  Microscopic origin of the magnetic field observed in compact stars is studied
in quark matter. Spontaneous spin polarization appears in high-density region
due to the Fock exchange term. On the other hand, quark matter becomes unstable
to form spin density wave in the moderate density region, where restoration of
chiral symmetry plays an important role. Coexistence of the magnetism and color
superconductivity is briefly discussed.
