Mechanical generation of spin current by spin-rotation coupling

Spin-rotation coupling, which is responsible for angular momentum conversion between the electron spin and rotational deformations of elastic media, is exploited for generating spin current. This method requires neither magnetic moments nor spin-orbit interaction. The spin current generated in nonmagnets is calculated in the presence of surface acoustic waves. We solve the spin diffusion equation, extended to include spin-rotation coupling, and find that larger spin currents can be obtained in materials with longer spin lifetimes. Spin accumulation induced on the surface is predicted to be detectable by time-resolved Kerr spectroscopy.

Figure 1

Snapshot of mechanical generation of spin current induced by SAW. (a) In the presence of a SAW propagating in the $x$ direction, a gradient of mechanical rotation around the $z$ axis is induced. The rotation couples to electron spins, and then the $z$-polarized spin current flows in the $y$ direction. (b) Spin accumulation induced on the surface. Because spins are polarized parallel to the rotation axis ($\pm z$), the striped pattern of spin accumulation arises at the surface.

Figure 2

(a) Spin current induced by SAW $J_s^z$ plotted as a function of $k_{t}y$ and $\omega t$ for fixed $x$ and $z$. The spin current oscillates with time. Maximum amplitude is located near the surface, $k_{t}y\approx 1$. (b) Maximum amplitude of the spin current scaled by ${\omega }^3$ plotted as a function of $\omega {\tau }_{\mathrm{sf}}$. When $\omega {\tau }_{\mathrm{sf}}\ll 1$, the scaled amplitude, $J_s^{\mathrm{Max}}{\omega }^{-3}$, increases linearly. On the other hand, it saturates when $\omega {\tau }_{\mathrm{sf}}\gg 1$. Accordingly, the maximum amplitude, $J_s^{\mathrm{Max}}$, is proportional to ${\omega }^4$ in the former case, whereas $J_s^{\mathrm{Max}}\propto {\omega }^3$ in the latter case.