Rare-Earth Kagome Magnets: Challenges and Advances in First-Principles Modeling of 4f Magnetism

Rare-earth kagome magnets RMn₆Sn₆ have recently emerged as a rich platform for studying the interplay between 4f magnetism and topological electronic structure. Variations in the rare-earth element across the isostructural series offer unique opportunities to tune both the easy spin direction and the underlying band topology. However, accurately modeling 4f magnetism remains challenging due to the many-body nature of 4f electrons. We will discuss the fundamental limitations of conventional density functional theory (DFT)-based approaches applied to rare-earth magnetism. In particular, we will show how the orbital dependence of the self-interaction error contradicts Hund’s rules for 4f electrons and undermines magnetocrystalline anisotropy (MA) calculations, and how analyzing DFT states that enforce Hund’s rules mitigates this issue for heavy rare-earth elements. Additional challenges arise for light rare-earths due to the single-determinant description, which exaggerates 4f charge asphericity and MA energies. We will then introduce a constrained DFT+U approach combined with crystal-field analysis and a many-body correction to 4f multipole moments, enabling quantitatively accurate MA predictions across both heavy- and light-rare-earth systems. We benchmark this method in various rare-earth compounds, including kagome magnets such as RMn₆Sn₆ and SmCo₅. These advances establish a unified and predictive framework for understanding 4f magnetism and for designing magnetic topological materials with tunable anisotropy and electronic topology.