Search for topological magnons using band representations of magnetic space groups

In contrast to their electronic counterparts, a systematic framework to understand magnon band topology is still lacking. By combining the recently developed formalism of magnetic topological quantum chemistry with a general framework that maps an arbitrary linear spin wave system into a free-fermion Hamiltonian with the same band topology, we achieve a classification of possible magnon band structures that arise from localized magnetic moments in any crystalline symmetry setting. This allows us to perform an efficient search for candidate materials hosting topological magnons based on the pool of existing magnetic materials.