Phonon thermal Hall effect in a non-Kramers paramagnet

With an increasing number of experiments observing phonon thermal Hall effect in magnets, it is theoretically desired to have a minimal model for the effect. In this work, we study simple acoustic phonons and uncorrelated paramagnetic doublets. When doublets are non-Kramers, linear pseudospin-phonon coupling allowed by time-reversal symmetry yields resonant phonon-pseudospin scattering. We compute longitudinal conductivities find qualitative agreement with recent ${\mathrm{Pr}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ [Uehara et al., Nat. Commun. 13, 4604 (2022)].