Phonon thermal Hall effect in a metallic spin ice

It has been a subject of intense debate whether phonons are responsible for the Hall effect. We have investigated longitudinal kappa_xx and transverse kappa_xy thermal conductivity in a metallic analog of spin ice Pr2Ir2O7. Despite the presence of mobile charge carriers, we find that phonon contribution by far dominates electron contribution both in kappa_xx and kappa_xy. A T/H scaling of kappa_xx unambiguously reveals that resonant scattering of phonons on paramagnetic spins substantially impedes longitudinal heat current and provides glass like longitudinal thermal conductivity without a phonon peak. However, a development of spin ice correlation upon cooling modifies the resonant scattering, leading to the deviation from the scaling. A manifest correlation between kappa_xx and kappa_xy including a success of the T/H scaling and its failure at low temperature points to a definitive role of the resonant phonon scattering by spins for generating Hall signals. Given the ubiquitous nature of phonon scattering on spins, our results will open a new avenue for exploring the phonon thermal Hall effect in magnets in which spins couple to phonons.