  We study a two-dimensional fermionic cloud of repulsive alkali-metal atoms
characterized by two hyperfine states which are Rabi coupled. Within a
variational Hartree-Fock scheme, we calculate analytically the ground-state
energy of the system. Then we determine the conditions under which there is a
quantum phase transition with spontaneous symmetry breaking from a
spin-balanced configuration to a spin-polarized one, an effect known as
itinerant ferromagnetism. Interestingly, we find that the transition appears
when the interaction energy per particle exceedes both the kinetic energy per
particle and the Rabi coupling energy. The itinerant ferromagnetism of the
polarized phase is analyzed, obtaining the population imbalance as a function
of interaction strength, Rabi coupling, and number density. Finally, the
inclusion of a external harmonic confinement is investigated by adopting the
local density approximation. We predict that a single atomic cloud can display
population imbalance near the center of the trap and a fully balanced
configuration at the periphery.
