  We investigate the possibility of the spin polarization of quark matter at
zero temperature and moderate baryon density.The Nambu-Jona-Lasinio (NJL) model
including interactions in vector and axial-vector channel (coupling constant
$G_2$) as well as scalar and pseudoscalar channel (coupling constant $G_1$) is
used, and the self consistent equations for the spin polarization and chiral
condensate are solved numerically in the framework of the Hartree
approximation. Numerical calculations show that in the one flavor model the
spin polarization is possible at finite density if the ratio $G_2/G_1$ is
larger than O(1).We find that the interplay between the spin polarization and
the chiral symmetry plays an important role.If the chemical potential of quarks
reaches a certain finite value, the spin polarization begins to occur because
the quark still has relatively large dynamical mass, which is generated by
spontaneous chiral symmetry breaking.On the other hand, when the spin
polarization occurs, it operates to lower the dynamical quark mass a little.If
one increases the chemical potential furthermore, the spin polarization becomes
weaker and finally disappears because the dynamical quark mass is reduced by
restoring gradually the chiral symmetry.
