Spin-wave theory of the magnetocrystalline anisotropy in gadolinium metal

Magnetocrystalline anisotropy in gadolinium has been studied utilizing a spin-wave model in which a crystal field of hexagonal close-packed symmetry and magnetic dipole-dipole interactions are treated as a first-order perturbation to isotropic exchange. Corrections to the temperature dependence of K1, due to normal and magnetostrictive thermal expansion, are shown to be small. The resulting agreement with the measurements of Graham and of Corner et al. for K2(T), K3(T), K4(T) is good, but the temperature dependence of K1 is anomalous. Crystal-field parameters, evaluated by comparison with experiment, are about 100 times larger than the corresponding parameters in gadolinium ethyl sulphate.