Importance of enforcing Hund’s rules in density functional theory calculations of rare earth magnetocrystalline anisotropy
Yongbin Lee, Zhenhua Ning, Rebecca Flint, R. J. McQueeney, I. I. Mazin, Liqin Ke
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.