A study of ferromagnetic domains in perminvar possessing. A rectangular hysteresis loop

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A study of ferromagnetic domains in perminvar possessing. A rectangular hysteresis loop

E.W. Lee

To cite this version:

E.W. Lee. A study of ferromagnetic domains in perminvar possessing. A rectangular hysteresis loop. J.

Phys. Radium, 1959, 20 (2-3), pp.109-112. �10.1051/jphysrad:01959002002-3010900�. �jpa-00235998�

A STUDY OF FERROMAGNETIC DOMAINS IN PERMINVAR ^POSSESSING

A RECTANGULAR HYSTERESIS LOOP

By ^{E. W.} LEE,

University ^of Nottingham, England.

Résumé. 2014 Cette communication résume les résultats d’une série d’expériences qui ^avaient

pour but l’étude des domaines élémentaires dans un alliage, « Perminvar » et dans un ferronickel de

composition ⁶⁵ % Ni, ³⁵ % Fe, ^ces alliages possédant, tous les deux, ^des cycles d’hystérésis ^rectan- gulaires après ^un recuit dans un champ magnétique. L’utilisation de l’effet Kerr nous a permis ^de

constater que les domaines, ^{dans un} échantillon annulaire désaimanté sont eux-mêmes annulaires et d’une largeur voisine de ¹ mm. Les mesures de la perméabilité réversible indiquent que les parois

sont retenues par des forces intérieures ^très importantes. ^{Dans les} champs ^{forts et} alternatifs c’est le déplacement radial d’une seule paroi qui produit l’aimantation observée.

Abstract.

A brief account is given ^{of a series of} investigations directed towards understanding

the properties ^{of the} elementary domains in

Perminvar

and 65/35 Nickel-Iron, ^which acquire rectangular hysteresis loops ^after being annealed in a magnetic ^field. Investigations using ^the magnetic Kerr effect show that in a " demagnetized " state, annular rings of these materials contain annular domains about 1 mm wide. Reversible permeability measurements indicate that the domain walls are very strongly ^held by internal forces. At high inductions magnetization ^takes place by ^{radial movement of a} single wall from the inner edge.

20, 1959,

1. Introduction.

Ferromagnetic ^materials pos-

sessing ^à rectangular ^B-H loop ^are of interest because of their application ^as storage ^elements in magnetic memory arrays. Those in which the

rectangular B-B’loop ^{is a} conséquence of uniaxial

anisotropy ^induced by annealing ^{in a} magnetic

field are important ^{on account of} the simple

domain structure which they ^{possess. Bitter} pattern investigations by ^{Williams and Goertz} [1]

showed that an annular ring ^of Perminvar,

annealed in a circular magnetic field, usually ^con-

tains only ^{two or} three domains separated by ^cir-

cular 1800 walls concentric with the edges ^{of the} specimen. ^In consequence ^{of the} simple ^domain

structure, ^the process of magnetization ^is simple

and the theoretical consequences of ^a simple

domain model have a greater ^{relevance to the}

experimentallyobserved behaviourthan is the ^case with more complicated multi-domain materials.

The object ^of this work is to investigate ^as fully

as possible the domain structure and domain beha- viour in materials of this type. ^{The two materials}

chosen were Perminvar (45 % Ni, ³⁰ % Fe,

25 % ^{Co) and} 65/35 Ni-Fe. Unless otherwise stated all the specimens ^{were in the form of annular} rings ^{2.54 cm external and 2.04 cm internal dia-}

meter. After a suitable magnetic anneal each

specimen developed ^the anticipated ^rectan-

gular ^B-H loop.

2. Domain structure.

The domain structure in these materials was investigated using the magnetic

Kerr Effect technique ^described by ^us [2]. ^{In this}

method ^{a small} rectangular image (light probe) ^is

focussed ^{on to} the surface of the specimen ^under investigation. The reflected beam is passed

through ^a polarising ^{element and is collected} by

a photomultiplier. ^{If a small} alternating ^field

is applied ^{to the} specimen the domain walls

oscillate, ^{and il an} oscillating domain wall traverses the probe ^the output ^{of the} photomul- tiplier ^is lightly modulated. The _presence of an

alternating component ^{in the} photomultiplier

output ^{can then be taken as evidence of an oscill-} ating domain ^{wall. This} method, though ^{limited to}

FiG. 1. - Position of domain wall after A. C.

demagnetization.

the investigation ^{of materials with a coarse domain}

structure, ^{has the} advantage ^of requiring ^no special preparation ^{of the} surface since imperfections merely produce ^a steady signal ^{which is subse-} quently ^removed.

The ^domain structure of these specimens ^was investigated (a) ^{after the} magnetic anneal, (b) ^after demagnetization by gradua] ^{reduction of an alter-} nating ^{field and} (c) ^at remanence. In the first

case the rings ^{contained a} small number of domains

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-3010900

110

varying ^{from two to six. The} domain walls were

found to extend throughout ^{the thickness of the} rings ^{and in the case of the} 65/35 ^Ni-Fe alloy ^there

is evidence of ^a systematic variation in the ave-

rage number of walls with the thickness of the

specimen. ^{In Perminvar a} similar domain struc- ture was observed after demagnetizing by gradual’

reduction of a 50 c/s alternating ^field. However, repetition ^{of the} procedure always brings ^{about a}

structure slightly ^{different from the} previous ^one.

Fig. 1 ^{shows the} results of 50 successive demagne-

tizations during which the maximum number of walls observed was eight and the minimum three.

It was not ascertained that each " demagnetized state " actually possessed ^{zero intensity of magne-}

tization. It is evident that the walls have a certain

preference ^{for some} parts ^{of the} specimen ^and rarely ^{come to rest} in others. This point ^{is taken}

up ^later. At remanence traces of walls could sometimes be seen near the inside edge ^{but these}

were more like large ^Née] spikes than circular walls.

3. Reversible permeability ^and losses in Per- minvar.

Measurements ^of reversible permea-

bility and losses were made using ^{an A. C.} bridge operating ^{at 2.7} kc/s ^{at which} frequency eddy-

current screening ^{effects are small.} Fig. ^{2 shows}

FIG. 2.

the results obtained at room temperature. ^Measu-

rement°s taken at - 183 OC and 100 OC gave results not appreciably ^different from those at room tempe-

rature. The reversible permeability ^is always

small but varies with field in a manner similar to that observed in normal materials. The ^{losses were} f ound to varywith frequency ^like eddy-current ^fosses

and so it is convenient to express ^the results in terms of a dimensionless ratio, "’1), of the observed losses to those calculated from classical eddy-

current theory ^{which assumes a uniform scalar} permeability. ^{At remanence uR} and -1 ^are

observed to be alrnost independent ^of temperature

as shown in Fig. ^3. As may be seen -1 is signi- ficantly greater ^than unity, indicating ^{that even}

in the absence of a circular domain wall, magnetic

processes ^occur which are sufficiently important

to contribute a reversible permeability of ^about 100,

a permeability ^{moreover which must be} sufficiently

n on-uni f orm to account for the observed values of _q.

FIG. 3.

_uR and -1 ^{at remanence.}

To investigate the effect of a circular wall the

specimen ^was saturated and a wall nucleated by ^a

small pulsed field obtained from a condenser dis-

charge. ^{That this} procedure does nucleate a single

wall was verified by ^{use of the} Kerr effect. The

Wall position. Distance from inner edge.

Total width of specimen

^100.

.

FIG. 4

position ^{of the wall} was determined by saturating

the specimen ^and comparing the deflection on a bal- listic galvanometer with that obtained when the saturation magnetization ^was reversed. Results

are shown in Fig. ^{4. A wall seems to} be nucleated

and pushed ^{to a} position ^of only metastable equi-

librium by ^this process since ^{it was} observed that when small exciting ^{fields were} applied ^{to the} specimen uR ^was of the order 40(Y as shown in Fig. ^4.

Larger exciting fields caused a sharp ^and always

irreversible drop ⁱⁿ uR. The effect of the nucleated wall is to increase both _vR and _YJ. However, ^{in neither}

is the increase _very great ^{and it must} be inferred that the wall is strongly ^held by ^{interna] forces.}

Our tentative interprétation ^{of these} results is as

follows. Close examination of the powder patterns obtained on Perminvar [1] ^{shows that the domain}

walls are not truly ^{circular but} consist of a number of short straight segments. ^{It is now known} [3, 5]

that the effect of a magnetic ^{anneal is to induce}

uniaxial anisotropy ^with.an energy minimum lying

between one of the symmetry ^{axes of the} crystal

and the direction of the annealing ^{field. Conse-} quently ^the domain wall must be _very nearly plane

within a single crystal grain. ^The domain wall traverses the grain boundaries changing ^direction

as it does so to comply ^{with t he} requirements ^{of the}

induced anisotropy. ^{Thus it seems} likely ^that

there exist a large ^but finite number of stable wall

positions ^{and that the wall is not free to take} up intermediate positions. ^This is ⁱⁿ agreement ^with the results of the demagnetization experiments.

It also means that the positional ^{free energy of the}

wall is not derivable from a conservative internal field. As pointed ^out by ^Stewart [6] ^not only ^{is a}

conservative internal field conceptually ^inadmis-

sible but as demonstrated by Rodbell and Bean [7]

it predicts ^{behaviour which is not observed in} practice. The above hypothesis ^also explains

another observation so far not mentioned. Our Kerr effect measurements indicated quite clearly

that in the presence ^{of a small} alternating ^{field the} amplitude of oscillation of the circular wall is not

the same at all points ^{on the wall. This is to be} expected ^{since the} restoring ^{force on the wall will}

at any point ^be determined, ^{at least} partly by ^the

orientation ^of the crystal grain ^{at that} point ^and

this will _vary from point ^to point ^{round the wall.}

On this view the contribution _{to vn at} remanence comes from rotati on ^of the domain vectors within the crystal grain against ^{the uniaxial} anisotropy.

This permeability ^{will, for reasons} already given,

be sufficiently nôn-uniform to account for the

observed values of _{1). J}

4. Losses in 65-35 nickel iron.

As pointed oui by Williams, Shockley ^{and Kittel} [8] ^the eddy-

current losses ^{in a} material with large domains and in which the permeability ^is non-uniform should be much higher than those calculated assuming ^a

uniform permeability. ^{In a} rectangular specimen

of width 2L and thickness d it may be shown that

where _{p is} the number of walls. In Perminvar the observed value of _1J, though greater ^than unity, ^is

not nearly ^as large ^as anticipated ^because the mobi-

lity ^{of the walls is} low and most of the permeability

arises elsewhere. In 65/35 Nickel-Iron the wall

mobility ^{is much} higher ^{and so are} the losses.

Fig. ^{5 shows the measured values of} 1J, obtained

Fie. 5.

using ^{a stack of} specimens, ^{as a} function of (pd)-1,

p being the average number of domain walls (deter-

mined from Kerr èffect measurements) ^{in each} specimen ⁱⁿ the stack. The anticipated ^linear

relation is obeyed ^{but the} slope ^of the line is less than calculated by ^{a factor of about 4. This indi-}

cates as with Perminvar a considerable contri- bution to the permeability from processes other than the movement of circular walls.

5. Magnetization ^at high ^{induction in Perminvar.}

--

If the alternating ^field applied ^{to these} speci-

mens is increased in magnitude the characteristic

FIG. 6.

En abcisses est r mesuré en mm.

rectangular ^B-H loop appears and in this ^case the

magnetization ^{seems to come} predominantly ^from

radial movement of a single ^{wall from the inside}

112

edge ^{outwards. This was} investigated using ^a specimen ^{2.54 cm outside} diameter and only ^{4 mm}

internal diameter. The maximum excursion of the wall from the inside edge ^{was measured at 80} c/s using ^{the Kerr effect and this was} compared ^with

the change ^{in induction measured on an oscil-} loscope. ^If magnetization ^takes place by ^move-

ment of a single ^wall there should be a simple ^rela-

tion between the distance moved by the wall and the observed change in induction similar to that observed by ^{Williams and} Shockley [9] ^{in a} picture

frame single crystal ^{of Si-Fe.} Fig. 6 shows the results obtained. The slope ^{of the line is calcu-}

lated from the maximum change in induction

(i.e. saturation) and the difference in external and internal radii of the specimen. ^{At low inductions}

all the points ^{lie on} the line but a high ^inductions

the experimental points ^{tend to} lie above it. This is caused by nucleation ^and movement of an addi- tional wall from ^a point ^{near the outside} edge,

behaviour already ^inferred by ^{Rodbell and Bean} [7]

from switching time measurements.

Acknowledgements.

’The experiments ^were

carried out by ^{Mr. D. R.} Callaby ^{and Mr. A. G. H.}

Troughton ^{in the} laboratory ^{of Professor}

L. F. Bates ^{to whom thanks are} due for advice and interest.

REFERENCES

[1] ^WILLIAMS (H. J.) and GOERTZ (M.), ^J. Appl. Physics, 1952,23, ^316.

[2] ^LEE (E. W.), ^CALLABY (D. R.) ^{and LYNCH} (A. C.),

Proc. Phys. Soc., 1958, 72, ^233.

[3] ^NÉEL (L.), ^J. Physique Rad., 1954, 15, 225.

[4] ^TANIGUCHI (S.), ^Sc. Rep., RITU, 1955, ^A 7, 269.

[5] ^CHIKAZUMI (S.), ^J. Phys. Soc., Japan, 1956, 11, ^551.

[6] ^{STEWART (K. H.), J.} Physique Rad., 1950, 27,177.

[7] ^{RODBELL (D. S.) and BEAN (C. P.), J.} Appl. Physics, 1956, ^{26 994.}

[8] ^WILLIAMS (H. J.), ^SHOCKLEY (W.) ^{and KITTEL} (C.), Phys. ^Rev. 1950, ^{80 1093.}

[9] ^WILLIAMS (H. J.) ^{and SHOCKLEY} (W.), Phys Rev., 1949, 75 ^178.

DISCUSSION

Mr. Bozorth.

How small were you able to

make _your light probe ?

Mr. Lee.

For many purposes ^{it is} more neces-

sary ^to have ^a light probe ^{with one very} sharp edge

rather ^{than a} very small probe. ^{It is possible to}

reduce the width of the probe ^{to about 10 microns}

if _necessary.

Mr. Epelboin (remarque).

Cette communi.

cation est très intéressante car c’est la première ^fois

que l’on essaie de comparer les résultats obte’nus par l’étude du coefficient 1) d’anomalie des pertes

par ^courants de Foucault avec ceux donnés _par l’effet Kérr magnétique. ^Mais pour avoir des rensei- gnements ^sur la structure des domaines de Weiss,

il faut _que le coefficient -1 produise uniquement ^les phénomènes ^{liés à la} subdivision de la substance en

domaines. Il est donc nécessaire d’éliminer au préa-

lable les pertes ^{dues au} traînage de diffusion et

d’hystérésis ^{en se} plaçant dans des conditions

expérimentales de validité des lois de Rayleigh. ^En

outre, ^{il est} probable qu’avec ^vos échantillons, ^la perméabilité ^n’est pas répartie ^d’une façon ^uni-

forme dans l’épaisseur, ^{même à l’échelle macro-} scopique. Il faut donc soustraire de la valeur mesurée du coefficient -1 ^{un terme dû à cette hétéro-} généité, que l’on peut déterminer avec assez de

précision ^en faisant subir à l’échantillon des polis-

sages électrolytiques successifs.

En prenant ^{toutes ces} précautions, ^{nous avons}

trouvé que le coefficient -1 ^{est lié à} l’épaisseur d ^de

l’échantillon par ^une loi en 1) d2

^{cte et non} en 7) d.

Cette loi en -1 d2 _que nous avons vérifiée _{pour les} ferro-nickels et le _{fer pur} se détermine ^à partir ^d’un

modèle de structure des domaines proposé ^par

L. Néel (Annales de l’Institut Fourier,1951, p. 301).

M. Brissonneau.

Dans un champ alternatif,

avez-vous observé la fixité des parois ^{de Bloch en}

certains points ^à l’intérieur d’un cristal et ^non pas à la frontière du cristal ?

Mr. Lee.

We have not investigated ^{the nature}

of the surface pinning ^centres chiefly ^{because the} length of our light probe ^is considerablygreaterthan

the mean grain ^{diameter in our} specimen. ^{We are} intending ^to investigate ^this question using ^some large-grained ^material.

Mr. Hirsch.

Have _{you any} information about the variation of the shape ^{of the} magnetization loop ^{at different} températures ? ^An explanation ^of

the constant permeability ^{at remanence} may be related to these shapes.

Mr. Lee.

Between - 10 °C and 100 OC the B-H loops ^{retain their} rectangular shape.

Within this temperature range the higher ^{the tem-} perature the lower is the coercivity, ^{and the corners}

of the loop ^{become more} rounded. We think that

this might result from thermal activation of

domain walls in the manner suggested by ^{Néel and}

by Street and Woolley.