  We elucidate the itinerant ferromagnetism of a dipolar Fermi gas with a
Raman-induced spin-orbit coupling by investigating the exotic phase diagrams at
zero and finite temperature. It is revealed that the dipolar interaction along
with spin-orbit coupling can corroborate the formation of ferromagnetism and
the Raman coupling adversely eliminates the tendency to this ferromagnetism
transition, which greatly transcends the general understanding of this subject
with contact interaction only. We explore the ground states through the density
and spin-flip distribution in momentum space, which exhibits novel degeneracy
at strong Raman coupling indicated by a non-zero entropy at zero temperature.
We calculate the transition temperatures well within the reach of an
experimental system when altering the dipolar and spin-orbit coupling strength,
which paves a way to the further experimental realization.
