  An exciton-polariton microcavity that incorporates magnetic ions can exhibit
a spontaneous self-trapping phenomenon which is an analog of the classical
polaron effect. We investigate in detail the full model of a polariton
condensate that includes pumping and losses, the spin degree of freedom,
external magnetic field and energy relaxation. In the quasi-one-dimensional
case, we show that the polaron effect can give rise to a spontaneous lattice of
perfectly arranged polarization domains in an antiferromagnetic configuration.
We find that partial polarization of the condensate at moderate magnetic field
strengths facilitates the formation of such "polaron lattices", which are
qualitatively different from self-trapped polarons that appear in a fully
polarized condensate. Within the Bogoliubov-de Gennes approximation, we
calculate the instability condition which marks the appearance of the patterns.
Surprisingly, we find that the stability condition displays a discontinuity at
the point of partial-full polarization threshold.
