Linear theory of magnetocrystalline anisotropy and magnetostriction in exchange-dominated 3d-4fintermetallics

Temperature dependence of the rare-earth contribution to magnetocrystalline anisotropy constants and magnetorestriction of 3d-4f intermetallic compounds is calculated in an approximation linear in the crystal-field and single-ion magnetoelastic interactions, which are regarded as perturbations with respect to a stronger 3d-4f exchange interaction. The results for an arbitrary quantum number J are compactly formulated in terms of new generalized Brillouin functions which coincide with the known reduced hyperbolic Bessel functions in the classical limit, J{→}{∞}. It is shown, however, that the quasiclassical approximation is inapplicable to the systems concerned. Specific cases of some uniaxial crystal structures are considered, being of interest for permanent magnet applications.