We develop a theory of designing slit experiments in two-dimensional electron systems with the Rashba spin-orbit interaction. By investigating the spatiotemporal dynamics of electrons passing through a single slit or a double slit both analytically and numerically, we find that the interference fringes of the electron probability density attain specific spin orientations via the precession of spins around effective magnetic fields mediated by the Rashba spin-orbit interaction the directions of which are determined by the propagation path. The spin orientations of the fringes can be controlled by tuning the Rashba spin-orbit parameter, which can be achieved by applying an electric gate voltage. This phenomenon can be exploited to implement electrically tunable transmission of spin information and to generate spin-polarized currents.
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