The role of electron correlations in the electronic structure of putative Chern magnet TbMn${}_6$Sn${}_6$

Abstract

A member of the RMn${}_6$Sn${}_6$ rare-earth family materials, TbMn${}_6$Sn${}_6$, recently showed experimental signatures of the realization of a quantum-limit Chern magnet. In this work, we use quantum Monte Carlo (QMC) and density functional theory with Hubbard $U$ (DFT$+U$) calculations to examine the electronic structure of TbMn${}_6$Sn${}_6$. To do so, we optimize accurate, correlation-consistent pseudopotentials for Tb and Sn using coupled-cluster and configuration-interaction (CI) methods. We find that DFT$+U$ and single-reference QMC calculations suffer from the same overestimation of the magnetic moments as meta-GGA and hybrid density functional approximations. Our findings point to the need for improved orbitals/wavefunctions for this class of materials, such as natural orbitals from CI, or for the inclusion of multi-reference effects that capture the static correlations for an accurate prediction of magnetic properties. DFT$+U$ with Mn magnetic moments adjusted to experiment predict the Dirac crossing in bulk to be close to the Fermi level, within $\sim 120$ meV, in agreement with the experiments. Our non-stoichiometric slab calculations show that the Dirac crossing approaches even closer to the Fermi level, suggesting the possible realization of Chern magnetism in this limit.

This is the peer-reviewed, accepted version of the manuscript. 17 pages, 10 figures. https://doi.org/10.1038/s41535-023-00583-6

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