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 kappa(xx) and transverse kappa(xy) thermal conductivity in Pr2Ir2O7, which is a metallic analog of spin ice. Despite the presence of mobile charge carriers, we find that both kappa(xx) and kappa(xy) are dominated by phonons. A T/H scaling of kappa(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 kappa(xx) deviates from the scaling in an anisotropic way with respect to field directions. Strikingly, a set of the kappa(xx) and kappa(xy) data clearly shows that kappa(xy) correlates with kappa(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. The thermal Hall effect, or a temperature gradient transverse to a heat current and a magnetic field, has been observed in many materials, but its mechanism is not fully understood. Uehara et al. demonstrate the dominant phonon contribution to both longitudinal and transverse thermal response in a metallic spin ice Pr2Ir2O7.