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Unconventional Thermal Magnon Hall Effect in a Ferromagnetic Topological Insulator

We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekulé-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal magnon Hall conductivity ${κ^{xy}}$ at low temperature in each of these phases. We predict an unconventional conductivity due to a non-zero Berry curvature emerging from band proximity effects in the topologically trivial phase. We find sign changes of ${κ^{xy}}$ as a function of the model parameters, associated with the local Berry curvature and occupation probability of the bulk bands. Throughout, ${κ^{xy}}$ can be easily tuned with external parameters such as the magnetic field and temperature.