Band-filling effect on magnetic anisotropy using a Green's function method

We use an analytical model to describe the magnetocrystalline anisotropy energy (MAE) in solids as a function of band filling. The MAE is evaluated in second-order perturbation theory, which makes it possible to decompose the MAE into a sum of transitions between occupied and unoccupied pairs. The model enables us to characterize the MAE as a sum of contributions from different, often competing terms. The nitridometalates ${\mathrm{Li}}_{2}[({\mathrm{Li}}_{1\ensuremath{-}x}{T}_{x})\mathrm{N}]$, with $T=$ Mn, Fe, Co, Ni, provide a system where the model is very effective because atomiclike orbital characters are preserved and the decomposition is fairly clean. Model results are also compared against MAE evaluated directly from first-principles calculations for this system. Good qualitative agreement is found.