Topology of magnons: classification and application to honeycomb Kitaev magnets

Compared to their electronic counterparts in topological band theory, much less in known about the topology of spin wave excitations in a general magnetic order. Here we provide a generic theory framework to classify and compute the topology of magnons, by mapping an arbitrary linear spin wave into a local free-fermion Hamiltonian with exactly the same spectrum, symmetry implementation and band topology. This allows us to achieve a full classification and calculation on any topological properties of magnon bands. We apply this fermionization approach to honeycomb Kitaev magnet α-RuCl₃, and show the existence of topologically protected magnon band crossings, and field-induced magnon Chern bands under small magnetic fields.