Phonons bend in a magnetic field

According to the electrical Hall effect, when a magnetic field is applied perpendicular to an electric current in a conductor, the Lorentz force deflects the electrons in a direction transverse to that current. In what’s known as the thermal Hall effect of phonons, the presence of the magnetic field has an analogous effect on a temperature gradient in an insulator: It induces a heat flow transverse to the gradient. The effect is puzzling. As neutral quasiparticles, phonons are the primary carriers of heat in an insulating solid, but they don’t carry the spin or charge usually needed to couple them to a magnetic field.

To address the puzzle, doctoral student Amirreza Ataei, his adviser Louis Taillefer (both at the University of Sherbrooke in Quebec, Canada), and their colleagues present evidence that phonons couple to magnetic fields by scattering with impurities or defects in the antiferromagnetic insulator Sr₂IrO₄. More specifically, they studied how the thermal Hall effect in the material is boosted—and then diminished—by introducing impurities.

The researchers substituted nonmagnetic rhodium impurities for the spin-carrying iridium atoms in the planes of the lattice, shown in the figure. A mere 2% replacement of Ir with Rh gives rise to a 30-fold enhancement of the thermal Hall conductivity—the value of the transverse heat flow—and 5% doping boosts it 70-fold. But further doping (up to 15%) suppresses the antiferromagnetic order and reduces the thermal Hall conductivity to a negligible value.

The experiments lay out a straightforward case: Without impurities in the insulator’s IrO₂ planes, the thermal Hall signal is almost negligible. And outside the antiferromagnetic phase at high doping, the signal is also vanishingly small. Impurities and magnetic order both appear to be essential ingredients to the thermal Hall effect from phonons. The connection is clarified by theories being developed independently by Harvard University’s Subir Sachdev and Stanford University’s Steven Kivelson and their colleagues. In both theories, the phonons undergo a special type of resonant scattering off impurities that deflects them in a preferred direction in the presence of a magnetic field.

Taillefer, Ataei, and their collaborators argue that phonons scattered by impurities in a magnetic environment may be relevant to several other materials, such as cuprate high-temperature superconductors, whose magnetic order and crystal structure are quite similar to those of Sr₂IrO₄. From work done so far, it appears that short-range magnetic correlations are also important for the cuprate’s thermal Hall effect, which was detected in 2019 in the material’s enigmatic pseudogap phase. (A. Ataei et al., Nat. Phys., 2024, doi:10.1038/s41567-024-02384-5 .)