Temperature dependence of magnetic anisotropy: An ab initio approach

We present a first-principles theory of the variation of magnetic anisotropy, K, with temperature, T, in metallic ferromagnets. It is based on relativistic electronic structure theory and calculation of magnetic torque. Thermally induced local moment magnetic fluctuations are described within the relativistic generalization of the disordered local moment theory from which the T dependence of the magnetization, m, is found. We apply the theory to a uniaxial magnetic material with tetragonal crystal symmetry, L1₀-ordered FePd, and find its uniaxial K consistent with a magnetic easy axis perpendicular to the Fe∕Pd layers for all m and proportional to m² for a broad range of values of m. This is the same trend that we have previously found in L1₀-ordered FePt and which agrees with experiment. We also study a magnetically soft cubic magnet, the Fe₅₀Pt₅₀ solid solution, and find that its small magnetic anisotropy constant K₁ rapidly diminishes from 80.3em0exμeV to zero. K₁ evolves from being proportional to m⁷ at low T to m⁴ near the Curie temperature. The accounts of both the tetragonal and cubic itinerant electron magnets differ from those extracted from single ion anisotropy models and instead receive clear interpretations in terms of two ion anisotropic exchange.