Topological magnons on a kagome lattice

A system of spins on a kagome lattice interacting via the nearest-neighbor XXZ interaction (anisotropy ratio △) and Dzyaloshinskii-Moriya interaction (strength D) is found to have a very rich phase diagram. In the classical limit, five distinct phases with different ground-state spin configurations are found by varying the two interaction parameters. In some of these phases, spin-wave theory using the Holstein-Primakoff transformations is used to find the bulk energy bands of the magnons. In the ferromagnetic phase, where all the spins point along the +z direction, the bulk bands are separated from each other by finite energy gaps. Finding the Chern numbers here, one finds that there are four topologically distinct phases sharing the same ground state spin-configuration. Hence an infinite strip of the system hosts robust edge states which are directly related to the Chern number of the bands. The other phases, however, are found to have gapless magnon bands.