  We investigate the polarization of a two-component three-dimensional
fermionic gas made of repulsive alkali-metal atoms. The two pseudo-spin
components correspond to two hyperfine states which are Rabi coupled. The
presence of Rabi coupling implies that only the total number of atoms is
conserved and a quantum phase transition between states dominated by
spin-polarization along different axses is possible. By using a variational
Hartree-Fock scheme we calculate analytically the ground-state energy of the
system and determine analytically and numerically the conditions under which
there is this quantum phase transition. This scheme includes the well-known
criterion for the Stoner instability. The obtained phase diagram clearly shows
that the polarized phase crucially depends on the interplay among the Rabi
coupling energy, the interaction energy per particle, and the kinetic energy
per particle.
