Intrinsic Second-Order magnon Thermal Hall Effect

In this paper, we study the intrinsic contribution of nonlinear magnon thermal Hall Effect. We derive the intrinsic second-order thermal Hall conductivity of magnon by the thermal scalar potential method and the thermal vector potential method. We find that the intrinsic second-order magnon thermal Hall conductivity is related to the thermal Berry-connection polarizability. We apply our theory to the monolayer ferromagnetic Hexagonal lattice, and we find that the second-order magnon thermal Hall conductivity can be controlled by changing Dzyaloshinskii-Moriya strength and applying strain.