Magnon thermal Hall effect induced by symmetric exchange interaction

By analyzing the spin-group symmetry of magnons, we establish two generalized Onsager's relations in the magnon thermal Hall effect, which reveals the rich and complicated structures of the magnon Berry curvature in the parameter space of different types of the exchange coupling. As an important consequence, we find that the diagonal and off-diagonal part of the symmetric anisotropic exchange coupling together can support the planar magnon thermal Hall effect without the DM interaction. This removes the local inversion-symmetry-breaking condition for generating the magnon thermal Hall effect. Moreover, we predict an exotic phenomenon that the thermal conductivity exhibits angular dependence with respect to the in-plane magnetization. Our work lays the ground for decoding the coupling between magnon transport and different types of exchange interactions.