Temperature Dependence of the Anisotropy Constants of Gd, Tb, and Dy

The sources of magnetocrystalline anisotropy have been studied for the ferromagnetic rare earth metals Gd, Tb, and Dy. In the weak anisotropy case of Gd the contributions to the anisotropy constants from the crystal field have been calculated by spin-wave theory treating the crystal-field terms as a perturbation. Estimates have also been made of the contributions to K1(T) from real and pseudo-dipole-dipole interactions and from the magnetoelastic coupling making use of magnetostriction data. The resulting agreement with the measurements of Graham and others of K2(T), K3(T) and K4(T) is good, but the situation is less satisfactory for K1(T). From the available experimental data the various crystal-field parameters have been estimated. In Tb and Dy, in which there is a strong axial crystal field, the anisotropy constants are no longer well defined, except for small-angle deviations from the easy direction. The data of Rhyne and Clark for the effective anisotropy coefficients K20(T) and K66(T) have been analyzed in this light taking account of the torque balance conditions. The measured value of K20(0) for Tb leads to a value of the effective crystal-field parameter about 100 times larger than the corresponding value for Gd.