Magnetic band representations, Fu-Kane-like symmetry indicators, and magnetic topological materials

To realize novel topological phases and to pursue potential applications in low-energy consumption spintron-ics, the study of magnetic topological materials is of great interest. Starting from the theory of nonmagnetic topological quantum chemistry [Bradlyn et al., Nature 547, 298 (2017)], we have obtained irreducible (co)representations and compatibility relations (CRs) in momentum space, and we constructed a complete list of magnetic band (co)representations (MBRs) in real space for other magnetic space groups (MSGs) with antiunitary symmetries (i.e.,type-III and type-IV MSGs). The results are consistent with the magnetic topological quantum chemistry [Elcoro et al., Nat. Commun. 12, 5965 (2021)]. Using the CRs and MBRs, we reproduce the symmetry-based classifications for MSGs, and we obtain a set of Fu-Kane-like formulas of symmetry indicators (SIs) in both spinless (bosonic) and spinful (fermionic) systems, which are implemented in an automatic code-TOPMAT-to diagnose topological magnetic materials. The magnetic topological materials, whose occupied states cannot be decomposed into a sum of MBRs, are consistent with nonzero SIs. Lastly, using our online code, we have performed spin-polarized calculations for magnetic compounds in the materials database, and we find many magnetic topological candidates.

Automated summary

The study of magnetic topological materials is of great interest for realizing novel topological phases and pursuing potential applications in low-energy consumption spintronics. In this research, starting from the theory of nonmagnetic topological quantum chemistry, the researchers obtained irreducible (co)representations and compatibility relations in momentum space and constructed a complete list of magnetic band (co)representations in real space. They also developed symmetry indicators (SIs) to diagnose topological magnetic materials and identified numerous magnetic topological candidates through spin-polarized calculations.