Insolid-state physics, thethermal Hall effect, also known as theRighi–Leduc effect, named after independent co-discoverersAugusto Righi andSylvestre Anatole Leduc,^[1] is the thermal analog of theHall effect. Given a thermal gradient across a solid, this effect describes the appearance of an orthogonal temperature gradient when a magnetic field is applied.

Forconductors, 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. TheMaggi–Righi–Leduc effect, named afterGian Antonio Maggi [it], describes changes inthermal conductivity when placing a conductor in amagnetic field.^[2]

A thermal Hall effect has also been measured in a paramagnetic insulators, called the "phonon Hall effect".^[3] In this case, there are no charged currents in the solid, so the magnetic field cannot exert aLorentz force. Phonon thermal Hall effects have been measured in various classes of non-magnetic insulating solids,^[4][5][6][7] but the exact mechanism giving rise to this phenomenon is largely unknown. An analogous thermal Hall effect for neutral particles exists in polyatomic gases, known as theSenftleben–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 studyingsuperconductors.^[8]

Given a conductor or semiconductor with a temperature difference in thex-direction and a magnetic fieldB perpendicular to it in thez-direction, then a temperature difference can occur in the transversey-direction,

${\displaystyle \frac{\mathrm{\partial }T}{\mathrm{\partial }y}=R_{\mathrm{T}\mathrm{H}}B\frac{\mathrm{\partial }T}{\mathrm{\partial }x}}$

The Righi–Leduc effect is a thermal analogue of the Hall effect. With the Hall effect, an externally applied electrical voltage causes an electrical current to flow. The mobile charge carriers (usually electrons) are transversely deflected by the magnetic field due to theLorentz force. In the Righi–Leduc effect, the temperature difference causes the mobile charge carriers to flow from the warmer end to the cooler end. Here, too, the Lorentz force causes a transverse deflection. Since the electrons transport heat, one side is heated more than the other.

The thermal Hall coefficient${\displaystyle R_{\mathrm{T}\mathrm{H}}}$ (sometimes also called the Righi–Leduc coefficient) depends on the material and has units oftesla⁻¹. It is related to the Hall coefficient${\displaystyle R_{\mathrm{H}}}$ by the electrical conductivity${\displaystyle \sigma }$, as

${\displaystyle R_{\mathrm{T}\mathrm{H}}=\sigma R_{\mathrm{H}}}$.

• Hall effect

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