  We report on the experimental observation of the non-linear analogue of the
optical spin Hall effect under highly non-resonant circularly polarized
excitation of an exciton polariton condensate in a GaAs/AlGaAs microcavity.
Initially circularly polarized polariton condensates propagate over macroscopic
distances while the collective condensate spins coherently precess around an
effective magnetic field in the sample plane performing up to four complete
revolutions.
