The role of electron correlations in the electronic structure of putative Chern magnet TbMn₆Sn₆

A member of the RMn6Sn6 rare-earth family materials, TbMn6Sn6, 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 TbMn6Sn6. 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 singlereference 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 the experiment predict the Dirac crossing in bulk to be close to the Fermi level, within similar to 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.