, 180, 211, 212, 216, 220, 222, 228, 237, 239, 249, 257, 263 compounds, viii, 20, 21, 22, 24, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 43, 46, 47, 49, 52, 54, 55, 56, 58, 71, 118, 180, 214 computation, x, 133, 136, 138

computing, 149 concentration, 21, 36, 45, 51, 80, 98, 248, 263 condensation, 24, 28, 78, 158, 160 condensed matter, 2 conduction, ix, x, 20, 32, 37, 68, 71, 133, 140, 141, 143, 144, 146, 147, 151 conductive, 71, 72, 185 conductivity, 1, 14, 24, 63, 140, 141, 147, 150, 152, 185, 189, 196 conductor, x, 1, 126, 133, 134, 136, 138, 139, 140, 141, 143, 144, 145, 146, 147, 149, 150 configuration, 22, 32, 35, 46, 47, 48, 52, 91, 135, 138, 234 confinement, 24 connectivity, ix, 117, 212, 214, 223, 228, 229, 230, 235, 237, 239, 250, 251, 255, 258, 266, 268 consensus, 31 construction, viii, 77 consumption, 13, 140 contamination, ix, 117 continuity, 14 contracts, 143 control, 21, 34, 62, 118, 267 cooling, ix, x, 13, 90, 91, 100, 102, 103, 106, 133, 134, 140, 147, 180, 185, 197, 203, 213, 214, 248, 257 Cooper pair, vii, 13, 19, 20, 23, 25, 28, 55, 67, 79, 99 Cooper pairing, vii, 19, 20, 23, 28 Cooper pairs, 13, 25, 79, 99 coordination, 30, 51, 52, 53, 64, 70 copper, vii, viii, xi, 2, 19, 20, 27, 28, 30, 31, 32, 49, 50, 51, 57, 58, 69, 70, 134, 211 copper oxide, 2, 28, 30, 31, 32 correlation, xi, 34, 51, 71, 85, 89, 156, 211, 223, 249 correlation function, 85, 156 correlations, 26, 27, 31, 243 costs, 2, 248 Coulomb, 23, 28, 96 Coulomb interaction, 23 couples, 27 coupling, viii, 3, 4, 5, 6, 11, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 33, 34, 40, 42, 43, 53, 59, 60, 62, 68, 69, 71, 79, 84, 274 covalency, 30 covalent, 3, 30, 31, 32, 47, 50 covalent bond, 3 covalent bonding, 3 covering, 139 CRC, 269 creep, 189 critical current density, ix, x, xi, 13, 14, 82, 91, 92, 118, 119, 120, 125, 129, 153, 154, 155, 157, 158, 159, 160, 161, 162, 171, 175, 178, 190, 197, 199, 211, 212, 239, 247, 267 critical state, x, 175, 176, 187, 190, 192, 193, 194, 195, 196, 197, 198, 201, 206, 214, 287, 288, 289 critical temperature, viii, ix, 5, 77, 100, 101, 102, 118, 125, 129, 130, 133, 154, 158, 165, 216, 222, 275

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

295

Index crossing over, 171 cross-sectional, 36, 39 cryogenic, 140 crystal growth, vii, 1, 9 crystal lattice, 13, 205, 281 crystal structure, 2, 3, 8, 21, 22, 32, 35, 46, 50 crystalline, xi, 11, 46, 54, 58, 247, 248, 250, 253, 254, 255, 256, 257, 260, 267, 268, 287 crystallinity, xi, 247 crystallites, 282 crystals, 2, 6, 8, 10, 11, 13, 64, 79, 80, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 107, 108, 109, 231, 249, 287 cuprate, vii, viii, 11, 19, 20, 21, 22, 24, 26, 28, 29, 30, 32, 33, 34, 35, 37, 39, 41, 42, 43, 46, 49, 50, 52, 53, 54, 55, 59, 62, 63, 64, 67, 70, 72, 73, 88, 276, 278 cuprates, viii, 3, 12, 19, 20, 21, 22, 24, 25, 28, 32, 33, 34, 35, 37, 42, 55, 58, 69, 70 current limit, 254 cycling, 285

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

D damping, 164 data analysis, 220 decay, 45, 141, 143, 168 decomposition, 8, 122, 258, 266 decoupling, 33, 46, 68 defects, ix, x, xi, 13, 84, 91, 98, 99, 118, 125, 156, 211, 212, 228, 230, 232, 237, 239, 242, 244, 250 deficiency, 203, 249, 258, 262, 264, 266 deficit, 118 definition, 30, 31, 177 deformation, 36, 122, 125, 127, 130, 156, 212, 232, 233, 237, 239, 243 degradation, 214, 233, 235, 238, 242 degrading, 234, 248, 266 delocalization, 25, 31, 32 Department of Energy, 244 depolarization, 45 deposition, 11, 53 depressed, 21, 40, 42, 46, 48 depression, 41, 46, 128 derivatives, 42, 47, 49, 54 detection, 51, 140, 143, 283 deviation, 118, 128 differential scanning, 120 differential scanning calorimetry, 120 differentiation, 13 diffraction, xi, 36, 190, 203, 204, 215, 216, 220, 221, 230, 237, 247, 253, 256, 263 diffusion, 37, 134, 140, 143, 151, 190 diffusivities, 218 diffusivity, xi, 128, 211, 219, 244 dimensionality, vii, 19, 21, 46, 54, 55 dipole, 49, 71 direct measure, 46 discs, 119

dislocation, 99 dislocations, x, 84, 90, 91, 99, 153, 154, 155, 163, 266 disorder, viii, x, xi, 77, 78, 79, 81, 84, 85, 86, 87, 89, 90, 91, 99, 106, 109, 153, 154, 155, 157, 160, 163, 168, 169, 170, 171, 212, 247, 258, 260, 264, 265, 266, 268 dispersion, 7, 33, 89, 161, 162, 288 displacement, 85, 155, 156, 164 distortions, 80, 84, 89 distribution, 6, 28, 29, 45, 91, 99, 133, 134, 150, 158, 160, 190, 217, 222, 228, 252, 253, 254, 267, 282 distribution function, 158, 160, 282 domain walls, 28, 29 dopant, 250, 266 dopants, 266 doped, xi, 13, 20, 22, 28, 60, 92, 102, 108, 130, 168, 171, 190, 197, 207, 211, 212, 213, 216, 222, 224, 225, 227, 228, 229, 230, 231, 239, 240, 242, 243, 250, 260 doping, x, xi, 5, 12, 13, 24, 28, 29, 33, 53, 55, 70, 79, 80, 108, 122, 127, 153, 154, 155, 179, 197, 202, 203, 207, 211, 212, 214, 217, 223, 227, 228, 230, 233, 237, 239, 244, 248, 251, 266 DSC, 120, 122, 123 ductility, 122, 130, 274

E elastic constants, 91 elasticity, 89, 91 electric field, 136, 147 electrical conductivity, 14 electrical properties, 12 electricity, 24 electromagnetic, 279, 287 electromagnetic fields, 287 electron, vii, 1, 3, 4, 5, 6, 11, 13, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 36, 39, 40, 47, 48, 50, 52, 53, 55, 59, 63, 64, 66, 67, 68, 69, 70, 79, 80, 96, 99, 120, 185, 214, 218, 250, 254, 264, 265 electron beam, 36, 265 electron density, 1, 3, 23, 33, 79 electron diffraction, 29, 39, 40, 254, 265 electron gas, 23 electron microscopy, 123, 179, 181, 188, 200, 203, 207 Electron Paramagnetic Resonance, 76 electronic structure, vii, 3, 21, 30, 46, 49, 50, 52, 54, 58, 69, 97, 109 electronic systems, 37 electron-phonon, 3, 4, 6, 11, 79 electron-phonon coupling, 3, 6, 11, 79 electrons, vii, 3, 5, 13, 24, 25, 26, 30, 31, 32, 47, 48, 50, 51, 53, 60, 69, 70, 71, 203, 279, 281 Eliashberg theory, 4 elongation, 51 ELS, 250 emission, xi, xii, 120, 121, 273, 274, 283, 287, 288,

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

296

Index

289 energy, x, 2, 4, 5, 6, 8, 13, 14, 22, 23, 24, 26, 27, 36, 37, 44, 48, 49, 50, 52, 53, 69, 70, 78, 79, 84, 89, 92, 119, 128, 133, 138, 139, 140, 141, 143, 145, 147, 150, 153, 154, 155, 156, 158, 160, 163, 165, 166, 214, 250, 276, 279, 289 environment, 59, 70, 140, 150 epitaxial growth, 11 epoxy, 140, 141, 143, 149, 151 EPR, 55, 56, 57, 58, 59, 60, 62, 63, 64, 68, 69, 70, 71, 72, 274 equilibrium, x, 8, 105, 166, 175, 178, 184, 188 equilibrium state, 105 equipment, 63 ESR, 70 evacuation, ix, 133 evaporation, 8, 9, 10, 258 evolution, 11, 37, 42, 52, 55, 69, 70, 101 EXAFS, 22, 29, 35, 46, 48, 49, 50, 51, 52, 57 excitation, viii, 23, 24, 77, 80, 185, 189 exclusion, 222 expansions, 275 exponential functions, 167 external magnetic fields, ix, 118, 120, 125, 280 extrapolation, 216, 221, 222, 227, 232

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

F fabricate, xi, 12, 179, 185, 211, 212, 233 fabrication, 2, 11, 12, 14, 119, 150, 154, 212, 214, 232, 233, 237, 238 faults, 99, 250, 266 FEM, 141, 144, 149 Fermi, vii, 3, 4, 5, 6, 7, 11, 20, 21, 23, 25, 26, 31, 46, 79, 80, 96, 97, 98, 191, 203, 205 Fermi energy, 6, 23 Fermi level, vii, 3, 5, 31, 46, 80, 191, 203, 205 Fermi liquid, 20, 21 Fermi surface, 6, 11, 23, 25, 26, 79, 96, 97, 98 ferromagnetic, x, 28, 60, 66, 67, 68, 69, 70, 133, 134, 136, 138, 149, 150, 151 Ferromagnetic, 133 ferromagnetism, 22, 54, 60, 67 fiber, 212 field theory, 78, 83 field-dependent, viii, 20, 62, 156, 164, 165, 167 filament, 128, 129, 141, 235, 237, 251 film, vii, 1, 11, 170, 251 films, 10, 11, 21, 128, 157, 163, 170, 212, 223, 251 finite element method, 134, 138, 147 flow, xi, 43, 44, 45, 120, 122, 163, 273, 278, 280, 281, 289 fluctuations, 25, 27, 28, 45, 55, 78, 79, 81, 84, 85, 86, 87, 109, 164 fluid, 25, 278, 279, 288 flux pinning, ix, 2, 13, 117, 118, 119, 125, 129, 188, 229, 230, 232, 250 focusing, vii, 1 Fourier, 39, 40, 156

Fourier transformation, 156 fracture, 257, 266 free energy, 7, 91 free radical, 22, 54, 55, 59, 60, 62, 67, 70, 71, 72 free-radical, 60 freezing, 46 fusion, 9

G gas, x, 11, 24, 120, 175, 180, 185, 190, 197, 202, 203, 249 gases, 249 gasification, 10 Gaussian, 69 generation, 134, 140, 141, 143, 146, 149, 287 glass, viii, 77, 78, 79, 84, 87, 90, 91, 103, 105, 106, 176 grain, ix, 2, 11, 12, 14, 43, 117, 118, 119, 120, 121, 122, 123, 125, 127, 128, 129, 201, 212, 213, 214, 229, 230, 232, 234, 237, 239, 242, 247, 248, 249, 250, 254, 256, 258, 259, 262, 263, 265, 266, 268, 282, 287, 288 grain boundaries, ix, 2, 11, 12, 14, 118, 119, 125, 128, 129, 212, 214, 232, 237, 247, 248, 250, 258 grain refinement, ix, 117 grains, 43, 118, 119, 122, 128, 129, 190, 218, 223, 229, 230, 234, 235, 237, 239, 241, 242, 248, 250, 254, 256, 258, 266, 268, 287, 288 graphite, 2, 3, 64, 220 groups, 12, 126, 181, 182, 204, 205, 239 growth, vii, 1, 8, 9, 11, 12, 85, 92, 100, 122, 249, 282 growth temperature, 11, 92

H H2, 78, 180, 185, 190, 197, 203, 213, 257 halogen, 40 Hamiltonian, 26, 155, 156, 157 hanging, 212 hardness, 233, 239 harmonic frequencies, 274, 283 harmonics, 287 heat, 7, 8, 9, 105, 119, 120, 121, 123, 124, 125, 127, 133, 134, 140, 141, 143, 144, 146, 147, 149, 150, 212, 213, 233, 234, 235, 236, 237, 238, 239 heat conductivity, 140, 147, 150 heaths, 151 heating, 35, 36, 55, 83, 90, 91, 106, 120, 180, 214, 237, 249, 257 heating rate, 120, 249 height, 100, 123, 141 Heisenberg, 28 helium, ix, 133, 248, 275 heterogeneous, 34 heterostructures, 22, 55, 62, 72 hexane, 36 high pressure, x, 2, 81, 175, 190, 191, 197, 203, 250, 251

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

297

Index high resolution, 99, 263 high temperature, 8, 10, 11, 20, 21, 45, 46, 105, 114, 118, 127, 181, 185, 190, 203, 232, 233, 234, 235, 237, 243, 247 high-frequency, 274 high-Tc, vii, viii, 3, 11, 14, 19, 20, 21, 22, 23, 24, 25, 26, 30, 32, 33, 34, 35, 41, 42, 43, 53, 54, 55, 62, 63, 67, 68, 70, 72, 73, 78, 79, 84, 109, 154, 155, 159, 169, 276, 278, 283, 287, 288, 289 HIP, 233, 234 histogram, 45 Hm, 86, 87, 177, 178, 195, 196 HOMO, 53 homogeneity, 189 homogenized, 134, 135, 140, 149 host, viii, 20, 21, 22, 33, 35, 36, 37, 40, 46, 47, 48, 50, 51, 52, 53, 54, 58, 59, 60, 62, 64, 66, 67, 68, 70, 71, 72 hot pressing, 124, 125, 250, 251, 266 HSP, 94, 97 HTS, 13, 134, 136, 150, 152, 248 human, 5 hybrid, viii, 11, 20, 21, 22, 41, 54, 55, 62, 63, 67, 71, 72, 212 hybridization, 54 hybrids, 35, 54 hydrocarbon, 38, 53 hydrogen, ix, x, 11, 133, 175, 179, 248 hypothesis, 89, 282, 287, 288 hysteresis, 88, 101, 104, 105, 177, 285 hysteresis loop, 88

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

I IFW Dresden, 117 images, 12, 36, 39, 99, 220, 228, 230, 254, 257, 267 imagination, 5 imaging, 248, 254, 268 implementation, 274 impurities, ix, x, 79, 98, 118, 121, 122, 125, 130, 153, 154, 155, 179, 185, 189, 190, 196, 197, 198, 203, 204, 214, 218, 220, 230, 248, 253, 268, 282, 287 in situ, xi, 247, 250, 251, 257, 258 inactive, 59, 63, 67 incompressible, 24 independence, 26 indication, 91, 264 indices, 121 induction, 80, 88, 136, 151, 279 industrial, 11 industrial application, 11 industry, 10 inequality, 176 inert, 20, 249 inhomogeneities, 81, 99 inhomogeneity, 255, 263, 283 inorganic, viii, 20, 21, 22, 35, 36, 37, 39, 40, 43, 44, 45, 54, 55

inspection, 60, 68 inspiration, 72 instability, 13, 190 insulation, 140, 147, 150 insulators, 32 integrated circuits, 13, 14 integration, 158, 176 integrity, 215 intensity, xii, 7, 47, 50, 57, 58, 69, 70, 119, 135, 186, 190, 241, 257, 258, 260, 264, 265, 273, 274, 283, 284, 285, 286, 288, 289 interaction, vii, viii, 2, 4, 5, 8, 19, 20, 21, 22, 23, 26, 27, 28, 32, 33, 36, 37, 41, 46, 50, 51, 52, 53, 54, 55, 56, 62, 67, 69, 70, 71, 79, 227 interactions, 24, 25, 26, 35, 41, 52, 54, 58, 62, 68, 69, 70, 127, 225, 281 intercalation, viii, 20, 21, 22, 33, 34, 35, 36, 37, 39, 40, 41, 42, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 60, 62, 63, 64, 67, 71, 72 interface, 53, 71, 128 interference, 22, 35, 36, 41, 56, 61, 64 intermetallic compounds, x, 153, 154 intermolecular, 59, 70 interpretation, 64, 68, 71, 99 interstitial, 122, 125 interstitials, 118 interval, 85, 101, 106, 154 intrinsic, 42, 53, 67, 70, 287 inversion, 287, 288 iodine, 40, 42, 46, 47, 48 ionic, 3, 30, 32, 36, 37, 40, 47, 71 ions, 13, 21, 30, 32, 33, 36, 55, 69 IOP, 132 iron, ix, 12, 118, 134, 135, 151 irradiation, x, 118, 153, 154, 155, 212, 259 isolation, 96 isostatic pressing, 237 isothermal, 91, 100, 143 isotope, 4, 5 isotropic, 242

J joints, 146 Josephson coupling, 29, 30 Josephson junction, 13, 14, 250, 287 Josephson vortices, 45

K K+, 47, 178 kinetic energy, 24, 26

L L2, 85 lamella, 33 lamellar, viii, 19, 33 Landau theory, 95 large-scale, 11

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

298

Index

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

lattice, viii, x, 3, 5, 12, 13, 20, 22, 27, 29, 35, 37, 39, 41, 45, 46, 47, 48, 51, 52, 53, 54, 58, 59, 64, 78, 80, 84, 85, 86, 87, 89, 90, 91, 100, 120, 121, 122, 125, 128, 153, 154, 155, 158, 176, 215, 216, 217, 220, 221, 222, 225, 228, 230, 231, 232, 249, 263, 266, 287 lattice formation, 176 lattice parameters, 3, 64, 100, 120, 121, 215, 249 law, xi, 82, 135, 141, 273, 280, 289 lead, 2, 14, 28, 62, 63, 79, 85, 86, 98, 118, 134, 170, 265 leakage, 71 LEO, 120 Lewis acidity, 52 ligand, 30, 32, 49, 50 ligands, 37 limitations, ix, 78 linear, 24, 51, 53, 64, 69, 90, 94, 95, 125, 138, 139, 149, 176, 274, 279, 288 linear model, 138, 139 links, xii, 11, 14, 128, 129, 237, 273, 274, 287, 288, 289 liquid helium, ix, 133, 248, 275 liquid hydrogen, x, 175, 179, 248 liquid phase, 90, 176, 266 localization, 31 location, 7, 84, 90, 92, 93, 141 locus, 85 long period, 248 losses, xi, 14, 79, 88, 143, 273, 274, 275, 276, 278, 279, 289 low temperatures, ix, xi, 118, 136, 228, 273, 274, 275, 279, 280, 281, 287, 289 low-temperature, 79 LUMO, 53

M magnesium, ix, 5, 8, 13, 117, 118, 119, 150, 154, 213, 248, 249, 267, 268, 273, 275 magnesium diboride, 5, 150, 154, 273 magnet, x, 80, 133, 134, 136, 143, 150, 151, 157, 211, 212, 214 magnetic effect, 60, 68 magnetic moment, 27, 67, 86, 100, 101, 103 magnetic properties, 56, 64, 72, 266 magnetic resonance, 248 magnetic resonance imaging, 248 magnetism, viii, 20, 22, 24, 54, 59, 62, 67 magnetization, x, xi, 41, 43, 45, 59, 60, 61, 62, 63, 64, 80, 82, 88, 91, 92, 94, 100, 101, 106, 109, 120, 126, 134, 135, 138, 139, 140, 175, 176, 177, 182, 183, 184, 187, 188, 189, 191, 192, 193, 194, 195, 198, 199, 200, 201, 203, 206, 211, 214, 216, 217, 218, 222, 223, 224, 229, 233, 236, 287 magnetizations, 40, 41, 42, 43, 45, 61, 62, 66, 67 magnetometry, viii, 77, 83 magnetoresistance, 11, 62, 258 magnets, viii, 45, 77, 134, 136, 143, 150, 151, 248

manipulation, 63 manufacturing, 130, 143 matrix, x, 22, 25, 34, 62, 96, 133, 134, 138, 139, 140, 149, 150, 151, 212, 214, 228, 267 MBI, 64 measurement, viii, x, 19, 22, 36, 43, 45, 60, 62, 64, 80, 82, 101, 104, 133, 134, 135, 136, 137, 144, 146, 147, 149, 150, 151, 179, 185, 191, 195, 260, 268, 275, 282 measures, 78, 83, 88 mechanical properties, 12 melting, 8, 9, 46, 78, 86, 87, 89, 90, 249 mercury, 37 mesoscopic, 29 metal ions, 55, 69 metallurgy, 118 metals, 1, 3, 9, 10, 28, 31, 32, 203, 233 methanol, 64 Mg2+, 13 mica, 32 micrometer, 128 microscope, 36, 120, 214 microscopy, ix, 118, 185 microstructure, ix, xi, 118, 119, 124, 125, 129, 130, 211, 212, 213, 229, 233, 234, 235, 237, 238, 243, 266 microstructures, xi, 211, 212, 214, 234, 258 microwave, xi, xii, 14, 273, 274, 275, 276, 278, 281, 283, 288, 289 mixing, 47, 49, 50, 179, 180, 257 model system, 54, 72 modeling, 150 models, x, 20, 21, 39, 57, 65, 79, 81, 91, 102, 122, 138, 149, 150, 152, 175, 212, 225, 274, 287 modulation, vii, xii, 19, 28, 29, 34, 35, 64, 273, 287, 288, 289 modulus, 86, 91, 156, 164 molar ratio, 35, 64 mole, 179, 180, 185, 197, 203 molecular orbitals, 52 molecular oxygen, 64 molecular structure, 53 molecules, 21, 22, 37, 52, 54, 55, 70, 71 momentum, 8, 25, 26, 156 monochromator, 64 monomers, 69 morphology, 214, 220 motion, x, 5, 24, 26, 46, 58, 153, 154, 155, 156, 163, 166, 168, 169, 170, 171, 275, 278, 279, 280, 287 motivation, vii, 1, 212 movement, 141, 143 MRI, 248 multilayered structure, 53 muon, viii, 19, 22, 31, 35, 44, 45, 46, 72 muons, 45 mw, 274, 280, 283

N

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

299

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Index nanocrystalline, ix, 12, 117, 118, 119, 124, 125, 127, 129, 130 nanomaterials, vii, 1, 63 nanometer, 127, 128 nanometers, ix, 117, 122 nanoparticles, 186, 212 nanostructures, 12, 55, 62 nanotubes, xi, 211, 212, 220, 222, 228 nanowires, 12 National Science Foundation, 244 NATO, 290 natural, 5, 24, 25, 48, 139, 145 Nb, x, 13, 14, 21, 79, 91, 175, 197, 198, 199, 200, 201, 203, 233, 239, 248 NCS, 2 neglect, 29 neon, 248 network, 68, 69, 118 neutrons, 29 nickel (Ni), 64, 134, 135, 139, 239 niobium, 247, 248 nitrogen, 36, 64, 213 NMR, 24 noise, 260, 284 nonlinear, xi, 51, 138, 139, 149, 273, 274, 283, 287, 288, 289 nonlinear dynamics, 287 nonlocality, 89 non-magnetic, 248 non-uniform, 259 normal, ix, x, 11, 13, 20, 24, 46, 67, 69, 70, 77, 78, 88, 120, 133, 140, 141, 143, 144, 146, 147, 150, 221, 222, 223, 242, 249, 259, 273, 275, 276, 278, 279, 281, 282, 288 normalization, 183 nuclear, 31 nucleus, 47

O observations, 52, 80, 220, 250 observed behavior, 99, 105 oil, 22, 54 onion, 220 operator, 156 optical, ix, 4, 21, 118, 120, 121 optical microscopy, ix, 118 optical properties, 21 optics, 24 optimization, 118, 212 organ, 28 organic, viii, 1, 2, 19, 20, 21, 22, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 63, 64, 70, 72 organic compounds, viii, 19, 21, 22, 35, 37, 55 organization, 28 orientation, 11, 40, 45, 282 orthorhombic, 176 oscillation, 163, 164, 166

oscillations, 50, 163, 164 oscillator, 283 overdoped, 36 oxidation, 11, 24, 30, 31, 48, 50, 51, 54, 119, 248, 249 oxide, ix, 2, 14, 20, 22, 27, 28, 30, 31, 34, 117, 118, 121, 250, 256, 268 oxides, 2, 14, 28, 30, 31 oxygen, vii, viii, ix, 3, 19, 20, 30, 31, 32, 50, 55, 60, 63, 64, 69, 99, 117, 124, 128, 129, 203, 212, 214, 248, 249, 250

P pairing, vii, 4, 5, 19, 20, 21, 22, 23, 25, 26, 27, 28, 30, 32, 54, 55, 70 paper, 127, 190, 243, 244, 274, 283 paramagnetic, viii, 20, 22, 54, 55, 58, 59, 60, 62, 63, 67, 68, 69, 70, 71 parameter, xii, 5, 14, 45, 59, 78, 85, 87, 89, 95, 96, 98, 107, 121, 125, 215, 216, 217, 219, 220, 221, 245, 273, 274, 280, 282, 287, 288, 289 Parkinson, 12, 17 particles, 13, 23, 36, 44, 119, 120, 123, 127, 128, 180, 181, 183, 185, 186, 188, 190, 202, 203, 207 passive, 143, 283 pathways, 71 performance, 139, 197, 212, 223, 233, 237, 248 periodic, 39, 40, 43 periodicity, 281 permeability, 80, 134, 135, 136, 149, 158 perturbation, 53, 70, 104, 275 phase diagram, viii, ix, 8, 9, 10, 46, 77, 78, 79, 81, 83, 84, 86, 87, 94, 97, 99, 103, 106, 107, 108, 109, 118 phase transitions, 43 phenomenology, viii, 77 phonon, vii, 3, 5, 13, 79, 96, 154, 191, 260 phonons, 4, 6, 25 photochemical, 63 photoelectron spectroscopy, 8, 24 photoemission, 5, 6, 263 photons, 7 physical properties, 7, 55, 65, 72, 99 physicists, 2 physicochemical, 67 physico-chemical properties, 22, 34 physics, ix, 2, 21, 24, 77 pinning effect, 228, 230, 274, 276, 279, 281, 289 planar, 23, 24, 49, 62, 70, 99 planetary, 12, 119 plasma, 120, 121 point defects, 118 polycrystalline, vii, xi, 1, 5, 10, 11, 43, 44, 79, 99, 202, 212, 214, 230, 231, 247, 251, 259, 260, 265, 282 polystyrene, 283, 288 poor, 11, 20, 147, 223, 236, 237, 249, 250, 263 population, 70, 72

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

300

Index

porosity, 234, 235, 250, 251, 258 potential energy, 156 powder, ix, xi, 10, 35, 36, 37, 44, 64, 80, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 179, 180, 185, 186, 190, 197, 198, 202, 203, 204, 212, 213, 214, 220, 239, 241, 242, 247, 248, 249, 251, 252, 253, 263, 264, 275, 282, 283, 288, 289 powders, ix, xi, 12, 117, 118, 119, 120, 121, 122, 124, 127, 129, 190, 213, 247, 248, 249, 252, 253, 254, 257, 264, 267, 268 power, ix, 13, 82, 133, 141, 144, 258, 274, 275, 283, 284, 285, 286, 288 power-law, 258 precipitation, 99, 128 prediction, 5, 28, 87 pressure, vii, x, 1, 2, 5, 8, 9, 10, 11, 64, 81, 92, 100, 118, 119, 175, 181, 190, 191, 197, 203, 249, 250, 251 prices, 2 pristine, viii, ix, 20, 34, 35, 36, 37, 38, 40, 41, 42, 43, 46, 49, 50, 51, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 77, 78, 80, 81, 91, 92, 94, 95, 98, 99, 100, 101, 106, 108, 109, 155, 283 probe, viii, 20, 22, 35, 46, 54, 62, 64, 119, 214, 264 production, 249 program, 10, 140, 149 proliferation, 90 propagation, x, 133, 143, 144, 147, 150, 151, 152 property, x, 24, 32, 35, 36, 42, 43, 62, 67, 71, 164, 168, 175, 180, 181, 185, 190, 197, 203, 279 proposition, 89 protection, 140, 143 protocol, 102, 103, 104 p-type, 164 pulse, 143, 214, 283 purification, 64 pyramidal, 30, 69, 70

Q quadrupole, 49 quantum, 13, 22, 23, 24, 28, 29, 35, 36, 41, 43, 56, 61, 64, 78, 155, 156, 160, 176, 279 quantum fluctuations, 28, 43 quantum fluids, 24 quantum well, 23 quartz, 119, 179 quasiparticle, 28, 163, 274

R radiation, viii, 20, 36, 64, 120, 144, 213 radical, 22, 54, 59, 62, 63, 64, 67, 70, 71 radius, 89, 138, 139, 140, 141, 149, 176 Ramadan, 17 Raman, xi, 5, 57, 247, 260, 261, 264, 265, 268 Raman scattering, 5 Raman spectra, 5, 260, 261

Raman spectroscopy, xi, 57, 247, 268 random, x, 78, 84, 153, 154, 155, 156, 160, 163, 164, 165, 166, 167, 168, 171, 282 random walk, 163, 164, 165 range, ix, x, xi, 2, 14, 20, 21, 28, 38, 47, 60, 67, 68, 69, 71, 78, 91, 93, 118, 119, 123, 124, 125, 129, 133, 144, 153, 154, 155, 156, 157, 160, 161, 162, 163, 166, 213, 228, 237, 248, 249, 258, 259, 260, 262, 263, 273, 276, 278, 280, 282, 283, 285, 289 rare earth, 32 rare earths, 32 raw material, 211 reactant, 36, 64 reaction rate, 248, 253 reaction temperature, 180 reactivity, ix, 117, 119, 122, 123, 253, 264 reagents, 35 reasoning, 53, 70 recall, 258, 260 recovery, 48, 143 rectification, 287 reduction, 12, 21, 48, 50, 51, 54, 79, 91, 98, 119, 122, 158, 160, 179, 180, 181, 185, 186, 191, 196, 203, 234, 235, 248, 251, 268 reflection, 57, 274 regulation, 55 relationship, 11, 21, 46, 54, 55, 67, 123, 125, 212 relaxation, viii, 19, 35, 44, 45, 46, 105 relaxation rate, 45, 46 research, vii, 1, 2, 20, 21, 34, 79, 118, 126, 154, 215 reservoir, 30, 37 resin, 36 resistance, xi, 13, 14, 120, 143, 146, 273, 274, 275, 276, 278, 280, 282, 289 resistive, 222, 250, 260, 274 resistivity, xi, 11, 24, 83, 97, 100, 147, 162, 163, 168, 169, 170, 182, 186, 187, 191, 192, 198, 199, 204, 205, 214, 217, 221, 222, 223, 228, 229, 231, 247, 249, 250, 251, 254, 255, 256, 258, 259, 266, 267, 268, 275 resolution, 5, 6, 22, 35, 36, 39, 40, 99, 144, 263 returns, 143 rigidity, 37, 287 rings, 230 rolling, 119, 127, 130, 212, 213, 237, 239, 242, 243 room temperature, 3, 36, 56, 64, 249, 255, 256, 258, 266, 267, 275 root-mean-square, 164, 165, 167 runaway, 134, 136, 143, 144, 149

S safety, ix, 133, 134, 139, 140 salt, 1, 35, 36, 40, 46, 48, 49, 50, 52, 53, 54, 57, 58, 59, 63, 64, 70, 71, 72 salt formation, 36 salts, 36, 37, 54, 59 saturation, 242 scanning calorimetry, 122

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

Index scanning electron microscopy (SEM), ix, xi, 12, 118, 123, 128, 179, 183, 185, 188, 190, 200, 201, 203, 207, 211, 214, 234, 235, 236, 237, 254, 257, 258, 266 scattering, xi, 3, 5, 8, 11, 28, 50, 79, 80, 94, 96, 97, 98, 99, 109, 122, 211, 218, 219, 220, 223, 225, 227, 231, 232, 244, 245, 256, 258, 259, 265, 266, 274, 281 scavenger, 64, 67 scientific community, viii, 273 scientists, 1, 2, 22 search, 8 selectivity, 46 self-organization, 28 SEM micrographs, 235, 236 sensitivity, 11, 275 sensors, 144 separation, 24, 29, 33, 35, 37, 41, 42, 43, 46, 54, 80, 91, 249, 263 series, viii, xi, 20, 22, 38, 41, 42, 53, 123, 125, 179, 199, 220, 224, 233, 239, 243, 247, 257, 259, 260 shape, 7, 8, 69, 105, 138, 249, 275, 282, 285, 289 sharing, 27, 144 shear, 89, 91, 156, 164 short-range, x, 28, 153, 154, 155, 156, 157, 160, 161, 162, 163 shoulder, 93 shoulders, 260 sign, x, 6, 59, 62, 153, 162, 163, 168, 169, 170, 171 signals, xi, 45, 69, 105, 273, 274, 283, 286, 287, 288 simulation, 87, 135, 140, 143, 147, 149, 151 simulations, 141, 147, 150 single crystals, viii, 8, 77, 80, 81, 91, 92, 93, 94, 95, 97, 98, 99, 101, 102, 104, 106, 108, 109, 251, 252 sintering, 8, 13, 118, 122, 127, 179, 180, 181, 183, 185, 190, 191, 197, 203, 212, 250, 251, 266 SIS, 43 sites, 26, 30, 55, 63, 69, 122, 125, 166, 168, 169, 170, 171, 181, 204 skills, 63 skin, 279 smoothing, 86 software, 140, 141, 258 solid matrix, 22, 34, 62 solid phase, 180 solid-state, viii, 2, 10, 20, 21, 35, 36, 55, 62, 63, 72, 213 soliton, 27 solubility, 203, 214 solutions, 86, 90 solvent, 36, 56 solvents, 71 spacers, 20 spatial, 28, 89, 176 species, viii, 20, 21, 22, 34, 35, 37, 40, 46, 47, 48, 52, 53, 54, 55, 59, 62, 64, 69, 72 specific heat, ix, 5, 7, 8, 140, 194, 195 spectral component, 69 spectroscopy, viii, 5, 6, 7, 8, 28, 56, 63, 100, 120,

301

121, 250, 263 spectrum, 23, 28, 45, 59, 69, 157, 233, 260 speed, 13, 119 spin, viii, 6, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 35, 41, 44, 45, 46, 54, 55, 56, 58, 59, 60, 62, 63, 66, 67, 68, 69, 70, 71, 72 spin dynamics, 20 spin-1, 27, 28 SQUID, viii, 22, 35, 36, 41, 56, 61, 64, 77, 80, 97, 100, 101, 109, 182, 188, 191, 198, 204, 214, 255 stability, ix, x, 8, 11, 62, 133, 145, 147, 150, 195, 197, 237 stabilization, 55, 72, 201, 232, 237 stainless steel, xi, 211, 212, 213, 214, 233, 239 standard model, 28, 29 stars, 225 steel, xi, 211, 212, 213, 214, 233, 239, 243 stoichiometry, xi, 101, 118, 128, 180, 247, 248, 249, 256, 257, 262, 263, 266, 268 storage, 36, 249 storage ring, 36 strain, ix, 12, 53, 118, 120, 121, 122, 125, 222, 249, 250, 259 strains, 191 strength, 4, 21, 23, 28, 34, 40, 43, 78, 84, 87, 156 stress, 53, 88, 95 stretching, 3, 4 structural defect, 125 structural defects, 125 substances, ix, 117 substitutes, 80 substitution, viii, xi, 5, 12, 13, 36, 77, 79, 80, 91, 97, 98, 99, 100, 109, 128, 181, 203, 204, 205, 211, 212, 214, 228, 230 substitution effect, 79 substitution reaction, 36 substrates, 12 superconducting gap, 6, 79, 98 superconducting materials, 21, 33, 34, 274, 281 superconductivity, vii, viii, ix, 1, 2, 3, 4, 5, 13, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30, 32, 34, 35, 36, 37, 40, 41, 42, 43, 53, 54, 55, 59, 62, 63, 67, 71, 72, 73, 77, 79, 94, 131, 159, 191, 273, 274, 279 superconductor, vii, viii, ix, x, xi, 1, 2, 4, 5, 13, 14, 19, 21, 33, 34, 42, 43, 44, 45, 52, 53, 54, 63, 67, 77, 78, 79, 88, 91, 92, 95, 96, 98, 102, 103, 133, 145, 155, 158, 175, 179, 185, 186, 190, 192, 197, 211, 215, 218, 232, 244, 274, 280, 281 superlattice, 28, 29, 53, 265 superlattices, viii, 20, 21, 22 superposition, 57, 69 suppression, 27, 28, 55, 70, 71, 190, 191, 196, 197 surface area, 122 surface layer, 288 surplus, 118 susceptibility, viii, x, 19, 22, 35, 36, 60, 66, 67, 77, 80, 81, 82, 83, 84, 88, 89, 90, 92, 93, 94, 101, 102, 103, 104, 105, 106, 175, 255, 262, 283 s-wave, 4, 6, 13, 14, 79

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

302

Index

switching, 146 symbols, 121, 224, 227, 229, 232, 284, 285, 286 symmetry, 6, 14, 25, 26, 33, 69, 138, 284 synchrotron, viii, 20, 36 synchrotron radiation, viii, 20 synthesis, vii, 1, 5, 11, 12, 36, 54, 63, 212, 228, 231, 249 systems, viii, 24, 43, 54, 77, 146, 151, 186

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

T tantalum, 10, 249 technical assistance, 131, 289 technology, 2 temperature dependence, xii, 14, 45, 125, 182, 225, 254, 258, 273, 275, 276, 277, 282, 283, 284, 289 tension, 78 terminals, 181, 186, 191, 198, 204 thallium, 20 theory, vii, x, 1, 4, 8, 20, 26, 27, 35, 43, 73, 81, 109, 153, 154, 155, 159, 163, 165, 169, 170, 171, 194, 279, 281, 282, 289 thermal energy, 163 thermal stability, 237 thermal treatment, 118 thermodynamic, vii, 1, 8, 11, 46, 59, 78, 157 thermodynamic equilibrium, 157 thermodynamic stability, 11 thermomechanical treatment, 237 thin film, 2, 11, 14, 54, 125, 163, 169, 171, 197 three-dimensional, 3, 79, 159, 281 threshold, 102 time, vii, ix, 1, 2, 10, 29, 31, 35, 45, 105, 106, 117, 121, 122, 123, 124, 125, 126, 140, 141, 142, 144, 146, 147, 150, 163, 180, 189, 212, 215, 238, 248, 276, 281, 284, 288 titanium, xi, 211, 212, 213, 233 topological, 91 topology, 11, 96 torque, 83 transfer, 24, 31, 37, 40, 47, 48, 49, 51, 52, 53, 54, 58, 59, 70 transformation, 89, 105, 156, 177, 196 transformations, 156 transition metal, 55, 58, 69, 76 transition metal ions, 55, 69 transition temperature, vii, viii, xi, 1, 2, 4, 5, 8, 13, 19, 20, 28, 34, 35, 40, 44, 45, 46, 55, 67, 78, 79, 125, 168, 181, 186, 211, 247, 255, 277, 281 transitions, 4, 20, 49, 69, 87, 100, 176, 217, 222 translation, 13, 91 transmission, 22, 35, 99, 120, 181, 214 transmission electron microscopy, 181 Transmission Electron Microscopy (TEM), xi, 36, 123, 131, 181, 211, 214, 220, 228, 230, 244, 254, 266, 267, 268 transparent, 44, 45 transport, ix, xi, 3, 24, 62, 77, 83, 119, 126, 165, 211, 214, 216, 222, 233, 234, 236, 237, 238, 250, 260,

268, 281, 289 trend, 124 triggers, 91 tubular, 215 tungsten, 119 tungsten carbide, 119 tunneling, 7, 8, 21, 24, 25, 26, 41, 43, 44, 59, 62, 67 tunneling effect, 62 two-dimensional, 2, 3, 4, 24, 26, 27, 28, 34, 35, 55, 79, 281

U uniform, 13, 55, 89, 259, 279

V vacancies, 99, 250, 264, 266 vacuum, 8, 11, 36, 53, 55, 64, 119, 249 valence, 27, 31, 32, 33, 41, 49, 50 validity, 21, 81, 97 vapor, 8, 9, 10, 11, 12, 249, 251 vapor-liquid-solid, 12 variables, 51 variation, viii, xi, 7, 20, 43, 46, 48, 51, 54, 77, 82, 83, 86, 92, 93, 94, 95, 96, 100, 101, 107, 118, 136, 190, 202, 211, 225, 228, 239, 240, 244, 247, 255, 259, 266, 273, 276, 278, 281, 288 vector, 7, 135, 164 velocity, 26, 98, 144, 147, 150, 166 vibration, 5, 13 visible, 181, 183, 188, 191, 197 visualization, 141 voids, 250, 258 volatility, 8, 249, 250, 264 vortex, viii, ix, x, 43, 45, 46, 54, 59, 68, 77, 78, 79, 81, 83, 84, 85, 86, 87, 89, 90, 91, 94, 97, 98, 99, 102, 103, 105, 106, 107, 108, 109, 153, 154, 155, 156, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 212, 215, 275, 279, 281 vortex pinning, 84, 85, 86, 87, 212, 215 vortices, 68, 78, 84, 85, 89, 91, 104, 164, 228, 279, 281, 289

W water, 22, 54 wave vector, 7 wavelengths, 89 weak interaction, 53 weight ratio, 197 welding, 119, 120, 122 wetting, 254 wires, xi, 2, 10, 119, 130, 150, 185, 190, 197, 211, 212, 213, 214, 233, 234, 236, 237, 238, 239, 243, 274

X XANES, 22, 35, 46, 47, 48, 49, 50, 53, 64

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

Index X-ray absorption, viii, 20, 22, 35 X-ray diffraction (XRD), ix, xi, 12, 22, 35, 36, 37, 38, 39, 40, 46, 50, 56, 57, 64, 65, 118, 120, 121, 123, 128, 180, 186, 190, 191, 198, 201, 203, 204, 207, 211, 213, 215, 220, 222, 230, 241, 253, 256, 257, 258, 266, 268

Y YBCO, 14, 21, 24, 26, 53, 143, 281, 287 yield, 3, 23, 146, 274

Z

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

zirconium, 249 Zn, x, 5, 175, 202, 203, 204, 205, 207 ZnO, 203, 204, 207

Magnesium Diboride (MgB2) Superconductor Research, Nova Science Publishers, Incorporated, 2008. ProQuest Ebook Central,

303