Angular momentum of phonons and the Einstein-de Haas effect
By Lifa Zhang, Q. Niu. 2013
262 citations recorded by the source corpus.
We study angular momentum of phonons in a magnetic crystal. In the presence of a spinphonon 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. The Einstein-de Haas effect [1, 2], a phenomenon of mechanical rotation induced by a magnetization change, was originally designed to prove the existence of Ampere’s molecular currents; but subsequent experiments [3] showed that the magnetic moment of an atom is dominated by spin while contribution from orbital motion to the magnetic moment is almost absent. The Einstein-de Haas experiment together with the Barnett experiment [4, 5] (a change of magnetization resulting from a mechanical rotation) has provided an effective method of measuring the gyromagnetic ratio for various materials [6–8]. The accuracy of gyromagnetic ratio is crucial to determining of orbital and spin contribution in total magnetization [9–15]. Due to conservation of total angular momentum of the whole system in the Einstein-de Haas effect, the change of angular momentum of electrons (including both spin and orbital parts) has taken to be equal in magnitude but opposite in sign to the change of lattice angular momentum, which corresponds to mechanical rotation. However, the mechanical rotation only reflects angular momentum of the rigid-body lattice where atoms are assumed in the corresponding equilibrium positions; while phonons, which come from atomic vibrations around equilibrium positions, are assumed to have no macroscopic angular momentum. Recently, a remarkable phenomenon of phonon Hall effect was observed in a paramagnetic insulator [16, 17], which is indeed a surprise since phonons as neutral quasi-particles cannot directly couple to magnetic field via Lorentz force. The following theoretical studies [18, 19] showed that through Raman spin-phonon interaction the magnetic field can have an effective force to distort phonon transport, and thus drive a circulating heat flow [20]. Therefore a natural question arises: can such circulating phonons have nontrivial angular momentum and emergent macroscopic effects? In this Letter, we study angular momentum of phonons in a magnetic crystal in a microscopic picture. It is found that the Raman spin-phonon interaction induces a nonzero phonon angular momentum, which is an odd function of magnetization. In addition to a zero-point energy, phonon has a zero-point angular momentum at zero temperature. Such zero-point phonon angular momentum is offset by that of excited phonon modes such that the total angular momentum of phonons vanishes in the classical limit. Phonon angular momentum can not be ignored in total angular momentum especially in magnetic materials with large magnetization and spin-phonon interaction. Revisiting the Einstein-de Haas effect we find that phonon angular momentum needs to be subtracted in calculating angular momentum of electrons. With this correction, spin and orbital angular momentum can be precisely determined. Besides the Einstein-de Haas effect, nontrivial phonon angular momentum can be applied to the study of spin-phonon interaction, thermal Hall effect, and other topics related to phonons. Angular momentum of phonons – The lattice angular momentum related to mechanical rotation only reflects the rigid-body motion of the lattice. However, angular momentum of phonons has never been considered. In a microscopic picture, we can define angular momentum of phonons as
Subfields: Atomic and Molecular Physics, and Optics
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Orbital magnetic moments of phonons (2018, background): “where Q is the normal mode coordinate (or amplitude) vector in units of Å √ amu with amu being the atomic mass unit, and γ is the gyromagnetic ratio of the phonon [9, 12, 14].”
- Dynamical Multiferroicity (2016, background): “These include the phonon angular momentum arising from spinphonon interaction [71], the splitting of acoustic phonons due to the spin-orbit interaction [72], the splitting of nondegenerate Raman-active phonon modes accompanying a ferroelectric to paraelectric phase transition [73] and the magnetic-f”