Phonon thermal Hall effect in a metallic spin ice.

It has become common knowledge that phonons can generate thermal Hall effect in a wide variety of materials, although the underlying mechanism is still controversial. We study longitudinal κ and transverse κ thermal conductivity in PrIrO, which is a metallic analog of spin ice. Despite the presence of mobile charge carriers, we find that both κ and κ are dominated by phonons. A T/H scaling of κ unambiguously reveals that longitudinal heat current is substantially impeded by resonant scattering of phonons on paramagnetic spins. Upon cooling, the resonant scattering is strongly affected by a development of spin ice correlation and κ deviates from the scaling in an anisotropic way with respect to field directions. Strikingly, a set of the κ and κ data clearly shows that κ correlates with κ in its response to magnetic field including a success of the T/H scaling and its failure at low temperature. This remarkable correlation provides solid evidence that an indispensable role is played by spin-phonon scattering not only for hindering the longitudinal heat conduction, but also for generating the transverse response.