Symmetry-enforced third-order nonlinear thermal Hall effects in altermagnets

Thermal Hall effect (THE) is a powerful probe of material properties, even in insulators. Here we investigate the thermal response of altermagnets by developing a theory on Berry curvature driven nonlinear THE from both electrons and magnons. We identify symmetry conditions under which the third-order THE dominates while linear and second-order contributions vanish. Notably, d-wave and i-wave altermagnets with out-of-plane Neel order satisfy these conditions, whereas in-plane order yields a dominant linear THE. Using KV2Se2O (a d-wave altermagnetic metal) and MnF2 (an altermagnetic insulator) as concrete examples, we show nonzero third-order nonlinear THE from electrons and magnons, respectively, both exhibiting a pi-periodic dependence on the direction of temperature gradient. These symmetry-guaranteed Berry curvature phenomena provide a diagnostic for altermagnetism in candidate materials and enable determination of the Neel vector orientation.