Swapping Spin Currents: Interchanging Spin and Flow Directions

We introduce a previously unknown spin-related transport phenomenon, consisting of a transformation (swapping) of spin currents, in which the spin direction and the direction of flow are interchanged. Swapping is due to the spin-orbit interaction in scattering. It originates from the correlation between the spin rotation and the scattering angle. This effect is more robust than the skew scattering, since it exists already in the first Born approximation. Swapping may lead to the spin accumulation with spin polarization perpendicular to the surface, unlike what happens in the spin Hall effect.

Figure 1

Schematics of electron scattering by a negative charge. The electron spin sees a magnetic field $\mathit{B}\sim \mathit{v}\times \mathit{E}$ perpendicular to the trajectory plane. Note that the magnetic field (and hence the sense of the spin rotation) has opposite directions for electrons scattered to the left and to the right.

Figure 2

Schematics of a proposed experiment revealing the swapping of spin currents. (a) The $q_{yy}^{(0)}$ spin current is electrically injected in a semiconductor ($S$) through a ferromagnetic contact ($F$) with a magnetization along the $y$ axis. The wavy arrow symbolizes optical detection of the $z$ component of spin polarization near the surface. (b) The swapping effect transforms the primary spin current $q_{yy}^{(0)}$ into $q_{xx}$ and $q_{zz}$. This should lead to the appearance of excess spin polarization at the lateral boundaries of the sample ($P_z<0$ at the top face and $P_z>0$ on the bottom one). This polarization may be detected optically.