MEASUREMENT OF THE FARADAY EFFECT IN TRANSIENT MAGNETIC FIELDS

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The Pennsylvania State College The Graduate School Department of Physics

Measurement of the Faraday Effect in Transient Magnetic Fields

A thesis by Paul Rice Camp

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy June 19 £l

Approved*

Head of the Department

TABIE OF CONTENTS I.

II.

Introduction A, The Faraday Effect 1„ Early work 2. Theory 3. More recent work Methods of measurement Bo Present Study 1. Scope 2, Value of present study 3o Summary of the method Measurements A. Experimental Data 1 0 Calibration 20 New data

III o Me asurement A. Method 1. Transient fields 2. Detailed description of thesystem 3„ Interpretation of photographicdata U. Discussion of error Bo Operation of System Co Detailed Discussion of the Polarimeter 1, Analysis 2, Discussion of Figure 8 Do Field Equipment 1, Batteries 2« Switch 3, Coil IV,

Possible Further Work A. Energy Storage 1. Further study of battery storage 2. Investigation of magnetic fieldstorage Bo Refinements of Measuring Technique 1, Battery power supply 2, Do Co amplification before switching 3, Double image prism analyzer Uo Calibration mechanism 5, Sweep expansion C. Studies of Matter lo Stresses 2. Reaction rates

Appendix I 1, 2,

Energy Storage General considerations Possible methods

1 2 It 6 7 8 8

9 10

11 13 17 19 20 21 25 27 32 35

36 37 37 38 38 38 39 39 39 U0 U0

Appendix II Appendix III

Preliminary Investigation of the Battery Problem

I4.2

Bursting Strength of a Coil

Bibliography Acknowledgements

il9

I. A.

INTRODUCTION

The Faraday Effect, 1.

Early Work?

In the days when Physics was still the study of

"Natural Philosophy", there was, even as now, a division of the major mysteries into a few distinct categories. Light, and Magnetism,

Among these were Electricity,

A very tempting study, therefore, was the

interaction of one with another.

It was hoped that such a study would

establish some relationship between them.

The first interaction between

light and magnetism was found in 18U£ by Michael Faraday^^ after many months of fruitless experiment.

It is known today as the Faraday effect.

He found that if a beam of plane polarized light is passed through a medium in a magnetic field, and if the direction of propagation of the light is parallel to the lines of force of the field, then the plane of polarization of the light is rotated.

The angle of rotation,

he discovered, is proportional to the field strength and the length of path in the field, the constant of proportionality being a property of the material, Faraday, a zealous experimenter, was content only after he had tested all the suitable materials which he could obtain.

However, his

apparatus was crude, and there were many materials in which he was unable to find any effect at all. Subsequently, Verdet^'^, working with more refined apparatus, carried on such an extensive and careful study of this effect that the constant of proportionality has become known as Verdet's constant. Thus, if 0 is the angle of rotation In minutes of arc, H the magnetic field strength in Oersteds, and Jl the length of path in centimeters, Verdetrs constant (V) is defined by the equation

Q —

f~/

It is found that V is a function of temperature and wavelength.

Except

as noted later, It is not a function of field strength. 2.

Theory;

Natural Rotation was first theoretically analyzed by

Fresnel in terms of a decomposition of plane polarized light into two circularly polarized beams, one right handed and one left handed.

He

further postulated that the index of refraction was different for the two beams.

The same explanation holds for the rotation caused by the

Faraday effect.

Righi and Becquerel demonstrated this experimentally

by producing interference between two circularly polarized beams, one of which passed through material in a magnetic field.

When the field

was turned on, the fringes moved and the direction of displacement of the fringes depended on whether right or left handed circularly polar­ ized light had been used.

The index of refraction increased for one

and decreased for the other. It was not until the advent of the electromagnetic theory of light that a satisfactory explanation of the Faraday effect was given by fo 'S W. V o i g t « A better and more satisfying explanation was given by Larmor and is based on the Larmor precession.

This analysis is covered

in an interesting manner by R. W. Wood in his book "Physical Optics"^) from which the following treatment was taken. If a beam of right circularly polarized light of angular frequency W passes through a medium in a magnetic field, it is reduced in velocity by an amount corresponding to the index of refraction.

Let curve (a)

of Figure 1. give the dispersion of the index of refraction.

If now

the field be turned on, the electron configuration in each atom rotates with an angular frequency CJ (the Larmor precession).

Let us suppose

that this rotation is in the same direction as that of the rotation of

-

2

-

t

the electric vector or the light*

Then -we must increase the frequency

of the light to W + to for the refractive index to be the same as we had before.

For this increases the angular velocity of rotation of the

light (i.e. its frequency) by an amount sufficient to compensate for the Larmor precession.

If we had supposed the Larmor rotation to be in

the opposite sense to that of the light, we would have had to reduce the frequency to W — (*) ,

Thus for right handed circularly polarized light,

we have dispersion curve lb, and for left handed polarization, curve lc. Then at a given frequency, there is a different velocity for each component. Velocity = V ± (dV/dST) GO If

is the velocity of the right handed component and V 2 is that of

the left handed component, and if the path length in the medium is L,

-

3

-

then the rotation of the plane of polarization will be # = - ¥ ( % - % * )

=

But V = c/n and W = 2 V w h e r e

e is the velocity of light in a vacuum

and n is the index of refraction.

Fa

-'*•

/

R

-

radi^ns

(*¥$*)

The rotation is therefore

-£jlJK a Zfnc*

jdn_ dA

since the angular frequency of the Larmor precession is Figure Id, shows the resultant rotation.

Go = eH/2mc,

For the case illustrated,

that of the normal Zeeman doublet,, note that the rotation is symmetrical about the resonant frequency.

If one component were partially absorbed,

obviously the symmetry would be destroyed, 0 'Connor^ ^ has used this equation in conjunction with the LorenzLorentz equation for the index of refraction with considerable success to determine the Verdet constant throughout the visible and ultra violet range. More Recent Works

It was stated in section 1, that Verdet found

the constant to be independent of field strength,

Wood^^ and others

have investigatei this effect in thxn films of iron, ruckle, and cobalt. As might be expected on the basis of the foregoing analysis, the effect was found to depend on magnetization rather than II, (7) Konigy' J has done a remarkable piece of work in which he formed a

thin film of iron in a vacuum and then examined it by electron diffrac­ tion methods while measuring the magnetic rotation.

He gradually

admitted air to the system as he made measurements.

He concluded that

the presence of an oxidized surface layer had caused the prevlous results for iron films to be in error by a factor of about two. results were in good agreement with theory.

His

The Faraday effect takes place almost immediately after the field is established.

Early experiments by Abraham and Lemoine^^ have o determined that the time lag is less than 10 seconds,, Beams and

Allisonw > have measured the clifferences in time lag for various _9 materials and found that these differences are of the order of (l-lO)xlO seconds. When the rotation produced by the field is in the same direction as the current producing the field, the Verdet constant is defined as positive.

Verdet found that paramagnetic substances produced a negative

rotation.

Subsequent investigation showed that even some diamagnetic

substances produce negative rotation.

The positive rotation was found

to be independent of temperature and the negative rotation dependent on temperature.

Hence the terms diamagnetic rotation and paramagnetic

rotation are used although they do not relate to the type of magnetic material involved.

Gr o ss m an ^ ^ has shown that the negative Faraday

effect may be temperature independent and therefore the distinction may not be made solely on the basis of the sign of the Faraday effect.

It

is customary to refer to the temperature dependent part as paramagnetic and the temperature independent part as diamagnetic^-1--1-). The Verdet constant, as mentioned earlier, is dependent on X° This is evident from the fact that both X and d n / d X enter into equation 1.

A very complete investigation of frequency dependance has been

carried out.

Kartschagin and Tschetwerikov (12 ) ' have made measurements

in the X ray region.

0*C o n n o r a n d others(^3) -j_n yhe ultra violet.

Others too numerous to mention have concerned themselves with the visible, many values being tabulated in the International Critical Tables.

I n g e r s o l ^ ^ has done some very good work in the infra-red. -

5

-

Wilson and Hull (I' v d ) have extended the range still further by carrying out measurements in the micro-wave region0 Much interest has been shown in the effect of phase of the material on the Verdet c o n s t a n t ^

^

^„ G a b l e r ^ ^ has studied the problem

in doubly refracting media,, Li

Methods of Measurement;

In general, when rotation of the plane

of polarization is to be measured, some sort of null method is used0 The simplest method, of course, is merely to rotate an analyzing nicol until a visual minimum is perceived and to measure the angle. There have been numerous improvements on this simple extinction method.

Perhaps the most obvious is to substitute a photoelectric cell

for the eye.

R a n k ^ 0 ^ has used this method in conjunction with a

recording potentiometer to plot the intensity curve in the vicinity of a null.

By extropolation to the null point, he has obtained accuracies

of .003° which, he suggests, may be a limit imposed by the nicols themselves. Walkerhas

extended this method to high measuring speeds by

revolving an analyzer in front of a photo-multiplier tube at 10,000 r.p.m, and feeding the output to the vertical deflection plates of an oscilloscope.

The horizontal sweep was synchronized with the rotation

of the analyzer.

Thus the position of the null was changed by an amount

proportional to the rotation. Since an ordinary extinction method is unsatisfactory in the presence of even a small amount of unpolarized light (due to scattering and other causes), a number cf ingenious methods have been contrived for balancing intensities a few degrees on either side of the nullc shadow, the biquartz

, and the Cornu-Jellet

-

6

~

(2 3)

The Lippich half

prism methods all use

■this technique*

Measurements of this kind are possible in the presence

of as much as 95% unpolarized light An interesting "mechaid.zation11 of the biquartz technique is used by (25) Roualt . He has only one half of the biquartz in the field at a time and uses as a detector a photoelectric cell connected to a ballistic galv »nometero

If, when he flips the biquartz through the field so that

the other half Is now in place, there is no deflection of the ballistic gal? anometer, the system is balanced* Other methods have been used In which the actual measurement is not one of angle.

A compensating cell filled with material h .ving a large

Verdet constant in a compensating field has been used f9 ). Then the current in the compensating coil necessary to bring the whole system back to a null condition is measured. These methods all involve the finding of a null or balance point and are consequently poorly adapted to very rapid measurement0 In section III, a new method specifically designed for high speed measure­ ment is discussed* Bo

Present Study 1.

Scope;

An attempt has been made in the present work to make

possible the extension of the study of the Faraday arid other magneto­ optical effects to very nigh magnet:.c field strengths*

To this end,

a system has been conceived and built which takes into account the special problems with which the worker at high field strengths is confronted*

A decisive start has been made on the achievement of very

high field strengths and the basic switching and measurement apparatus constructed.

Measurements have been taken at fields up to about 20,000

Oersteds and provision for extending the range to more than £0,000 Oersteds

■with the additj on of a relatively small amount of equipment have been made*

A brief survey of methods of measurement of rotation and a study

of the problem of rapid measurement are included. 2.

Value of Present Study:

Present methods

are limited

to samples which are available in reasonable quantity.

Since the

rotation is proportional to field strength, the ability to make measure­ ments at very high field strengths makes it possible to measure samples which are either too expensive to be obtained in bulk or which naturally occur in small size (as, for example, certain crystals).

Furthermore,

the method developed can be used to measure materials which are too opaque or introduce too much scattered light for measurement in large samples.

The appartus is specially designed to be unaffected by large

amounts of unpolarised light. For measurement of the Cotton Mouton effect, in which the relative 2 retardation is proportional to H , high fields are particularly desir­ able.

There is also now good reason to believe that for the region , (27) where H/kT is large, the Verdet constant will vary with H 0 3. apparatus.

Summary of the I.tethod.‘. Figure 2. xs a simplified 'diagram of the Its operation is as follows;

Light from microscope illuminatxng lamp S is collimated by lens L-j_ and passes through inter ferenee filter F.

It xs plane polarized by

polarizor P, and focused on the sample space by lens emerging from the sample space is focused by lens are slightly converging. this beam.

The light so that the rays

Totally reflecting prism LI intercepts part of

The. part of the beam above the prism passes through analy­

zing polarizor

and on to photoelectric cell 2.

The lower part of

/

9o

S L,

F

P

La

C

Ls

M

P£ 3

i

a nd C t>mf>a.Kison /? ccordt ng

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