Theory of generation and conversion of phonon angular momentum

Mechanical rotations in solids can be converted to magnetization and spin current via the spin-rotation coupling. Recently, in general solids, the phonon angular momentum has been formulated as the microscopic local rotation in the lattice. However, it usually cancels between phonon modes. In this talk, we propose the two ways of generation of phonon angular momentum in non-magnetic and magnetic insulators. In nonmagnetic insulators without inversion symmetry, a heat current induces the phonon angular momentum, in analogy with the Edelstein effect [1]. In magnetic insulators preserving the product of the inversion and time-reversal symmetries, the electric field can induce the phonon angular momentum, in analogy with the magnetoelectric effect. We also discuss microscopic mechanisms how the microscopic local rotations of atoms, i.e. the phonon angular momentum, is converted into electronic spins.
[1] Hamada et al., arXiv: 1810.05359, to appear in Phys. Rev. Lett.