The thermal Hall effect is the thermal analog of the Hall effect. Here, a thermal gradient is produced across a solid instead of an electric field. When a magnetic field is applied, an orthogonal temperature gradient develops.
For conductors, a significant portion of the thermal current is carried by the electrons. In particular, the Righi–Leduc Effect describes the heat flow resulting from a perpendicular temperature gradient and vice versa, and the Maggi–Righi–Leduc effect describes changes in thermal conductivity when placing a conductor in a magnetic field.
A thermal Hall effect has also been measured in a paramagnetic insulator and dubbed the "phonon Hall effect." In this case, there are no charged currents in the solid so the magnetic field cannot exert a Lorentz force. An analogous thermal Hall effect for neutral particles exists in polyatomic gases (known as the Senftleben-Beenakker effect).
Measurements of the thermal Hall conductivity are used to distinguish between the electronic and lattice contributions to thermal conductivity. These measurements are especially useful when studying superconductors.