Intersublattice magnetocrystalline anisotropy using a realistic tight-binding method based on maximally localized Wannier functions

Using a realistic tight-binding Hamiltonian based on maximally localized Wannier functions, we investigate the two-ion magnetocrystalline anisotropy energy (MAE) in $L1_0$ transition metal compounds. MAE contributions from throughout the Brillouin zone are obtained using magnetic force theorem calculations with and without perturbation theory. The results from either method agree with one another, and both reflect features of the Fermi surface. The intra-sublattice and inter-sublattice contributions to MAE are evaluated using a Green's function method. We find that the sign of the inter-sublattice contribution varies among compounds, and that its amplitude may be significant, suggesting MAE can not be resolved accurately in a single-ion manner. The results are further validated by scaling spin-orbit-coupling strength in density functional theory. Overall, this realistic tight-binding method provide an effective approach to evaluate and analyze MAE while retaining the accuracy of corresponding first-principles methods.