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J.B. Staunton, L. Szunyogh, A. Buruzs, B.L. Gyorffy, S. Ostanin, L. Udvardi:
"Temperature dependence of magnetic anisotropy: An ab initio approach";
Physical Review B, 74 (2006), 1444111 - 144411113.

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 8 eV 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.

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