On the basis of a first-principles, relativistic electronic structure theory
of finite temperature metallic magnetism, we investigate the variation of
magnetic anisotropy, K, with magnetisation, M, in metallic ferromagnets. We
apply the theory to the high magnetic anisotropy material, L1_0-ordered FePt,
and find its uniaxial K consistent with a magnetic easy axis perpendicular to
the Fe/Pt layering for all M and to be proportional to M^2 for a broad range of
values of M. For small M, near the Curie temperature, the calculations pick out
the easy axis for the onset of magnetic order. Our results are in good
agreement with recent experimental measurements on this important magnetic
material.Comment: 4 pages, 2 figure