# Spin-wave interactions in an anisotropic ferromagnet

## Abstract

In the presence of anisotropic interactions the spin-wave dispersion parameter D(T) acquires an aT32 dependence in addition to the bT52 dependence due to isotropic exchange. We have used Van Vleck's anisotropic exchange, and the largest effect consistent with the magnetocrystalline anisotropy of a cubic ferromagnet is found to come from the pseudodipolar coupling. While the anisotropy appears only in the second order of perturbation theory, there is a first-order contribution to D(T) which varies as the third power of the magnetization, itself a function of temperature. Thus aC(gHADkBTc)12, where C is the coefficient in the Bloch law, HAD is the pseudodipolar contribution to the anisotropy field, and Tc is the Curie temperature. The coefficient a depends upon the direction of spin-wave propagation and averages to zero over a sphere. In a first approximation, then, there is no T3 term in the magnetization. In an experiment dealing with selected propagation directions, such as spin-wave resonance or inelastic neutron scattering, since bCTc, an effect important when TTc(gHADkBTc)12 is predicted. © 1964 The American Physical Society.