  We investigate the possible existence of spin polarization and color
superconductivity in the Nambu--Jona-Lasinio model with a tensor-type
interaction at finite density and temperature. The thermodynamic potential is
calculated by the functional integral method. Numerical results indicate that
at low temperature and quark chemical potential the chiral condensed phase
exists, and at intermediate chemical potential the color superconducting phase
appears. In addition, depending on the magnitude of the tensor coupling, at
large chemical potential and low temperature, a color superconducting phase and
a spin polarized phase may coexist while at intermediate temperatures only the
spin polarized phase occurs.
