CONFIGURATIONAL HYSTERESIS IN DOMAIN STRUCTURES : A STUDY BY IMAGE PROCESSING TECHNIQUES

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CONFIGURATIONAL HYSTERESIS IN DOMAIN

STRUCTURES : A STUDY BY IMAGE PROCESSING

TECHNIQUES

Y. Souche, J. Porteseil

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C8, Supplement au no 12, Tome 49, decembre 1988

CONFIGURATIONAL HYSTERESIS IN DOMAIN STRUCTURES: A STUDY BY

IMAGE PROCESSING TECHNIQUES

Y. Souche and J. L. Porteseil

Lab. Louis Ne'el, C.N.R.S., 3804% G~enoble Cedex, France

Abstract. - Image processing allows to measure the changes induced by field cycles in a domain structure. Irreversibility and stabilization effects are discussed in terms of metastability due to frustrated dipolar energies.

Hysteresis can take place in practically defect- free materials [l] due to intrinsic energy barriers be- tween allowed, topologically different domain structures (DS). This work aims at quantifying the irreversible changes brought about in the geometry of a DS by field cycles.

The sample was a layer of yttrium-gallium gar- net (bubble material) with the following characteristics: 4xM, = 213 G , uniaxial anisotropy

K, =

13 700 ergs.cm-3, collapse field 146 Oe. We dealt with the maze pattern (Fig. la) obtained by applying a sat-

urating field normal t o the layer, then suppressing it. The sample and mechanisms leading to such DS were described in [2].

The DS were observed by means of the transmission Faraday effect. They were digitized onto 512 x 512 frames of 8-bit pixels by a graphic card (Matrox VP- AT/NP) hosted in a microcomputer. Image subtrac- tion was used t o calculate the pixel-to-pixel difference of two patterns, and thresholding procedures allowed to display in white-on-black contrast the regions which were found different in the two patterns.

An as-prepared maze was subjected to cycles of in- creasing strength 0

-

HI

-

0

-

H2

-

O... with field increment Hn+l

-

Hn

= 9 Oe. Comparison of the successive patterns in zero field with the initial one re- vealed differences: some branches of the tree-like pattern collapsed, or burst out, or changed their lengths and curvatures, leading t o reorganizations of the stripe array over finite regions which are highlighted in figure l b (the thresholding and area-filling procedures are responsible for the coarse aspect of white areas). The fraction 6 of white pixels is the difference of the cycled DS with the initial one and is plotted against H in figure 2.

Another virgin maze was first subjected to an alternating field-which slowly decreasedfrom 100 Oe to 0, then the same field cycles 0

-

HI

-

0

-

H2

...

were applied (Fig. 2).

I

Finally, another virgin maze was subjected to field cycles 0

-

H

-

0

-

H... with H = 36 Oe. At every step, the patterns before and after the cycle of rank n were

Fig. 1.

-

(a) Maze DS; the easy axis is normal to the 0 + + +

sheet, the black and white stripes are "up" and "down" 0 + , H (Oe) *

domains. (b) A typical result of the pixel-to-pixel difference 5 0 100

procedure. The white areas represent the regions of the DS

which were significantly changed by a field cycle, viz. the Fig. 2. - Fraction of the DS modified by a field cycle. stripes were moved by at least a half-width. Circles: virgin DS. Crosses: AC stabilized DS.

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C8 - 1936 JOURNAL DE PHYSIQUE

compared. Figure 3 shows on a single frame the areas in which changes took place during two successive cycles of ranks n and n f 1 : obviously, the areas An+l are included in areas A,.

The above results show that the metastability linked with domain geometry can be measured. The following points are worth stressing:

- apparently similar DS can feature different energy levels and stabilities. Whereas two virgin mazes are expected to be statistically equivalent, visually similar AC stabilized mazes lie in deeper wells. The two curves of figure 2 merge together near H = 100 Oe, which is the strength of the stabilizing field. This shows that only part of the energy barriers can be overcome by a non-saturating field: the DS is only partially stabilized. Moreover, the

S

(H) curves in the virgin and stabilized states seem to be closer to H

and

H 2

laws respectively. That would be in agree- ment with the irreversible magnetization laws found on a Gd sample, depending on the previous demag- netization [3]: respectively thermal (leading to highly metastable states) and alternating (leading t o lesser metastability and Rayleigh laws). The H and H 2 laws can be accounted for by a statistical analysis of the "double well" situations in which the system jumps back and forth;

- figure 3 exhibits a threshold field of approximately 25 Oe for both the virgin and stabilized states (al- though more difficult to determine in the latter case, because of slow initial rate). This confirms the exis- tence of a finite, totally reversible basin for a hysteretic system. Indeed this threshold depends on the energy barriers involved, which in turn depend on the material characteristics: magnetization, wall energy. That theoretical prediction [4] had already been confirmed by experiments on samples featuring wall pinning, but in the present case the reversible region is quite macro- scopic ( ~ 2 5 Oe instead of 2 x

lo-"

in [5]);

The finite sizes, comparable to the domain period, of the irreversibly modified areas suggest to consider them as "Preisach grains"

,

that is basic entities to describe hysteresis. That would allow t o define a dis- crete set of degrees of freedom in an initially continuous problem;

-the hierarchical aspect of stabilization (Fig. lb) could be a consequence of the complex interplay of long-range, frustrated dipole interactions, which would allow to consider a maze domain structure as some kind of "domain glass"

. A more detailed investigation,

to be published elsewhere, shows that during successive field cycles of fixed strength the difference 6,+1 is on the average close to 6,

/

2, leading to exponential decay proportional to 2-". This is consistent with many other data on stabilization effects in various hysteresis systems [6].

[I] Molho, P., Porteseil, J. L., Souche, Y., Gouzerh, J., Levy, J. C. S;, J. Appl. Phys. 61 (1987) 4188. [2] Molho, P., Porteseil, J. L., Proc. PMM3, Szczyrk-

Bila (1986) p. 162.

[3] Molho, P., Porteseil, J. L., J. Phys. fiance 46 (1985) 1355.

[4] Erber, T., Guralnick, S. A., Latal, H. G., Ann.

Fig. 3. - Stabilization by successive field cycles of fixed Phys.

N.

Y.

69 (1972) 161.

strength H = 36 Oe : hierarchical aspect of the irreversible

changes brought about in the DS. Black: unchanged; white: [51 Weinstock, He, Erber, T.3 Phys. Rev. B 31 (1985)

changed by the lst cycle; hatched: changed by the 2nd 1535.