  We consider the interaction of a ferromagnetic spinor Bose-Einstein
condensate with a magnetic field gradient. The magnetic field gradient realizes
a spin-position coupling that explicitly breaks time-reversal symmetry T and
space parity P, but preserves the combined PT symmetry. We observe using
numerical simulations, a first-order phase transition spontaneously breaking
this re-maining symmetry. The transition to a low-gradient phase, in which
gradient effects are frozen out by the ferromagnetic interaction, suggests the
possibility of high-coherence magnetic sensors unaffected by gradient
dephasing.
