
A phenomenon where heat flow is deflected sideways in materials under a magnetic field, often due to phonon or electron behavior.The thermal Hall effect is a phenomenon where a temperature gradient applied to a material produces a heat flow that is deflected sideways when a magnetic field is present. This is the thermal analogue of the electrical Hall effect, where a magnetic field deflects electric current. In the thermal case, the 'charge carriers' are heat carriers—electrons, phonons (quantized lattice vibrations), or magnons (quantized spin waves)—and their trajectories are bent by the magnetic field, creating a transverse temperature difference.
The thermal Hall effect was first predicted and observed in the 20th century, with early experiments on metals and semiconductors. It gained renewed attention in the 2000s with the discovery of the thermal Hall effect in insulating magnets, where it is carried by magnons or phonons.
In a material with a magnetic field applied perpendicular to the heat flow, the heat carriers experience a Lorentz-like force (or a similar deflection due to their magnetic moment). This causes them to accumulate on one side of the sample, creating a transverse temperature gradient. The magnitude and sign of the thermal Hall effect depend on the type of carrier, the band structure, and the magnetic ordering. In some materials, the effect is driven by the Berry curvature of the electronic bands, which acts as a fictitious magnetic field in momentum space.
It is used as a sensitive probe of magnetic ordering and phase transitions in materials, particularly in the study of exotic magnetic states like spin liquids and topological magnon insulators.
In some materials, the thermal Hall effect can be carried entirely by phonons, which are neutral particles, showing that the effect does not require charged carriers.
| η_H | variable | Hall viscosity — hall viscosity kilogram per metre second |
| A_abcd | variable | geometric tensor — geometric tensor |
| E^ab | variable | strain tensor — strain tensor |
| ∫ dA | operator | Integration over the two-dimensional area — area integral |
| ∂_t | operator | Partial derivative with respect to time — partial time derivative |



















