REVERSAL MODES IN FINE PARTICLES

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REVERSAL MODES IN FINE PARTICLES

Ying Yan, Edward Della Torre

To cite this version:

JOURNAL DE PHYSIQUE

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

REVERSAL MODES IN FINE PARTICLES

Ying Dong Yan and Edward Della Torre

Electrical Engineering and Computer Science Department, George Washington University, Washington, DC 20052, U.S.A.

~ b s t r a c t . - A numerical micromagnetic model has been used to analyze equilibrium and reversal modes. For small Cobalt fine particles, the magnetization rotated quasi-coherently; for intermediate sized particles, the magnetization reversed in a quasi-curling mode; and for larger particles, the magnetization was multidomain, and columnar switching was observed.

Introduction

A numerical micromagnetic model [I] for magnetic fine particles has been improved [2] and used t o analyze equilibrium and reversal modes. The magnetization was initialized by applying a very large field, which was then slowly relaxed. For cubic particle results are similar t o other results [3]. For parallelepiped-shaped Cobalt particles with an aspect ratio of 6:1, three types of reversal modes are observed. In all cases, the re- versal begins at both ends of the particle and propa- gates towards the center similar t o the Knowles' flip- ping mode [4].

A set of systematic micromagnetic calculations has been performed on a single Cobalt fine particle, that has a saturation magnetization of 1.431 kA/mm, an exchange constant of 15 pJ/m, and a uniaxial mag- netocrystalline anisotropy constant of 430 k ~ / m ~ . The easy-axis saturation remanence, obtained by applying a very large field that is gradually reduced to zero, as a function of particle size, is illustrated in figure 1. Be- low 450 nm the equilibrium magnetization is uniform in the center of the particle, but is flared a t each end to reduce the demagnetizing energy. Only very small superparamagnetic particles can be uniformly magne- tized.

Between 450 and 750 nm, the magnetization curls a t the end surfaces perpendicuIar t o the easy axis in or- der t o reduce the demagnetizing energy. Since curling takes place only a t the surfaces, the remanence is not appreciably reduced. Above 750 nm, the saturation remanence is multi-domain.

388 188 588 688 788 888 -8

Particle Length ( nm )

Fig. 1. - Remanence variation with particle size.

Axial applied field

For a particle aligned with the applied field and shorter than about 120 nm, magnetization reversal is accomplished in the quasi-coherent mode. Cross- sections perpendicular t o the particle axis are uni- formly magnetized during reversal, but differ from other different cross-sections. The magnetization a t both ends begin t o rotate in opposite directions, as shown in figure 2. Since the particle is symmetrical, both the magnetization and the demagnetizing field have mirror symmetry. The reversal is similar t o the coherent Stoner-Wohlfarth model, except that it is ac- complished by flipping and the magnetization ,is not uniform.

/ / / / I

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/ / f f f Longitudinal Cross Section

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Fig. 2. - Magnetization patterns in a 100 nm particle.

As particles become longer than 120 nm, their mag- netization becomes increasingly curled at the ends, but the basic reversal mechanism is unchanged. As shown in figure 3, the magnetization is increasingly bent t~ wards the x - y plane as one approaches the surface, similar t o a Bloch wall structure. As this pattern starts t o reverse, the ends of the particle reverse first, and then flip the next magnetizations successively un- til the reversals meet a t the center. The symmetry is then broken t o avoid singularity in the exchange energy. This mode is analogous to the classical curl- ing mode. Columnar switching is possible for parti- cles longer than 190 nm, and minor loops can produce multi-domains.

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Oblique applied field

The angular dependence of coercivity as a function of particle size is similar to the model of Aharoni, et at, [5], but with substantially different numerical values. We note that the basic flipping mechanism is unchanged, but the modes are no longer symmetric. In some cases it is observed that the propagation of the flipping cross sections can actually start from one end instead of always starting from both ends. For large angles, the particle exhibits the coherent rotation.

For 100 nm particles, the quasi-coherent rotation is unchanged for small angles, but the magnetization at the ends rotate in the same direction; thus, when the reversals join at the center the configuration can simply unwind. For some field angles the propagation starts from one end only. Above 50 degrees, coherent reversal occurs. Figure 4 shows the major hysteresis loops for a 100 nm particle a t various angles with re- spect to the applied field.

npplied Field ( kA/m )

Fig. 4. - Major loops for particles at various angles. At about 150 nm, the propagation of the curling cross section is also non-symmetric for very small an- gles. Around 15 degrees, the propagation becomes more difficult to characterize, and curling no longer ex- ists. Above 55 degrees, the reversal resembles coherent rotation. For 200 nm particles, asymmetric columnar switching takes place. Above 60 degrees, the rotation is coherent.

A plot of the coercivities and the switching fields as a function of the applied field angle is shown in figure 5 for the above three sizes of the particle. The switching field is the point at which there is a discontinuity in the

288

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' angular Dependence

~ i e l d Angle ( degree ) Fig. 5. - Coercivity variation with field angle.

major ascending hysteresis loop, while the coercivity is the point at which the major ascending hysteresis loop crosses the horizontal axis, whether the curve is con- tinuous there or not. The coercivity and the switching fields have the same value when the loop crosses the horizontal axis at the discontinuity.

These results can be readily compared with the clas- sical results. For 100 nm particles, both the coercivity and the switching fields behave similarly to the Stoner- Wohlfarth model, as in other incoherent models. For lengths equal to 150 nm and 200 nm, the results are comparable to incoherent models qualitatively. Above 200 nm, the particles can be multi-domain.

Discussion and conclusions

Reversal modes for three ranges of particle sizes are characterized for all angles between the partickaxis and the external field. The quasi-coherent mode and the quasi-curling mode are similar to the classical re- sults. Our results are consistent with Knowles' conclu- sion that reversal occurs by the nucleation and subse- quent propagation of a "quasi-180'" wall, with config- urations analogous to ,fanning, buckling, and curling, and agree with single-particle experimental results.

Acknowledgement

This work was supported by a grant from the Na- tional Security Agency.

[I] Della Torre, E., IEEE Trans. Magn. MAG-21 (1985) 1423.

[2] Yan, Y. D. and Della Torre,

E.,

INTERMAG Conf. (1988) AG-3.

[3] Schabes, M. and Bertram, N., J. Appl. Phys. 64 (1988).

[4] Knowles, J. E., IEEE Trans. Magn. MAG-17

(1981) 84.

[5] Aharoni, A,, IEEE Trans. Magn. MAG-22