Prediction of Magnetic Topological Materials Combining Spin and Magnetic Space Groups

Abstract: The scarcity of predicted magnetic topological materials (MTMs) by magnetic space group (MSG) hinders further exploration towards realistic device applications. Here, we propose a new scheme combining spin space groups (SSGs)--approximate symmetry groups neglecting spin-orbit coupling (SOC)--and MSGs to diagnose topology in collinear magnetic materials based on symmetry-indicator theory, enabling a systematic classification of the electronic topology across 484 experimentally synthesized collinear magnets from the MAGNDATA database. This new scheme exploits a symmetry-hierarchy due to SOC induced symmetry-breaking, so that nontrivial band topology can be revealed by SSG, that is yet invisible by the conventional MSG-based method, as exemplified by real triple points in ferromagnetic CaCu$3$Fe$_2$Sb$_2$O${12}$, Dirac nodal lines at generic $k$-points in antiferromagnetic FePSe$3$ and Weyl nodal lines in altermagnetic Sr$_4$Fe$_4$O${11}$. Notably, FePSe$3$ is topologically trivial under MSG but hosts Dirac nodal lines within the SSG framework. Upon including SOC, these nodal lines are gapped and generate a sizable anomalous Hall conductivity. Despite a vanishing bulk net magnetism, FePSe$_3$ can host topologically protected surface states with large non-relativistic band spin-splitting. Moreover, topology in MTMs is tunable by rotating the magnetic moment direction once SOC is included, as exemplified in Sr$_4$Fe$_4$O${11}$.The interplay of topology with non-relativistic and SOC-induced control of properties via magnetic moment reorientation in the predicted MTMs is worthy of further studies in future.