  Spin transitions are studied theoretically and experimentally in a resonantly
excited system of cavity polaritons in a magnetic field. Weak pair interactions
in this boson system make possible fast and massive spin flips occurring at
critical amplitudes due to the interplay between amplitude dependent shifts of
eigenstates and the Zeeman splitting. Dominant spin of a condensate can be
toggled forth and back by tuning of the pump intensity only, which opens the
way for ultra-fast spin switchings of polariton condensates on a picosecond
timescale.
