Magnetic hysteresis and domain structure

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Magnetic hysteresis and domain structure

R.S. Tebble

To cite this version:

R.S. Tebble. Magnetic hysteresis and domain structure. J. Phys. Radium, 1959, 20 (2-3), pp.98-100.

�10.1051/jphysrad:01959002002-309800�. �jpa-00236075�

98

MAGNETIC HYSTERESIS AND DOMAIN STRUCTURE

By R. S. TEBBLE,

The University ^of Sheffield, England.

Résumé. 2014 On expose quelques problèmes ^{relatifs au} développement ^{des méthodes} expéri-

mentales pour l’examen des processus d’aimantation mis ^en jeu ^{dans les} champs ^{faibles sur des}

substances polycrystallines.

Abstract.

A brief survey is made of ^some of the problems involved in the development ^of experimental methods of obtaining information on the domain processes involved ⁱⁿ the low field

magnetization ^of polycrystalline ^materials.

LE JOURNAL DE PHYSIQUE ^{ET LE RADIUM TOME} 20, ^FÉVRIER 1959,

This _paper represents ^an attempt ^{to summarise} briefly ^{some of the} problems ^{involved in the deve-} lopment ^{of an} understanding ^{of the} elementary

processes involved ^{in low} field magnetic hyste-

resis in polycrystalline materials such as iron and

nickel, ^{to discuss some of the methods of} obtaining

further information, ^{and to} indulge ^{in the exercise}

of estimating ^{orders of} magnitude.

The magnetic properties ^of the materials with which this paper is concerned ^{are a} coercivity ⁱⁿ

the _range 0.1 to 10 oersted, ^{a remanent} magne- tization of about one half the saturation value.

In addition there is the information from the Barkhausen effect that the discontinuous changes ⁱⁿ magnetization ^take place ⁱⁿ steps ^{of 10-7 to}

10-5 e. m. u. corresponding ^to reversals in magne- tization in volumes in 10-1° to 10-8 cm3 ; ^{there are} probably ^a considerable number of smaller discon- tinuities but this range ^covers those which make up the greater part ^{of the} change in magne- tization (an average value for hard drawn iron is 1. 6 X 10-6 e. m. u.).

The theoretical treatment of coercivity ⁱⁿ single crystals ^{and of the} mechanism ’whereby the magne- tization is reversed has been exhaustively ^treated particularly ^{by Néel and the processes involved}

are fairly well understood. The transference of these ideas to polycrystalline ^{materials however} presents considerable difficulty and, ^without any wish to labour this point, ^{it may be of use to} give

an example of what is involved. The reversal of

magnetization ^{in a} single crystal of iron is consi- dered as taking place ^{with a 1800} boundary moving

across a domain ; ^this boundary ^{is held} up ^as it unites with ^a 900 Néel " spike " domain structure around a non magnetic ^{inclusion and as it breaks}

away produces ^a discontinuous change in magne- tization. This has been confirmed in the well known Bitter patterns ^{of Williams and} Shockley (1949) ; ^{from the} published photographs ^{it appears}

that the linear dimensions of the inclusions were

about 6 X 10- 3 cm and the length ^{of the Néel}

spikes ^{about 7 X 10-2 cm. Now in a} poly- crystalline material, ^{unless one is to} postulate ^such

a close coherence in crystal orientation between

neighbouring grains ^{that a domain} boundary

passes with little distortion across a grain boundary,

it is necessary ^to suppose ^that the whole course of events is carried out in a single grain. ^{A "} typical"

grain ^{size for a} polycrystalline material such as

that described earlier, ^{would be about 10-3 cm in}

linear dimensions, ^{so that the whole} scale of the above process ^is much too large. ^{Even if the}

scale of the system ^{is reduced to a} minimum, ^{it is} unlikely that, ^{with a} boundary ^{thickness of}

1.4 x 10-5 cm (for iron), ^one could obtain any

subsidiary ^{domain structure on a cubic} inclusion.

with a side of much less than 1 X 10-4 _{cm ;} the

cross sectional dimensions of the associated Néel

spike ^{would take} up the greater part ^{of the cross}

section of the grain with little ^room for the 1800

boundary. ^An alternative suggestion ^{would be}

that the movement of the 1800 boundary is held up because of the free pole produced ^{at the inter-}

section of the boundary ^{with an} inclusion, ^without

the formation of any subsidiary ^{domain structure.}

It has been shown by ^{a number of} workers that in such cases those inclusions with linear dimensions

approximately equal ^{to the} boundary ^{thickness are}

of the greatest importance ⁱⁿ producing hysteresis (see below). (Néel, ^{in his} disperse ^field theory

also allowed for the possibility ^of regions ^of strain,

instead of non-magnetic inclusion, with the energy of the system dependent ^on strain and anisotropy).

It may be worth mentioning ^{that if the} deciding

factor is whether ^or not there is room for the ^for- mation of subsidiary ^{domain structure around an}

inclusion there might ^{well be a} close inter-relation between grain size and inclusion size in the control of coercivity. An additional possibility ^{would be}

that the Néel spike ^{structure itself could} provide ^a

means whereby ^{the increase} and diminution in the size of the spikes would result in a change ^{in magne-} tization ; ^however enough ^{has been said to indicate}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-309800

99

the range of domain _processes which could take

place.

The methods of approach ^{to a} study ^{of the} problem ^{fall into} three broad categories

^the

"

magnetic ", " ^indirect

^{and "} direct " methods.

Firstly ^{there is} the magnetic ^{method of} correlating

in a quantitative manner some magnetic property

such as coercivity with the measurable physical properties ^{of the} material, ^{as in the} way which

Djikstra ^{and Wert} (1950) ^for instance have shown that the coercivity ^is dependent ^{on the size of the} non-magnetic inclusions in the material, ^{and is a}

maximum when the linear dimensions of the inclu- sions are approximately equal ^{to those of thé}

domain boundary. ^The possibilities ^{of this} type

of experiment ^{are however limited} by ^the difficulty

of obtaining quantitative information on the phy-

sisal state of the material in a form which can be of

use in ^an analysis ^{of the} magnetic measurements.

The second group of methods involves the ^identi- fication of the _process taking place " indirectly " by

the examination of the change ^{in some} parameter, such as temperature ^or resistance, accompanying ^a change ⁱⁿ magnetization, bearing ^{in mind that}

several ^of these processes could be taking place simultaneously. ^{Included in} this group could be included the methods making ^{use of} changes ⁱⁿ Young’s ^modulus (described ^{in the} pâper presented by ^Dr. Street), ^the magneto-resistance ^{effect and}

the magneto-thermal effect. For instance, ^Parke (1956) ^{has shown in} his work. on the change ⁱⁿ

resistance with magnetization ^{that it is} possible ^tô identify ⁹⁰⁰ boundary changes ^or rotations of the

magnetization ^{vectors as} distinct form 180° changes

in magnetization, ^{since with a reversal in} magne-

tization there is no change ⁱⁿ resistance. His results for single crystals ^{show in a} convincing

manner the change ^{in the nature of} the processes in différent regions ^{of the} hysteresis curve, from the low field region where’ 180° changes predo-

minate to high fields, ^{where the} changes ⁱⁿ magne- tization take place by rotation, ^and this method

might ^{well be} applied ^to polycrystalline ^materials.

The work ^on the magneto-thermal effect, ^{on which}

the author has beefi closely connected for some

years, ’ provides ^a good example ^{of some of the}

difficulties involved by ^this type ^of approach. ^It

may be helpful ^to look upon ^the magneto-thermal

effect as in some ways analogous ^{to the Joule-}

Kelvin effect in gases, in which information ^{on the}

atomic " structure " of a gas ^{can be derived from}

the deviations from the perfect gas behaviour.

Here ^an adiabatic expansion ^is replaced by ^an

adiabatic change ⁱⁿ magnetic ^{field and the corés} ponding temperature change is measured (or ^alter- natively the related quantity ((JII()T)H ; ^{this for}

certain puposes is ^more convenient). ^Provided

the clianges ⁱⁿ magnetization ^are reversible, ^the

method ^of analysis ^{is as follows. The} change ⁱⁿ temperature, usually written in the form of a heat

change, AQ ^can be considered as made _{up of} a part due to the change ^{in intrinsic} magnetization AQ2

and the remainder due tone of the _processes already mentioned,- rotation of the magnetization etc.,

OQb ^{so that} IlQ’ =IlQ + AQ,-. ^The quantity AQ’

can usually ^{be estimated without undue error so}

that the method of analysis is reduced to providing

an explanation of the value of àQ§ ^{or of the coef-}

ficient b" = AQ’ b 1 f H dl ; ^{for instance, if only}

rotations of the magnetization ^{vector are} present b’

is given by ( T jK) (dKldT) ^{with K the aniso-} tropy coefficient. A typical ^{set of curves for nickel}

is shown in figure 1, and it will be seen that outside

n .

FIG. 1.

Magneto-thermal ^{effect H in nickel.} Q’rev ^is

heat measured under reversible conditions. Q’tot includes both reversible and irreversible heat changes.

- - - -

-, Q’tot ^measured by Bates and Davis

on a similar specimen. The estimated value for b" for rotation only ^is

^4.5 (see ^table 1).

the hysteresis region the value of b" is reasonably

constant and approximately equal ^to that appro- TABLE 1

VALUE OF bH WHEN THE CHANGE IN MAGNETIZATION IS DUE TO THE SINGLE MECHANISM INDICATED

100

priate for rotations. In the coercive region ^{it is}

clear that rotational changes ^{are of little} impor-

tance and that other _processes are taking place.

Teale and Rowlands (1957), ^{have made estimates}

of the value of b" for a number of processes (see

Table 1), provided only ^one such process is present.

If this condition could be satisfied, the identifi- cation of the process would in many ^cases be _pos- sible. In particular ^{the Néel} disperse field mecha- nism gives ^{for nickel and cobalt a} value of b’ not

only reasonably large, ^{but of} opposite sign ^{to most}

of the other processes. ^{It so} happens ^however

that the magnetic properties ^{of most materials are}

such that one could hardly hope ^{for one form of} magnetic change ^to predominate ^{in low field. In}

fact the future of the method would seem to lie in the provision of materials which will lend them- selves to this method of analysis ^{rather than in a} generalized application. ^What is in many ways

a development ^{of the method of} analysis (but ^{not of}

the experimental method) ^{has been} developed by Gugan ^{and Rowlands} (1958) ^{in an} investigation ^of

the change ⁱⁿ magnetization ^with pressure, ^i.e.

(7/)F) ^{instead of} (I I T)H, ^{and a} coefficient d"

is obtained in much the same way ^as b". It is difficult to say ^at present ^{what are the} possibilities

of this method but the main requirement ^{at the}

moment would seem to be dependable experi-

mental values of (IiP)H ^{measured under rever-}

sible conditions.

Finally ^{there are the "} direct " methods which have already proved ^{to be} probably ^{the most}

fruitful in the branch ^of physics, the Bitter pattern method. The difficulty ^here is that with the standard techniques the limit of resolution is set

by ^the maximum size of colloid particles, ^say

10-4 cm or more, whereas a resolution of about 10-5 cm is required ; both this and the polarized light ^{method are of course limited} by ^the resolving

power ^of visible light. ^The application of electron

microscopy ^{to the} problem by Craig, in which the colloid particles ^are deposited ^{in a surface} replica,

has resulted in improvement in resolution but only

to the extent allowed by ^the minimum size of the colloid and the further progress ^{in this} technique

will be controlled by development ^{in the} produc-

tion of the colloid. One is led naturally ^therefore

to the direct application of electron microscopy ^as

in the work ^of Germer (1942), ^{and of Blackman}

and Grunbaum (1957) ^or possibly ^{in the electron} scanning technique (Smith ^and Oatley, 1955).

Although ^{there is here no} problem of limited reso-

lution the difficulties in the interpretation ^{of the}

results ^are very great ^{but is seems} that any further

developments ^{in our} knowledge ^of the domain structure of polycrystalline materials may well

depend ^{on our} ability ^{to make use of these tech-} niques ^{in work on} single crystals.

REFERENCES

BLACKMAN (M.) and GRUNBAUM (E.), ^Proc. Roy. Soc., 1957, ^A 241, ^508.

DIJKSTRA (L. J.) ^{and WERT} (C.), Phys. Rev., 1950, 79, ^979.

GERMER (L. H.), Phys. Rev., 1942, 62, 295.

GUGAN (D.) and ROWLANDS (G.), ^{In the} press, 1958.

PARKER (R.), ^Phil. Mag., 1956, 1, 1133.

TEALE (R. W.) and ROWLANDS (G.), ^Proc. Phys. Soc., 1957, B 70,1123.

SMITH (K. ^D. A.) and OATLEY (C. W.), ^{Brit. J.} Appl.

Phys., 1955, 6, 391.

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

DISCUSSION

Mr. Kaczer.

1800 wall motion is not conti-

nuous as a whole but can be compared ^{with the} blowing up of ^a balloon having ^weak spots. ^Small portions of the wall move discontinuously forming

"

bubbles " on the walls. This kind of motion could explain ^{the small volumes arrived at in} Barkhauseri jump experiments.

Mr. Teale.

It must. be emphasized ^{that the} magnetothermal method of analysis of magne- tization curves mentioned by ^{Dr. Tebble and dealt}

with by Prof. Bates can be carried out using ^the

theoretical expressions ^{of Teale and Rowlands} only

if the magnetic specimen investigated ^conforms

to a fairly simple ^model. Briefly this model is one

in which magnetic magnetothermal changes ^result

from changes ^{of the intrinsic} magnetization ^and

from ône other mechanism (e.g. ^{rotations or}

domain wall movements). ^Under these circum- stances the coefficient b" (or c") ^{should be inde-} pendent ^{of H over the} range of H concerned. It is therefore _very important ^{to be sure that the} experi-

mental results satisfy this condition if the theory

is to be used for interpretation. ^{As much care is}

needed in this direction for the low field analysis

as has been taken in high ^fields.

The ^constants c" given ⁱⁿ Prof. Bates’ paper, table II, ^{column 6} correspond ^to domain wall motion impeded by disperse ^fields resulting ^from

stress in the specimen. Disperse ^fields can also arise from non-magnetic inclusions and this gives ^{rise to} quite différent theoretical values of c". This latter mechanism may predominate ⁱⁿ ferrites in low fields.

Mr. Tebble.

It is certainly ^{necessary to be}

sure that the conditions assured in the theory ^are

satisfied experimentally ^as indicated in Table I,the positive value for b" in nickel and cobalt is obtained for the Néel field mechanism for stress only.

Mr. Bates (Comment). ^{- At} Nottinghem ^{we have} recently ^made measurements on H. C. R. alloy (grain orientated ; 50Fe, 50Ni) and found that a

"

dip " is obtained in low fields by ^the Nottingham

method of measurement, ^{but is not} obtained with the Leeds method, ^{in which} (vIlvT)H ^is measured,

We cannot account for this discrepancy ^{at present.}