Importance of enforcing Hund’s rules in density functional theory calculations of rare earth magnetocrystalline anisotropy

Abstract

Density functional theory (DFT) and its extensions, such as DFT+ U and DFT+dynamical mean-field theory, are invaluable for studying magnetic properties in solids. However, rare-earth ( R ) materials remain challenging due to self-interaction errors and the lack of proper orbital polarization. We show how the orbital dependence of self-interaction error contradicts Hund’s rules and plagues magnetocrystalline anisotropy (MA) calculations, and how analyzing DFT states that respect Hund’s rules can mitigate this issue. We benchmark MA in R Co 5 , R 2 Fe 14 B, and R Fe 12 , extending prior work on R Mn 6 Sn 6 , achieving excellent agreement with experiments. Additionally, we illustrate a semi-analytical perturbation approach that treats crystal fields as a perturbation in the large spin-orbit coupling limit. Using Gd-4 f crystal-field splitting, this method provides a microscopic understanding of MA and enables rapid screening of high-MA materials.