Ferromagnetic Anisotropy in Cubic Crystals

Abstract

A re-evaluation has been made of Van Vleck's second-order perturbation theory of dipolar-type anisotropy in cubic ferromagnets. In the low-temperature limit of strong correlation between the direction of neighbor spins, the first anisotropy constant $K_1$ varies as the 10th power of the magnetization. The theory is somewhat analogous to a previous treatment of quadrupolar-type anisotropy in the strong-correlation limit. In both cases, the results are in agreement with the Akulov-Zener classical theory. For the dipolar case, complete agreement is also established between the Dyson-type spin-wave analysis of Charap and Weiss and the Holstein-Primakoff approach. Higher order terms in the latter are shown to lead to the Charap-Weiss correction from exchange interaction between spin waves, and this correction is extended to $S>\mathrm{}\frac{1}{2}$. Essentially the same correction is obtained very easily from a simple modification of the Van Vleck formalism to take careful account of the average energy involved in simultaneous reversal of neighbor spins. It is shown that spin-wave theory, in agreement with classical theory, predicts identical values of dipolar-type anisotropy whether measured statically in a torque experiment or dynamically in a microwave resonance experiment.