THE TEMPERATURE DEPENDENCE OF THE WAVE DOMAIN STRUCTURE

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THE TEMPERATURE DEPENDENCE OF THE WAVE DOMAIN STRUCTURE

R. Szymczak

To cite this version:

R. Szymczak. THE TEMPERATURE DEPENDENCE OF THE WAVE DOMAIN STRUCTURE.

Journal de Physique Colloques, 1971, 32 (C1), pp.C1-263-C1-265. �10.1051/jphyscol:1971187�. �jpa-

00214514�

JOURNAL DE PHYSIQUE

Colloque C 1, supplkrnent au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 263

THE TEMPERATURE DEPENDENCE OF THE WAVE DOMAIN STRUCTURE

R. SZYMCZAK

Institute of Electron Technology, Warsaw, Poland

Rksmk. - On rend compte ici, d'un travail theorique et expbimental sur la dependance de la temperature dans les structures en domaines ondules. Les Ctudes ont ete faites sur des monocristaux de ferrite de baryum, par la technique des poudres, dans un intervalle compris entre la temperature ambiante et 650

On a trouve que les domaines ondulb se redressaient a mesure que la temperature augmentait et qu'au-dela d'une tempkrature critique, on obtenait une struc- ture en domaines de Kittel. Les variations en fonction de la temperature de la largeur des domaines et de leur forme, ainsi que la temperature critique, dkpendent essentiellement de l'epaisseur du cristal examine. Les rCsultats experimentaux ont confirme les calculs theoriques.

Abstract. - Theoretical and experimental investigations of the temperature dependence of the wave domain struc- ture have been reported. The investigations have been carried out on single crystals of barium ferrite by the technique of magnetic powder patterns in the range from room temperature to 650

It has been found that the wave domain structure straightens with the increase of temperature and over critical temperature passes into the Kittel structure. The temperature variations of the domain width and the domain shape as well as the critical temperature essentially depend on the thickness of the examined crystal. Experimental results have confirmed the theoretical calculations.

I. Introduction.

The wave domain structure is a modification of the open Kittel structure [I]. It appears when the crystal thickness L exceeds a given value LC,. The quantitative theory of this structure consider- ing the magnetostatic energy of the poles on the basal plane, energy of the domain walls and the energy caused by the poles on the domain walls was presented by Szymczak [2] and [3]. The domain surface struc- ture is characterized by the domain width D, the wave amplitude a and the wavelength y. The changes of parameters D, a, y in the function of temperature has been investigated in this paper. The purpose of these investigations was to obtain an additional verification of the previously proposed model [2] in a wide range of material parameters such as saturation magnetiza- tion M, anisotropy constant K or energy density of domain wall ow that change with temperature. In the same time on the ground of the above mentioned inves- tigations the possibility of obtaining some information about the exchange interactions in ferrites was analy- sed.

XI. The temperature dependence of the wave domain structure. - On the ground of the papers [2] and [3]

one can find the following expression for the change of the domain width S with temperature T :

Index r denotes room temperature, p = 1 + 2 n M 2 / K .

When L < L C (Kittel region), the formula (1) takes the form :

It is obvious that the critical thickness of the crys- tal LC, depends on the temperature too :

Similar relations describe the dependence of para- meters a and y on the temperature. The values M(T) and K(T) which appear in the formulae (1)-(3) can be measured by classical methods. In order to deter- mine the temperature dependence of the energy density of domain wall o, the knowledge of A(T) is necessary, where A denotes the exchange constant. In the case of ferrimagnetics A is the function of different sublat- tice magnetizations and the exchange integrals Jij bet- ween magnetic ions of i-th and j-th sublattices. These parameters, especially in cases when many sublat- tices occur as for example in hexagonal ferrites, can be determined only by the methods of Mossbauer or NMR spectroscopy.

111. The temperature dependence of the wave domain structure in barium ferrite. - In barium ferrite BaFe1,019 in room temperature the wave domain structure occurs for crystals with thickness from

- 8.5 pm to

50 pm. In connection with this the investigations of the domain structure have been carried on crystals of thickness from 7 pm to 100 pm.

The domain structure was observed by the technique of magnetic powder patterns. A special magnetic suspension permitted the measurements to 650 OK.

In the range of the investigated crystal thicknesses and temperatures there was found a tendency of straightening of the domain walls with the increase of temperature. Typical changes of surface domain structure caused by the change of the temperature for BaFe,,O,, crystals of thickness L = 18 pm is shown for illustration in figure 1. It can be seen that when T = 300OC the wave domain structure goes over into the Kittel structure. The D(T), Lc,(T), a(T) and y(T) have been measured on the ground of similar photographs and they are plotted in figure 2, 3 and 4. The theoretical curves based on the calcula-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971187

C

-

^{R. SZYMCZAK}

FIG.

Domain structure of the monocrvstal BaFel?Olo.

18

pm in thickness, at various temperatures

OC,

OC, c)

OC, 1

x .

FIG.

-Temperature dependence of the relative domain width for BaFel2019. Curves

are calculated from the for- mula

and curves

from

for the cases a and b, respeo tively. Curve

(case a) for L

-

Experimental values of D(T)/D(r)

for L >

pm,

for L

-

^pm,

A f o r L

8pm.

tions from Chapter I1 are also given in these figures solid lines. The M(T) and K(T) dependences have been taken according to Shirk and Buessem 141. To determine A(T) the existence of five sublattices in

FIG.

Theoretical temperature dependence of the critical crystal thickness for BaFellOi9 (solid line), x-experimental

values.

FIG. 4. -Theoretical temperature dependence of the

and

for monocrystal BaFelz019,

pm in thickness,

experimentd values.

barium ferrite should be considered. Sublattice magne- tizations and the values of A(T) have been found by solving numerically a set of 5 equations of molecu- lar field theory, taking into account at the same time the exchange integrals determined either on the ground of Mossbauer spectroscopy [5]

case a, or from the spin echo measurements [6] - case b.

In the range from room temperature to 600-650

theoretical curves L,,(T), ct(T), y(T) for both cases differ very little. That is why the same curves represent both cases in figures 3 and 4. Only at high tempera- tures for D(T) there appears observable difference between the case a (curves 1 and 4) and the case b (curves 2 and 5), figure 2. The performed experimental measurements for crystals of thickness L > 30 pm give the results lying between curves 4 and 5 (Fig. 2).

These measurements simultaneously give the evi- dence of a possibility of utilizing the domain structure investigations to obtain the information about exchange interactions in the ferrites.

The dependence of the relative domain width

D(T)/D(r) on the crystal thickness L is characteristic

THE TEMPERATURE DEPENDENCE OF THE WAVE DOMAlN STRUCTURE C

-

for the wave structure (in contrary to the Kittel model, see Fig. 2). It results from the fact that LC, depends on temperature (Fig. 3) and from the fact that formula (1) is valid for L > LC, and the formula (2) for L < LC,.

In figure 4 there are presented dependences of a ( T ) and y(T) and the results of experimental measure- ments for crystals of thickness L = 26 pm. a as well as y decrease with increasing of the temperature. This indicates on the tendency to straighten the undulatory

of the domain walls. The same tendency is observed also in crystals of thickness L > 50 pm. For such L the domain structure has a form of a wave structure supplemented with dager-like domains. Experimental observations lead to conclusion that also in this case the domain walls straighten.

Acknowledgements. - The authors wishes to thank Prof. R. Wadas for helpful discussions.

References

[I] KITTEL (Ch.), Phys. Rev., 1946, 70, 965. [5] VAN LOEF (J. J.), BROESE (A.) and VAN GROENAU, [2] SZYMCZAK (R.), J. Appl. Phys., 1968, 39, 875. Proceed. Intern. Conference on Magn., Nottin- [3] SZYMCZAK (R.), Electron Techn., 1968, 1 , 5. gharn, 1964, 646.

[4] SHIRK (B. T.) and BUESSEM (W. R.), J. Appl. Phys., [6] STREEVER (R. L.), Phys. Rev., 1969, 186, 285.

1969, 40, 1294.