  Motivated by the remarkable experimental control of synthetic gauge fields in
ultracold atomic systems, we investigate the effect of an artificial Rashba
spin-orbit coupling on the spin polarization of a two-dimensional repulsive
Fermi gas. By using a variational many-body wavefunction, based on a suitable
spinorial structure, we find that the polarization properties of the system are
indeed controlled by the interplay between spin-orbit coupling and repulsive
interaction. In particular, two main effects are found: 1) The Rashba coupling
determines a gradual increase of the degree of polarization beyond the critical
repulsive interaction strength, at variance with conventional 2D Stoner
instability. 2) The critical interaction strength, above which finite
polarization is developed, shows a dependence on the Rashba coupling, i.e. it
is enhanced in case the Rashba coupling exceeds a critical value. A simple
analytic expression for the critical interaction strength is further derived in
the context of our variational formulation, which allows for a straightforward
and insightful analysis of the present problem.
