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We group materials into five symmetry classes and determine in which of theseclasses phonons carry angular momentum in the Brillouin zone, away from ahigh-symmetry point, line, or plane. In some materials phonons acquire angularmomentum via the forces induced by relative displacements of atoms out of theirequilibrium positions. However, for other materials, such as ferromagneticiron, phonon angular momentum arises from the forces induced by relativevelocities of atoms. These effects are driven by the spin-orbit interaction.

Classification of materials with phonon angular momentum and microscopic origin of angular momentum