  Spin-dependent Kapitza-Dirac scattering of electron beams from
counterpropagating bichromatic laser waves in various polarization geometries
is studied. The corresponding scattering probabilities are obtained by
analytical and numerical solutions of the time-dependent Dirac equation,
assuming a field frequency ratio of 2. When the fundamental field mode is
circular-polarized, we show that spin dynamics are generally suppressed at low
intensities, but can become distinct at high intensities. Conversely, when a
linearly or elliptically polarized fundamental mode is combined with a second
harmonic of circular polarization, strong spin effects arise already at low
field intensities. In particular, a polarization configuration is identified
which acts as a spin filter for free electrons.
