Interplay between magnetism and band topology in Kagome magnets $R$Mn$_6$Sn$_6$

TL;DR

This study investigates the magnetic and topological electronic properties of Kagome-lattice $R$Mn$_6$Sn$_6$ magnets, revealing the roles of rare-earth anisotropy, crystal-field effects, and band topology, and clarifying their influence on anomalous Hall effects.

Contribution

The paper provides a comprehensive ab initio analysis of magnetic anisotropy and topological bands in $R$Mn$_6$Sn$_6$, clarifying their relevance to transport phenomena and introducing an analytical model for anisotropy evolution.

Findings

Rare-earth anisotropy is influenced by higher-order crystal-field parameters.

Topological bands are mostly far from the Fermi level, limiting their impact on Hall effects.

Exchange-correlation effects do not significantly alter the electronic structure.

Abstract

Kagome-lattice magnets $R$Mn$_6$Sn$_6$ recently emerged as a new platform to exploit the interplay between magnetism and topological electronic states. Some of the most exciting features of this family are the dramatic dependence of the easy magnetization direction on the rare-earth specie and the kagome geometry of the Mn planes that in principle can generate flat bands and Dirac points; gapping of the Dirac points by spin-orbit coupling has been suggested recently to be responsible for the observed anomalous Hall response in the member TbMn$_6$Sn$_6$. In this paper, we address both issues with ab initio calculations. We have discovered the significant role played by higher-order crystal-field parameters and rare-earth magnetic anisotropy constants in these systems. We demonstrate that the microscopic origin of rare-earth anisotropy can also be quantified and understood at various levels: ab initio, phenomenological, and analytical. In particular, using a simple and physically transparent analytical model, we explain, with full quantitative agreement, the evolution of anisotropy across the series. We analyze the topological properties of Mn-dominated bands and demonstrate how they emerge from the multiorbital planar kagome model. We further show that the most pronounced quasi-2D dispersion are too far removed from the Fermi level, and therefore cannot explain the observed quasi-2D anomalous Hall effect. By employing ab initio many-body approaches, we demonstrate that the exchange-correlation effects for itinerant Mn-$d$ electrons do not significantly alter the obtained electronic and magnetic structure. Therefore, we conclude that, contrary to previous claims, the most pronounced 2D kagome-derived topological band features bear little relevance to transport in $R$Mn$_6$Sn$_6$, albeit they may possibly be brought to focus by electron or hole doping.