The Field-Space Perspective on Hysteresis in Uniaxial Ferromagnets

Abstract

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 5H x ( M x ), H z 5H 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 n21 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. © 1998 American Institute of Physics.@S0021-8979~98!23911-9#