Magnon Hall effect and topology in kagome lattices: A theoretical investigation

Abstract

Ferromagnetic insulators with Dzyaloshinskii-Moriya interaction show the magnon Hall effect, i.e., a transverse heat current upon application of a temperature gradient. In this theoretical investigation we establish a close connection of the magnon Hall effect in two-dimensional kagome lattices with the topology of their magnon dispersion relation. From the topological phase diagram we predict systems which show a change of sign in the heat current in dependence on temperature. Furthermore, we derive the high-temperature limit of the thermal Hall conductivity; this quantity provides a figure of merit for the maximum strength of the magnon Hall effect. Eventually, we compare the temperature and field dependence of the magnon Hall conductivity of the three-dimensional pyrochlore ${\mathrm{Lu}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{7}$ with experimental results.