Using a realistic tight-binding Hamiltonian based on maximally localized Wannier functions, we investigate the two-ion magnetocrystalline anisotropy energy (MAE) in $L{1}_0$ 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 both methods agree with each other, and both reflect features of the Fermi surface. The intrasublattice and intersublattice contributions to MAE are evaluated using a Green's function method. We find that the sign of the intersublattice 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 provides an effective approach to evaluate and analyze MAE while retaining the accuracy of corresponding first-principles methods.

• Received 29 October 2018
• Revised 25 January 2019

DOI:https://doi.org/10.1103/PhysRevB.99.054418