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 Li$_{2}$[(Li$_{1-x}$T$_{x}$)N], with $T$=Mn, Fe, Co, Ni, provide a system where the model is very effective because atomic like 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.