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 phonon thermal Hall effect. In this work, we study a simple model of acoustic phonons and uncorrelated paramagnetic doublets. When the doublets are non-Kramers, a linear pseudospin-phonon coupling is allowed by time-reversal symmetry and yields resonant phonon-pseudospin scattering. We compute the thermal longitudinal and Hall conductivities of the model and found qualitative agreement with recent experiments in $\rm{Pr}_2\rm{Ir}_2\rm{O}_7$ [Uehara et al.,Nat Commun 13, 4604 (2022)].