A perturbative DFT approach for magnetic anisotropy

We develop a perturbative formalism for computing magnetocrystalline anisotropy within density functional theory and the magnetic force theorem. Instead of computing eigenvalues of the spin-orbit Hamiltonian for selected spin polarizations, as in the conventional “force theorem” approach, we show that the effect can be cast into a redefined form of the spin-orbit operator. This allows to separate the large eigenvalue shift due to spin-orbit interaction common for both polarizations from the much smaller magnetic anisotropy splitting. As a consequence the anisotropy splitting may by considered as a perturbation.