Phonon Angular Momentum Induced by the Temperature Gradient

Abstract

Phonon modes in crystals can have angular momenta in general. It nevertheless cancels in equilibrium when the time-reversal symmetry is preserved. In this paper we show that when a temperature gradient is applied and heat current flows in the crystal, the phonon distribution becomes off-equilibrium, and a finite angular momentum is generated by the heat current. This mechanism is analogous to the Edelstein effect in electronic systems. This effect requires crystals with sufficiently low crystallographic symmetries, such as polar or chiral crystal structures. Because of the positive charges of the nuclei, this phonon angular momentum induces magnetization. In addition, when the crystal can freely rotate, this generated phonon angular momentum is converted to a rigidbody rotation of the crystal, due to the conservation of the total angular momentum. Furthermore, in metallic crystals, the phonon angular momentum will be partially converted into spin angular momentum of electrons.PACS numbers: 63.20.-e, 81.05.Cy, 81.05. Ea, Conversions between the magnetization and the mechanical generation can be realized in various ways, such as Einstein-de Haas effect [1] and Barnett effect [2]. In the Einstein-de Haas effect, when the sample is magnetized by the external magnetic field, the sample rotates due to the conservation of the angular momentum. On the other hand, in the Barnett effect, a rotation of the sample induces magnetization. The key mechanism of these effects is the spin-rotation coupling, which relates electronic spins with a mechanical rotation [3]. In addition, spin-rotation coupling also enables mechanical generation of spin current in various systems [4][5][6]. In these effects, rotational motions of phonons in solids are important, and in this context an phonon angular momentum is formulated theoretically [7-9].Here we focus on the phonon angular momentum introduced in [7], which represents rotational motions of the nuclei within each phonon mode. In crystals with timereversal symmetry, i.e. those without magnetic field or magnetization, the phonon angular momentum of each mode is an odd function of the wavevector k and the total angular momentum vanishes in equilibrium due to cancellation between phonons with the wavevector k and those with −k. Meanwhile, one can expect that this cancellation goes away by driving the system off the equilibrium, and nonzero phonon angular momentum is induced. In this letter, to theoretically show this scenario, we consider a crystal with a finite heat current, and show a nonzero total phonon angular momentum in the crystal due to its nonequilibrium phonon distribution. The crystal symmetry should be sufficiently low to allow this effect, and in particular the inversion symmetry should be absent. We calculate the phonon angular momentum generated by heat current for the wurtzite GaN as an example of polar systems and the Te (tellurium) and Se (selenium) as examples of chiral systems. For wurtzite GaN, we calculate the phonon properties by using the valence force field model ...

Angular momentum conservation and phonon spin in magnetic insulators

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Magnetization control by angular momentum transfer from surface acoustic wave to ferromagnetic spin moments

“…The phonon angular momentum is activated by the breaking of time-reversal or spatial-inversion symmetry 6,[10][11][12][13][14] . In timereversal symmetry-broken ferromagnets, the polarization of a transverse acoustic wave (low-energy phonon mode) is observed to rotate while propagating along the magnetization direction 15 , which indicates an eigenstate with circular polarization.…”

Phonon rotoelectric effect

“…However, in general, the spin-phonon interaction is weak, and thus the phonon angular momentum by this effect may be small. Similar to our previous work [24], when the sample is suspended by a string so that it can freely rotate, the angular momentum is transferred into phonons, electrons, and the rigid-body rotation of the crystal due to the conservation of the angular momentum. Only in ionic crystals where the nuclei have nonzero effective charge, the phonon angular momentum by this effect also leads to magnetization.…”