  In this letter we consider quantum phases and the phase diagram of a Fermi
Hubbard model under periodic driving that has been realized in recent cold atom
experiments, in particular, when the driving frequency is resonant with the
interaction energy. Due to the resonant driving, the effective Hamiltonian
contains a correlated hopping term where the density occupation strongly
modifies the hopping strength. Focusing on half filling, in addition to the
charge and spin density wave phases, large regions of ferromagnetic phase and
phase separation are discovered in the weakly interacting regime. The mechanism
of this ferromagnetism is attributed to the correlated hopping because the
hopping strength within a ferromagnetic domain is normalized to a larger value
than the hopping strength across the domain. Thus, the kinetic energy favors a
large ferromagnetic domain and consequently drives the system into a
ferromagnetic phase. We note that this is a different mechanism in contrast to
the well-known Stoner mechanism for ferromagnetism where the ferromagnetism is
driven by interaction energy.
