An ab-initio theory for the temperature dependence of magnetic anisotropy

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 generalisation of the disordered local moment’ (R-DLM) theory from which the T dependence of the magnetisation, m, is found. We apply the theory to a uniaxial magnetic material with tetragonal crystal symmetry, L1_0-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 m squared for a broad range of values of m. This is the same trend that we have previously found in L1_0-ordered FePt and which agrees with experiment. This account, however, differs qualitatively from that extracted from a single ion anisotropy model. We also study the magnetically soft cubic magnet, the Fe(50)Pt(50) solid solution, and find that its small magnetic anisotropy constant K_1 rapidly diminishes from 8 micro-eV to zero. K evolves from being proportional to the seventh power of m at low T to the fourth power near the Curie temperature.