Phonon Thermal Hall Transport from Coupling to Spin Defects

Recent thermal-Hall transport experiments in certain metals as well as Mott insulators have identified phonons as the major heat carrier, but the mechanism of phonon chirality remains unclear. In this work, we investigate the scenario of phonon coupling to spin-1/2 defects in the material. In our theory, we assume the spin defects break lattice inversion symmetry and therefore gives rise to a direct coupling between the defect spin and lattice displacement. When the spin is polarized by an external magnetic field, phonons acquire a chiral self energy, and it is strongest when the phonon energy resonates with the spin-flip transition. We discuss two mechanisms via which the phonons can demonstrate thermal-Hall effect: First, the phonons move in an effective Berry-curvature induced by the spin defect. Second, the phonons skew scatter on the spin defect.