Microscopic Theory of Directional-Order-Related Magnetocrystalline Anisotropy Energy of L10-Type Alloys

We have theoretically investigated the chemical order parameter (S) dependence of magnetocrystalline anisotropy energy (MAE) of L1(0)-type alloys by means of the second-order perturbation in terms of the spin-orbit interaction (SOI) combined with the coherent potential approximation. Using some approximations, we obtained MAE proportional to S-2 as well as the directional-order-induced magnetic anisotropy resulting from dipole-dipole interactions. The common feature that leads to this relation is the two-site interactions that reflect the polarity of atomic arrangements in the both anisotropy energies resulting from the SOI and the dipole dipole interactions. In the case of MAE resulting from SOI, some approximations are needed owing to the presence of electron itineracy, which is neglected in the conventional scenario of directional-order-induced magnetic anisotropy.