State-tracking first-principles determination of magnetocrystalline anisotropy

A state-tracking method is proposed for the determination of the magnetocrystalline anisotropy (MCA) energy, in which the spin-orbit coupling perturbed occupied states are defined according to their wave functions as related to the unperturbed occupied states, instead of their energies. This ensures that the force theorem is well satisfied—a very important feature in all non-self-consistent procedures. In calculations for the effect of strain on the MCA of an Fe monolayer (using the full-potential linearized augmented plane-wave method), highly stable results were obtained even with a small number of k points (${10}^2$ in the full Brillouin zone) versus the ${10}^4$ points needed previously.