Magnon valley thermal Hall effect in triangular-lattice antiferromagnets

Abstract

We study the magnetic excitations of the antiferromagnetic XXZ model on two-dimensional triangular lattice. We find there is a magnon valley thermal Hall effect. As far as we know, this effect has been studied on only the ferromagnetic honeycomb lattice. We reveal that the valley thermal Hall conductivity also conforms to the universal behavior of thermal Hall conductivity proposed by Yang et al. [Phys. Rev. Lett. 124, 186602 (2020)]. We derive a low-energy effective theory near the valleys and find that although the low-energy effective dynamic matrix is non-Hermitian, the Berry curvatures are mainly determined by its Hermitian part. We show that our results are general to some extent in the Y phase of the triangular lattice. By an explicit calculation with experimental parameters, we demonstrate that ${\mathrm{Rb}}_{4}\mathrm{Mn}{({\mathrm{MoO}}_{4})}_{3}$ is a suitable material to realize the magnon valley thermal Hall effect.