Millev, Y. T., Cullen, J. R., Oepen, H.-P.

The field-space perspective on hysteresis in uniaxial ferromagnets

Journal of Applied Physics

**83**, (11),pp 6500-6502 (1998)

A procedure for the analysis of hysteresis in the H space of a uniaxial ferromagnet with higher-order anisotropy is put forward. The formulation is valid to any order n in the anisotropy expansion. The critical boundaries separating stable from metastable states are cast in a formally decoupled parametric way as H

_{x}= H_{x}(M_{x}), H_{z}= H_{z}(M_{z}). The analytic expressions provide the basis for the construction of generalized astroids to any order. For n > 1, new features are found and interpreted in their relation to rotational hysteresis and possible spin-reorientation transitions in uniaxial materials. The shape and symmetry of the critical boundaries depend crucially on up to n - 1 independent ratios of the anisotropy constants against a suitable normalizing quantity; the normalizer can be any from among the set of constants or any linear combination thereof. Self-crossing of an astroid indicates the existence of additional extrema and, hence, of complicated hystereses.ki-1998-t03