Spin-Space Groups and Magnon Band Topology*

Band topology is both constrained and enriched by the presence of symmetry. The importance of anti-unitary symmetries such as time reversal was recognized early on leading to the classification of topological band structures based on the ten-fold way. Since then, lattice point group and non-symmorphic symmetries have been seen to lead to a vast range of possible topologically nontrivial band structures many of which are realized in materials.

We have shown that band topology is further enriched in many physically realizable instances where magnetic and lattice degrees of freedom are wholly or partially decoupled. The appropriate symmetry groups to describe general magnetic systems are the spin-space groups. We focus on magnon band topology where the theory of spin-space groups has its simplest realization and considered various types of coupling, including Heisenberg and Kitaev, revealing a symmetry-enforced proliferation of nodal points, lines, planes and volumes.