  We investigate the magnetic properties of spin-$1/2$ charged Fermi gases with
ferromagnetic coupling via mean-field theory, and find the interplay among the
paramagnetism, diamagnetism and ferromagnetism. Paramagnetism and diamagnetism
compete with each other. When increasing the ferromagnetic coupling the
spontaneous magnetization occurs in a weak magnetic field. The critical
ferromagnetic coupling constant of the paramagnetic phase to ferromagnetic
phase transition increases linearly with the temperature. Both the
paramagnetism and diamagnetism increase when the magnetic field increases. It
reveals the magnetization density $\bar M$ increases firstly as the temperature
increases, and then reaches a maximum. Finally the magnetization density $\bar
M$ decreases smoothly in the high temperature region. The domed shape of the
magnetization density $\bar M$ variation is different from the behavior of Bose
gas with ferromagnetic coupling. We also find the curve of susceptibility
follows the Curie-Weiss law, and for a given temperature the susceptibility is
directly proportional to the Land\'{e} factor.
