  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.
