  We demonstrate the theoretical feasibility of spin-dependent diffraction and
spin-polarization of an electron in two counter-propagating, circularly
polarized laser beams. The spin-dynamics appears in a two-photon process of the
Kapitza-Dirac effect in the Bragg regime. We show the spin-dependence of the
diffraction process by comparison of the time-evolution of a spin-up and
spin-down electron in a relativistic quantum simulation. We further discuss the
spin properties of the scattering by studying an analytically approximated
solution of the time-evolution matrix. A classification scheme in terms of
unitary or non-unitary propagation matrices is used for establishing a
generalized and spin-independent description of the spin properties in the
diffraction process.
