Theory of spin hydrodynamic generation

Spin-current generation by fluid motion is theoretically investigated. Based on quantum kinetic theory, the spin-diffusion equation coupled with fluid vorticity is derived. We show that spin currents are generated by the vorticity gradient in both laminar and turbulent flows and that the generated spin currents can be detected by the inverse spin Hall voltage measurements, which are predicted to be proportional to the flow velocity in a laminar flow. In contrast, the voltage in a turbulent flow is proportional to the square of the flow velocity. This study will pave the way to fluid spintronics.

Figure 1

Contribution to the self-energy $\mathrm{\Sigma }$ originating from the spin-vorticity coupling.

Figure 2

Representation of the spin current in the two-dimensional Poiseuille flow. The parallel flow between the two parallel planes, $y=\pm y_0$, creates the velocity field $\mathbf{v}=(v_0(1-y^2/y_0^2),0,0)$. The vorticity of the flow emerges in the $z$-direction: $\nabla \times \mathbf{v}=(0,0,2v_{0}y/y_0^2)$. Then, the gradient of the vorticity generates the $z$-polarized spin-current in the $y$ direction.

Figure 3

Representation of the spin current for the Hagen-Poiseuille flow. A steady viscous flow in a pipe of circular cross-section with radius $r_0$ creates the velocity field, $(v_x,v_r,v_{\theta })=(v_0(1-r^2/r_0^2),0,0)$, in the cylindrical coordinate $(x,r,\theta )$. In this case, the vorticity gradient generates the $\theta$-polarized spin current in the radial direction. The inset shows the cross section of the pipe.