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In a ferromagnet, the spin excitations are the well-studied magnons. Infrustrated quantum magnets, long-range magnetic order fails to develop despitea large exchange coupling between the spins. In contrast to the magnons inconventional magnets, their spin excitations are poorly understood. Are theyitinerant or localized? Here we show that the thermal Hall conductivity$\kappa_{xy}$ provides a powerful probe of spin excitations in the "quantumspin ice" pyrochlore Tb$_2$Ti$_2$O$_7$. The thermal Hall response is large eventhough the material is transparent. The Hall response arises from spinexcitations with specific characteristics that distinguish them from magnons.At low temperature ($T<$ 1 K), the thermal conductivity imitates that of adirty metal. Using the Hall angle, we construct a phase diagram showing how theexcitations are suppressed by a magnetic field.

Thermal Hall conductivity in the frustrated pyrochlore magnet Tb2Ti2O7