Origin of the Phonon Hall Effect in Rare-Earth Garnets

The phonon Hall effect has been observed in the paramagnetic insulator Tb3Gd5O12. A magnetic field applied perpendicularly to a heat current induces a temperature gradient that is perpendicular to both the field and the current. We show that this effect is due to resonant skew scattering of phonons from the crystal field states of superstoichiometric Tb3+ ions. This scattering originates from the coupling between the quadrupole moment of Tb3+ ions and the lattice strain. The estimated magnitude of the effect is consistent with experimental observations at T similar to 5 K and can be significantly enhanced by increasing temperature.