Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations

Abstract

Quite recently, magnon Hall effect of spin excitations has been observed experimentally on the kagome and pyrochlore lattices. Thermal Hall conductivity $κ^{xy}$, changes sign as a function of magnetic field or temperature on the kagome lattice, and $κ^{xy}$ changes sign upon reversing the sign of the magnetic field on the pyrochlore lattice. Motivated by these recent exciting experimental observations, we theoretically propose a simple realization of magnon Hall effect in a two-band model on the honeycomb lattice. The magnon Hall effect of spin excitations arises in the usual way via the breaking of inversion symmetry of the lattice, however, by a next-nearest-neighbour Dzyaloshinsky-Moriya (DM) interaction. We find that $κ^{xy}$ has a fixed sign for all parameter regimes considered. These results are in contrast to the Lieb, kagome and pyrochlore lattices. We further show that the low-temperature dependence on the magnon Hall conductivity follows a $T^{2}$ law, as opposed to the kagome and pyrochlore lattices. These results suggest an experimental procedure to measure thermal Hall conductivity within a class of 2D honeycomb quantum magnets and ultracold atoms trapped in honeycomb optical lattice.