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.