Thermal Hall effect of magnons from many-body skew scattering

We present a theory of magnonic thermal Hall transport driven by many-body skew scattering. In field-polarized chiral magnets, the Dzyaloshinskii-Moriya interaction induces three-magnon interactions that violate time-reversal symmetry and interfere with the four-magnon scattering, thereby breaking microscopic detailed balance and causing thermal Hall currents. This mechanism operates without disorder or Berry curvature and is intrinsic to interacting spin systems. We argue that it can be as significant as the band-geometric anomalous velocity, highlighting the importance of magnon interactions in thermal Hall physics.