Angular Momentum of Phonons and the Einstein–de Haas Effect

We study angular momentum of phonons in a magnetic crystal. In the presence\nof a spin-phonon interaction, we obtain a nonzero angular momentum of phonons,\nwhich is an odd function of magnetization. At zero temperature, phonon has a\nzero-point angular momentum besides a zero-point energy. With increasing\ntemperature, the total phonon angular momentum diminishes and approaches to\nzero in the classical limit. The nonzero phonon angular momentum can have a\nsignificant impact on the Einstein-de Haas effect. To obtain the change of\nangular momentum of electrons, the change of phonon angular momentum needs to\nbe subtracted from the opposite change of lattice angular momentum.\nFurthermore, the finding of phonon angular momentum gives a potential method to\nstudy the spin-phonon interaction. Possible experiments on phonon angular\nmomentum are also discussed.\n