  We develop a theory of designing slit experiments in two-dimensional electron
systems with the Rashba spin-orbit interaction. By simulating the
spatiotemporal dynamics of electrons passing through a single slit or a double
slit, 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 whose directions
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.
