Orientational Transition of Magnetization under Conditions of High-Order Single-Axis Anisotropy

The effect of high-order uniaxial anisotropy on the nature of orientational transition of magnetization is considered. In the geometry of normal magnetization of the medium with respect to the anisotropy axis, the energy density and the equilibrium position of magnetization are obtained depending on the magnitude of the applied field. The orientation of magnetization is considered for anisotropy from the second to the eighth even orders only. As an example, the simultaneous presence of anisotropy of the second and fourth orders is considered. For this case, an algebraic equation of the third degree is obtained for the analysis of which the Cardano discriminant is used. It is shown that in the case of a negative value of the discriminant, the dependence of the magnetization orientation on the field has a hysteresis character.