  How ferromagnetic phases emerge in itinerant systems is an outstanding
problem in quantum magnetism. Here we consider a repulsive two-component Fermi
gas confined in a two dimensional isotropic harmonic potential and subject to a
large Rashba spin-orbit (SO) coupling, whose single-particle dispersion can be
tailored by adjusting the SO coupling strength. We show that the interplay
among SO coupling, correlation effects and mean-field repulsion leads to a
competition between ferromagnetic and non-magnetic phases. At intermediate
interaction strengths, ferromagnetic phase emerges which can be well described
by the mean-field Hartree-Fock theory; whereas at strong interaction strengths,
a strongly correlated non-magnetic phase is favored due to the
beyond-mean-field quantum correlation effects. Furthermore, the ferromagnetic
phase of this system possesses a chiral current density induced by the Rashba
spin-orbit coupling, whose experimental signature is investigated.
