  In current work, we investigate the density and temperature dependence of
polarization parameter; using the relativistic formalism for the
electron-electron interaction within the Fermi liquid model. we calculate the
spin dependent scattering matrix elements in relativistic region, and then
obtain the non-relativistic behavior to study the magnetic properties of an
electron gas. By varying the polarization parameter, we minimized the free
energy and then obtain the polarization of the system as a function of density
and temperature. At zero temperature the exact results for polarization and
magnetic susceptibility have obtained. It has been shown that for a given
temperature (density) there is critical density (temperature) that the
ferromagnetic phase can appears in electron gas. Our results show that at
nonzero temperatures and in very low and very high densities the ferromagnetism
phase can not be exist.
