CM In the literature: contested

Why do phonons in many insulators show a thermal Hall effect?

In plain words

Sideways heat flow in a magnetic field appears in magnetic and non-magnetic insulators alike, with roughly similar size relative to the ordinary heat flow. No single coupling between phonons and the field explains all cases.

Precise statement

In insulators including SrTiO3, cuprate parent compounds, Kitaev candidates, garnets, quartz, MgO and intrinsic Si and Ge, fields of tens of kG produce a thermal Hall conductivity $\kappa_{xy}$ carried by phonons, with thermal Hall angle $\kappa_{xy}/\kappa_{xx}$ up to $\sim 3e-3\text{ at }9e4\,\mathrm{G}$, typically peaking near the maximum of $\kappa_{xx}$. Identify the coupling: intrinsic Berry curvature of phonon bands from spin-lattice or ionic Lorentz-type coupling, skew scattering off charged or magnetic defects, or resonant scattering by dynamical defects. An answer predicts magnitude, sign and temperature dependence across materials.

What would settle it

A theory predicting $\kappa_{xy}/\kappa_{xx}$ with sign in several unrelated insulators from measured parameters, confirmed by controlled defect doping.

Status in the literature

Unverified note

Phonon thermal Hall signals with a common scaling $\kappa_{xy} \sim \kappa_{xx}^2$ were reported in many nonmagnetic crystals (SrTiO3, quartz, MgO, MgAl2O4, Si, Ge; Jin et al., arXiv 2404.02863, 2024); no coupling mechanism accounts for magnitude and sign across materials.