  Spin Hall effect is the transverse flow of the electron spin in conductors
under external electric field. Similarly, thermal gradient in magnetic
insulators can drive a transverse flow of the spin angular momentum of magnons,
which provides a thermal alternative for spin manipulation. Recently, the
phonon angular momentum (PAM), which is the angular momentum of atoms as a
result of their orbital motion around their equilibrium positions, has garnered
attention as a quantity analogous to the magnon spin. However, can we
manipulate PAM like magnon spin? Here, we show that temperature gradient
generally induces a transverse flow of PAM, which we term the phonon angular
momentum Hall effect (PAMHE). The PAMHE relies only on the presence of
transverse and longitudinal acoustic phonons, and it is therefore ubiquitous in
condensed matter systems. As a consequence of the PAMHE, PAM accumulates at the
edges of a crystal. When the atoms in the crystal carry nonzero Born effective
charge, the edge PAM induces edge magnetization, which may be observed through
optical measurement. We believe that PAMHE provides a new principle for the
manipulation of angular momenta in insulators and opens up an avenue for
developing functional materials based on phonon engineering.
