Phonon Angular Momentum Hall Effect

The spin Hall effect is the transverse flow of the electron spin in response to an external electric field. Similarly, the temperature gradient in magnets can drive a transverse flow of the magnon spin, which provides a thermal alternative for spin manipulation. Recently, phonon angular momentum (PAM), the angular momentum of atoms resulting from their orbital motion around their equilibrium positions, has garnered attention as a quantity analogous to the magnon spin. Here, we report that the temperature gradient generally induces a transverse flow of PAM, which we term the phonon angular momentum Hall effect (PAMHE). The PAMHE arises whenever there are transverse and longitudinal acoustic phonons, and it is therefore ubiquitous in condensed matter systems. As a consequence of the PAMHE, PAM accumulates at the crystal edges. When the atoms in the crystal carry a non-zero Born effective charge, the edge PAM induces edge magnetization, which can be observed through optical measurement.