Angular Momentum of Phonons and Einstein-de Haas Effect

TL;DR

This paper investigates the angular momentum of phonons in magnetic crystals, revealing a nonzero phonon angular momentum influenced by spin-phonon interactions, which impacts the Einstein-de Haas effect and offers a new way to study spin-phonon coupling.

Contribution

It introduces the concept of phonon angular momentum in magnetic crystals and explores its temperature dependence and implications for the Einstein-de Haas effect.

Findings

Phonons can carry nonzero angular momentum due to spin-phonon interaction.

Phonon angular momentum decreases with temperature and vanishes in the classical limit.

The nonzero phonon angular momentum affects the angular momentum balance in magnetic systems.

Abstract

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