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 Pr 2 Ir 2 O 7 , 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.