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

A member of the RMn₆Sn₆ rare-earth family materials, TbMn₆Sn₆, recently showed experimental signatures of the realization of a quantum-limit Chern magnet. Despite the promising experimental results, theoretical studies with accurate electron correlations which probe these observations have been lacking. In this work, we use QMC and DFT+U calculations to examine the electronic structure of TbMn₆Sn₆. To do so, we optimize accurate, correlation-consistent pseudopotentials for Tb and Sn using CCSD(T) and 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 to either use improved orbitals, such as natural orbitals from CI, or to include multi-reference wave functions to capture the static correlations for an accurate prediction of magnetic properties. The necessity for multi-reference treatment is motivated by extrapolating the dynamic correlations to the exact limit. DFT+U with empirically adjusted Mn magnetic moments predict the Dirac crossing to be close to the Fermi level, within ~120 meV, in agreement with the experiments.