  In this paper, we investigate in some detail the holographic ferromagnetic
phase transition in an AdS${_4}$ black brane background by introducing a
massive 2-form field coupled to the Maxwell field strength in the bulk. In the
two probe limits, one is to neglect the back reaction of the 2-form field to
the background geometry and to the Maxwell field, and the other to neglect the
back reaction of both the Maxwell field and the 2-form field, we find that the
spontaneous magnetization and the ferromagnetic phase transition always happen
when the temperature gets low enough with similar critical behavior. We
calculate the DC resistivity in a semi-analytical method in the second probe
limit and find it behaves as the colossal magnetic resistance effect in some
materials. In the case with the first probe limit, we obtain the off-shell free
energy of the holographic model near the critical temperature and compare with
the Ising-like model. We also study the back reaction effect and find that the
phase transition is always second order. In addition, we find an analytical
Reissner-Norstr\"om-like black brane solution in the Einstein-Maxwell-2-form
field theory with a negative cosmological constant.
