Fermi surface origin of the interrelationship between magnetocrystalline anisotropy and compositional order in transitional metal alloys

Recently, we outlined a scheme to investigate the effects of compositional order on the magnetocrystalline anisotropy of alloys from a first-principles electronic structure point of view \{Phys. Rev. Lett. {\bf 83}, 5369 (1999)\} and showed that compositional order enhances the magnitude of magnetocrystalline anisotropy energy (MAE) of Co$_{0.5}$Pt$_{0.5}$ alloy by some two orders of magnitude as well as affecting the equilibrium magnetization direction. Here we describe our scheme in detail and present an in-depth study of the effect by demonstrating its Fermi surface origin. In Co$_{0.25}$Pt$_{0.75}$ alloy we find that the perfect $ L1_2 $ structure has a very small MAE whereas imposition of directional order enhances the MAE by two orders of magnitude. We also present the effect of lattice distortion (tetragonalization) on the MAE on the same footing and find that in the Co$_{0.5}$Pt$_{0.5}$ alloy it accounts for only about 20% of the observed MAE, thus confirming that compositional order is the major player in the enhancement of MAE. We also examine the directional chemical order that can be produced by magnetic annealing within the same framework. We extract a Fermi surface mechanism for the effect in an explicit study of permalloy. Finally, we propose that the Fermi surface plays a major role in the strong coupling between magnetocrystalline anisotropy and compositional order in many magnetic alloys.