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

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.

14+11 pages, 10+7 figures

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• Topological Hall effect induced by chiral fluctuations in ErMn6Sn6
• New insight into tuning magnetic phases of $R$Mn${}_6$Sn${}_6$ kagome metals
• Toward a first-principles theory of rare-earth ions in crystals
• Kagome metals
• Quantum oscillations in kagome metals (Ti, Zr, Hf)V6Sn6 at Van Hove filling
• Tunable topological transitions in the frustrated magnet HoAgGe
• The role of electron correlations in the electronic structure of putative Chern magnet TbMn${}_6$Sn${}_6$
• High-field magnetic phase diagrams of the $\text{R}$Mn${}_6$Sn${}_6$ kagome metals
• Giant coercivity and enhanced intrinsic anomalous Hall effect at vanishing magnetization in a compensated kagome ferrimagnet
• Giant Self Spin-Valve Effect in the Kagome Helimagnet
• Diverse Magnetic Phase Diagram and Anomalous Hall Effect in Antiferromagetic LuMn${}_6$Sn${}_6$
• Kagome Metal GdNb${}_6$Sn${}_6$: A 4d Playground for Topological Magnetism and Electron Correlations
• Characterization of the Magnetocaloric Effect in RMn6Sn6 including High Entropy Alloys
• Magnetic interactions and excitations in SrMnSb${}_2$
• Spin dynamics in itinerant antiferromagnet SrCr${}_2$As${}_2$
• Nature of quantum criticality in the Ising ferromagnet TbV${}_6$Sn${}_6$
• Modeling of a twisted-Kagome HoAgGe spin ice using Reduced-Configuration-Space Search and Density Functional Theory
• Distinct effect of Kondo physics on crystal field splitting in electron and spin spectroscopies
• Chiral Magnon Mixing by Symmetry-Breaking in Collinear Ferrimagnets