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 (TSP) method and the thermal vector potential (TVP) method. We find that the intrinsic second order magnon thermal Hall conductivity is related to the thermal Berry-connection polarizability (TBCP). 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.