Identifying and Constructing Complex Magnon Band Topology

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology.

Figure 1

Figure showing the magnetic sublattices of space group 75 Wyckoff position $2c$ and the accompanying Brillouin zone. The lower panel shows magnon dispersion relations along high symmetry directions with the $C_2$ and $C_4$ eigenvalues given according to the symmetry indicator formula Eq. (1).

Figure 2

Magnetic structure on the garnet hyperkagome lattice with 230.148 magnetic space group symmetry (top left) and (right) the Brillouin zone with high symmetry points indicated. Bottom: spin wave spectrum with multifold magnons at $\mathrm{\Gamma }$ and $H$.