Ferromagnetic properties of quark matter -an origin of magnetic field in compact stars-

Magnetic properties of quark matter are studied within the Landau Fermi-liquid theory, and magnetic phase diagram of QCD is presented in the density-temperature plane. The screening effect for gluon propagator is emphasized to see the characteristic behavior of the magnetic susceptibility; novel non-Fermi-liquid behavior is observed at finite temperature. Some implications on the origin of the magnetic field in compact stars, especially magnetars, are briefly discussed.