Prediction of Magnetic Topological Materials Combining Spin and Magnetic Space Groups

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.