COERCIVITY MECHANISMS IN OXIDE MAGNETS

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COERCIVITY MECHANISMS IN OXIDE MAGNETS

D. Craik, E. Hill

To cite this version:

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JOURNAL DE PHYSIQUE Collogue CI, supplement au n° 4, Tome 38, Avril 1977, page Cl-39

COERCIVITY MECHANISMS IN OXIDE MAGNETS

D. J. CRAIK and E. W. HILL Nottingham University, Nottingham, England

Résumé. — L'observation par microscopie électronique de spécimens de ferrite de barium ne révèle ni l'existence d'une seconde phase ni l'existence de défauts ou inclusions aux joints de grains.

En considérant les parois de Bloch comme une suite discrète de moments magnétiques on montre que les parois sont accrochées aux joints de grains. En réduisant l'énergie d'échange à 20 % de sa valeur normale le champ d'accrochage est trouvé égal au champ coercitif.

Le rôle des joints de grains dans les mécanismes de coercivité est discuté.

Abstract. — Transmission electron microscopy of thin specimens of high coercivity barium ferrite indicates that the grain boundaries have a simple structure with no apparent layers of second phase material or concentrations of defects or inclusions. A discrete-moment calculation shows that domain walls will be impeded by grain boundaries, with pinning fields equal to the coercivity, if the exchange coupling accross them is reduced to some 20 % of its normal value. The role of grain boundaries is discussed in relation to the coercivity mechanisms generally.

1. Introduction. — A typical anisotropic permanent magnet specimen of barium or strontium ferrite consists of well-oriented crystallites some 5 x 1 0- 4 cm in

dia-meter and has a coercivity of 2-3 kOe with a remanence only a few per cent below saturation. Magnetization loops can be quite rectangular with most of the reversal occurring over a small field range. Large single crystals of the same materials commonly have coercivities which are comparatively negligible. Since the aniso-tropy fields of barium and strontium ferrites are 17 and 20 kOe respectively it is apparent that magnetiza-tion reversal does not occur by coherent rotamagnetiza-tion, i. e. the nucleation and motion of domain walls must be involved and in the single crystals these processes are activated by very small fields.

If an oriented fine-grain specimen is regarded as being equivalent to a good single crystal which is simply subdivided by an array of grain boundaries it would seem likely that the nucleation processes would be similar in both types of specimen. Nucleation is presumably associated with crystallographic defects and geometrical discontinuities, and a range of such features should give rise to a range of nucleation fields. If there is a certain number of defects per unit volume, the probability of a low nucleation field being asso-ciated with a particular specimen would appear to depend more upon the size of the specimen than on the size of the crystallites, but no dependence of coercivity on specimen size for permanent magnets appears to exist.

If nucleation fields do in fact range down to compa-ratively low values for all specimens then the grain boundaries in high coercivity specimens must limit the effects of nucleation in some of the crystallites on the

reversal of the specimen as a whole. The boundaries must strongly impede the motion of domain walls from one crystallite to another.

Stablein [1] produced very interesting comparative magnetization curves for anisotropic barium ferrite

(Hc = 3.02 kOe) which had been either (a) thermally

demagnetized or (b) demagnetized by a DC reverse field. The curve for (a) rose steeply to about 0.6 Ms

at H = 1 kOe whereas in case (b) only about 0.1 Ms

was induced by H = 2 kOe after which the magneti-zation rose rapidly to approach saturation at about 2.5 kOe. One of the authors [2] has shown, by direct domain studies, that a considerable proportion at least of the crystallites of high coercivity specimens contain domain walls in the thermally demagnetized state. The high susceptibility state would thus appear to corres-pond to the relatively free motion of these domain walls within the crystallites.

The low susceptibility state can be interpreted in terms of a low number of domain walls which must thus be forced to move across the grain boundaries to effect substantial magnetization and it is indicated that the domain wall pinning field at the grain boundaries is itself close to the coercivity. The most reasonable interpretation of the demagnetization of a typical oxide magnet appears to be : (1) in fields approaching Hc

a few domains nucleate and effect demagnetization or reversal within the relevant crystallites, causing the very small changes in M observed v2) the coercivity, which is

effectively the switching field, is that field which forces domain walls to cross the grain boundaries.

Thus grain boundaries, and the associated pinning fields, appear to have a decisive role in the behaviour of oxide magnets.

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C1-40 D. J. CRAIK AND E. W. HILL

2. Microscopic Studies.

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Thin slices were cut from an anisotropic barium ferrite specimen

( H ,

--

2 000 Oe) and these were carefully mechani- cally polished and finally thinned to electron transpa- rency by ion beam machining (see acknowledgements). Considerable areas were available for study. The only two microstructural features of common occurrence were dislocations of very variable density and the grain boundaries. as illustrated by figure 1. Although it is not strictly relevant to the present work the denser dislocation clusters may be related to domain nucleation and would repay study from this point of view.

FIG. 1.

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Transmission electron micrograph of high-coercivity barium ferrite (see Acknowledgements).

The main conclusion is that the grain boundaries are revealed simply by diffraction contrast and show no special structural features. In particular there is no evidence for the formation of precipitates or layers of second phase material which might arise from natural impurities or sintering aids.

3. Grain Boundary Pinning Fields.

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Since it has been inferred that large pinning fields exist at grain boundaries which are very simple in structure their origin must be sought in relation to perturbations in the magnetic properties on a very fine scale. There must be some degree of strain or disorder at the interface between the lattices of adjoining crystallites since the orientation is never perfect, certainly in a three- dimensional sense. The property which seems to be most probably affected is the exchange coupling across

the interface since this is very sensitive to changes in interatomic spacings and angles. In the limiting case in which the exchange coupling goes to zero the magnetization in one crystallite exerts no torque on that in its neighbour and this corresponds to infinite wall impe- dance. It is of more interest to investigate the extent to which the coupling must be reduced to give pinning fields of practical magnitudes.

In materials, such as SmCo,, where the anisotropy constant

K,

is very large the calculation of wall shape and energy must take into account the discrete moment nature of the domain wall. We have shown [3] that as a consequence of this the domain wall can be strongly pinned by regions of weak exchange coupling as small as one intermoment spacing. In barium ferrite the anisotropy constant K, is an order of magnitude less than in SmCo, and so the continuum approximation will be valid for this material. If, however, it is required to consider the effect of a region of weak exchange on the domain wall it becomes convenient to consider the discrete moment nature of the wall around the anoma- lous region.

The shape and energy of a simple 1800 domain wall consisting of discrete moments depends upon three main parameters :

(a) The anisotropy constant

K,.

(b) The inter-moment spacing d.

(c) The exchange constant A .

In the calculations the constants K,, A and d enter

via a parameter

p

given by :

It is possible to compute the value of applied field required to move a domain wall through a region of

FIG. 2. - Calculated pinning fields for barium ferrite (left-

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COERCIVITY MECHANISMS I N OXIDE MAGNETS C1-41 weak exchange where the ratio of A within the region

to A in the rest of the material is given by a (0

<

a

<

1). The value of the parameter

fl

for barium ferrite may be estimated by assuming that the inter-moment spacing is equal to the basal plane lattice parameter

a, = 5.89

A.

The value of K , is assumed to be 3.3 x l ~ ~ e r g c m - ~ [4] and the estimate of 6.1 x lo-' erg cm-' obtained by Kaczer et al. [5] for

A is used. These values give a value of

fl

=

0.01 and the variation of pinning field with a for an anomaly of one inter-moment spacing in extent is given in figure 2. The equivalent curve for SmCo, is also given for compa- rison.

It is implicit in the calculation that the domain wall contains the plane of the anomaly and if this is not the case the pinning fields will be somewhat lower than those indicated.

Discussion. - The strong domain wall pinning which has been inferred at grain boundaries of simple structure can be accounted for in terms of the reduction in exchange coupling between adjoining crystallites. The questions of the likelihood of this modification of the exchange occurring in practice and of its microscopic origins are left open and so the present study can only be considered as tentative. Different grain boundary structures may exist in specimens produced using sintering aids and those which are nominally pure ferrite.

Other approaches to the problem are possible. Kneller (I) has pointed out that if a concentration

gradient exists near to the boundary, with a correspond- ing gradient in K,, a simple calculation of pinning fields can be based on the rate of change of the wall energy in this gradient. More intensive studies of structure and composition in the region of the grain boundaries appear to be called for. It should also be noted that Globus [6] explained the behaviour of soft ferrites in terms of domain wall pinning at grain boundaries, due to magnetostatic effects.

The grain boundary pinning field may not represent the coercivity itself, but may in fact be so high that nucleation occurs in most of the crystallites before the domains can cross the boundaries. This would appear to be the case for SmCo, magnets (Ziljstra and den Broeder [7]). Some of Stablein's results indicate the extensive motion of domain walls in the oxides, and comparisons between the two types of material are complicated by the greater relative importance of magnetostatic effects in the oxides.

Acknowledgements.

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The microstructural studies were very kindly carried out by M. Paulus of CNRS, Meudon Bellevue, using the ALBA ion bombardment equipment. We are grateful for the support of the Science Research Council.

(1) Kneller E. (Bochum University) Private Communication.

References

[I] STABLEIN, H., IEEE Trans. Mag. MAG-6 (1970) 172. [5] KACZER, J., GEMPERLE, R., ZELENP, M., PAEES, J., SUDA, P., [2] CRAIK, D. J., The Study of Ferromagnetic Domains by FRAIT, Z. and ONDRIS, M., J. Phys. Soc. Japan 17B-1

Electron Microscopy (Nottingham) '1959. (1962) 530.

[3] CRAIK, D. J., and HILL, E. W., IEEE Trans. Mag. MAG-11 [6] GLOBUS, A., C. R. Hebd. Sdan. Acad. Sci. 255 (1962) (1975) 1379. 1709.

[4] SMIT, 5. and WIJN, H. P. J., Ferrites (John Wiley and Son, [7] ZULSTRA, H. and DEN BROEDER, F. J. A., PYOC. Intern. Con$