Crystal-field splittings in rare-earth-based hard magnets: An ab initio approach

We apply the first-principles density functional theory + dynamical mean-field theory framework to evaluate the crystal-field splitting on rare-earth sites in hard magnetic intermetallics. An atomic (Hubbard-I) approximation is employed for local correlations on the rare-earth 4f shell and self-consistency in the charge density is implemented. We reduce the density functional theory self-interaction contribution to the crystal-field splitting by properly averaging the 4f charge density before recalculating the one-electron Kohn-Sham potential. Our approach is shown to reproduce the experimental crystal-field splitting in the prototypical rare-earth hard magnet SmCo5. Applying it to RFe12 and RFe12X hard magnets (R=Nd, Sm and X=N, Li), we obtain in particular a large positive value of the crystal-field parameter A20(r2) in NdFe12N resulting in a strong out-of-plane anisotropy observed experimentally. The sign of A20(r2) is predicted to be reversed by substituting N with Li, leading to a strong out-of-plane anisotropy in SmFe12Li. We discuss the origin of this strong impact of N and Li interstitials on the crystal-field splitting on rare-earth sites.