  The linear birefringence of uniaxial crystal plates is known since the 17th
century, and it is widely used in numerous optical setups and devices. Here we
demonstrate, both theoretically and experimentally, a fine lateral circular
birefringence of such crystal plates. This effect is a novel example of the
spin-Hall effect of light, i.e., a transverse spin-dependent shift of the
paraxial light beam transmitted through the plate. The well-known linear
birefringence and the new circular birefringence form an interesting analogy
with the Goos-H\"anchen and Imbert-Fedorov beam shifts that appear in the light
reflection at a dielectric interface. We report the experimental observation of
the effect in a remarkably simple system of a tilted half-wave plate and
polarizers using polarimetric and quantum-weak-measurement techniques for the
beam-shift measurements. In view of great recent interest in spin-orbit
interaction phenomena, our results could find applications in modern
polarization optics and nano-photonics.
