  We have investigated the transport of spin polarization through a classically
chaotic semiconductor loop with a strong Rashba spin-orbit interaction. We
found that if the escape time of a particle is long enough, the configuration
averaged spin conductance oscillates strongly with the geometric spin phase. We
predict a sizable rotation of spin polarization along its flowing path across
the loop from the injector to the collector. We have also discovered a
quantized universal spin relaxation in a 2D reservoir connected to such a
semiconductor loop.
