Two-dimensional electron scattering in regions of nonuniform spin-orbit coupling

We present a theoretical study of elastic spin-dependent electron scattering caused by a nonuniform Rashba spin-orbit coupling strength. Using the spin-generalized method of partial waves the complete scattering wave function is derived exactly for the case of a circular scattering region. The asymptotic properties of the wave function and its behavior close to the scattering center are investigated. In both of these regimes we show that an unpolarized incoming beam becomes almost fully polarized around the direction of forward scattering. This feature could be utilized in spintronic devices.

Figure 1

(Color online) The plane wave of an incident electron with wave vector $\mathbf{k}$ gets scattered by a scattering region defined by a nonuniform Rashba coupling strength $\alpha \left(\mathbf{r}\right)$ (see the text), and a portion propagates along the direction given by the scattering angle $\phi$.

Figure 2

The magnitude of polarization $\mid {\mathbf{P}}^{\mathrm{sc}}\mid$ (main panel) and the differential scattering cross section $d\sigma ∕d\phi$ (left inset) as functions of the scattering angle $\phi$ (in units of degrees) for unpolarized $({\mathbf{P}}^{\mathrm{inc}}=\mathbf{0})$ incident waves. The large scale $\phi$ (in units of degrees) dependence of $\mid {\mathbf{P}}^{\mathrm{sc}}\mid$ is shown in the right inset. The parameters are $ka=20$ and $k_{\mathrm{so}}a=4$.

Figure 3

The spatial dependence of (a) the magnitude of polarization and (b) the ratio of the charge densities of the complete wave function and the incoming plane wave. The parameters are $ka=7$ and $k_{\mathrm{so}}a=1$. The white circle is the region with finite SOI. The coordinates are measured in units of $a$. The incoming beam is unpolarized and propagates along the $x$ axis.