Spin Space Groups: Full Classification and Applications

In this work, we exhaust all the spin space symmetries, which fully characterize collinear, noncollinear, and commensurate spiral as well as incommensurate spiral magnetism, etc., and investigate enriched features of electronic bands that respect these symmetries. We achieve this by systematically classifying the so-called spin space groups (SSGs)—joint symmetry groups of spatial and spin operations that leave the magnetic structure unchanged. Generally speaking, they are accurate (approximate) symmetries in systems where spin-orbit coupling (SOC) is negligible (finite but weaker than the energy scale of interest), but we also show that specific SSGs could remain valid even in the presence of strong SOC. In…

• NN
  National Natural Science Foundation of China

  Awards: 12074008, 11674011, 12274005, 2019YFA0308401
• NK
  National Key Research and Development Program of China

  Awards: 2019YFA0308401, 2021ZD0302403, 2021YFA1401903