Spin space group and quasi-symmetry In Mn₃Sn

Mn3Sn is a non-collinear antiferromagnetic material with a kagome structure. Notably, it exhibits a substantial room-temperature anomalous Hall effect (AHE). Recent Density Functional Theory (DFT) calculations have revealed that in the absence of spin-orbit coupling (SOC), a Weyl nodal line exists near the Fermi surface along K-H, and SOC only introduces a small gap with 0.3 Mev. In our study, we have developed an effective Hamiltonian near the K point based on the spin space group of Mn3Sn. It is important to note that, in the absence of SOC, the spin space group, rather than the magnetic space group, accurately describes the symmetry of Mn3Sn. Our effective model matches the DFT results and confirms the the Weyl nodal line is protected by the spin space group. Furthermore, we demonstrate that SOC acts as a secondary perturbation, so that there is a quasi-symmetry protecting the Weyl nodal line. Additionally, we illustrate that out-of-plane spin canting induced by a magnetic field can open the Weyl nodal line and induce Berry curvature, thereby giving rise to in-plane Hall responses. Our work elucidates the application of the spin space group in the study of magnetic topological materials."