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_xx and transverse κ_xy thermal conductivity in Pr₂Ir₂O₇, which is a metallic analog of spin ice. Despite the presence of mobile charge carriers, we find that both κ_xx and κ_xy are dominated by phonons. A T/H scaling of κ_xx 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_xx deviates from the scaling in an anisotropic way with respect to field directions. Strikingly, a set of the κ_xx and κ_xy data clearly shows that κ_xy correlates with κ_xx 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.