Accurate calculation of light rare-earth magnetic anisotropy with density functional theory

Density functional theory (DFT) has long struggled to treat light rare-earth magnetism. We show that this difficulty arises from an overestimate of the $4f$ charge asphericity, and thus the magnetic anisotropy energy, due to the inadequacy of single Slater-determinant representations. We propose an effective solution by combining constrained DFT+U with crystal field theory and a systematic many-body correction to the charge asphericity. We confirm the validity of this combination on TbV$_6$Sn$_6$ and TbCo$_5$, and then show how the many-body correction adjusts the calculated magnetic anisotropy energy of SmCo$_5$ to match experiment. Our method is an efficient DFT-based approach to address light-rare-earth magnetism.