Spin–vorticity coupling in viscous electron fluids

Abstract

We consider spin-vorticity coupling-the generation of spin polarization by vorticity-in viscous two-dimensional electron systems with spin-orbit coupling. We first derive hydrodynamic equations for spin and momentum densities in which their mutual coupling is determined by the rotational viscosity. We then calculate the rotational viscosity microscopically in the limits of weak and strong spin-orbit coupling. We provide estimates that show that the spin-orbit coupling achieved in recent experiments is strong enough for the spin-vorticity coupling to be observed. On the one hand, this coupling provides a way to image viscous electron flows by imaging spin densities. On the other hand, we show that the spin polarization generated by spin-vorticity coupling in the hydrodynamic regime can, in principle, be much larger than that generated, e.g. by the spin Hall effect, in the diffusive regime.

Origin of the magnetic spin Hall effect: Spin current vorticity in the Fermi sea

“…Similarly, the vorticity of a fluid couples to spin. Such effects are studied, for example, in nuclear physics [97] or in the context of spin hydrodynamic generation [98][99][100][101]. Concerning the latter, spin currents brought about by the vorticity of a confined fluid generate nonequilibrium spin voltages.…”

Hydrodynamic modes of homogeneous and isotropic fluids

“…[19] for a recent example, quantum critical transport in strange metals, see e.g. [20], and viscous electron fluids [21].…”

Nonlocal Spin Transport as a Probe of Viscous Magnon Fluids

“…Very recently, it has been shown that electrons in almost defectfree solid-state conductors can reach the hydrodynamic regime where the electrons collide more frequently among each other than with phonons or impurities [8][9][10][11]. In this regime, the electron viscosity becomes important and has been shown to lead, for example, to super-ballistic charge transport through point contacts [12,13], to the possibility of measuring the Hall viscosity [14,15], and, in the case of finite spin-orbit coupling, to large current-induced spin densities [16].The realization of viscous electron systems begs the question of whether there may be other solid-state platforms for fluid dynamics. Based on the work of Hohenberg and Halperin [17], Reiter and Schwabl answered this question affirmatively by theoretically proposing magnons, the quanta of spin waves in ferromagnets, as the entities for making up this fluid [18][19][20].…”

“…Very recently, it has been shown that electrons in almost defectfree solid-state conductors can reach the hydrodynamic regime where the electrons collide more frequently among each other than with phonons or impurities [8][9][10][11]. In this regime, the electron viscosity becomes important and has been shown to lead, for example, to super-ballistic charge transport through point contacts [12,13], to the possibility of measuring the Hall viscosity [14,15], and, in the case of finite spin-orbit coupling, to large current-induced spin densities [16].…”