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

Abstract

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 4$f$ 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 4$f$ 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 SmCo${}_5$. Applying it to $R$Fe${}_{12}$ and $R$Fe${}_{12}X$ hard magnets ($R=$Nd, Sm and $X=$N, Li), we obtain in particular a large positive value of the crystal field parameter $A_2^0⟨r^2⟩$ in NdFe${}_{12}$N resulting in a strong out-of-plane anisotropy observed experimentally. The sign of $A_2^0⟨r^2⟩$ is predicted to be reversed by substituting N with Li, leading to a strong out-of-plane anisotropy in SmFe${}_{12}$Li. We discuss the origin of this strong impact of N and Li interstitials on the crystal field splitting on rare earth sites.

17 pages, 11 figures

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