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

## TL;DR

This paper develops an ab initio method combining density functional theory and dynamical mean field theory to accurately compute crystal field splittings in rare earth-based hard magnets, successfully reproducing experimental results and predicting effects of interstitial substitutions.

## Contribution

It introduces a novel computational approach that improves the accuracy of crystal field splitting calculations in rare earth magnets, accounting for local correlations and self-interaction corrections.

## Key findings

- Reproduces experimental crystal field splitting in SmCo₅.
- Predicts large positive crystal field parameter in NdFe₁₂N.
- Shows N and Li interstitials significantly alter magnetic anisotropy.

## 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 $A_2^0\langle r^2\rangle$ in NdFe$_{12}$N resulting in a strong out-of-plane anisotropy observed experimentally. The sign of $A_2^0\langle r^2\rangle$ 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.