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

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