  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.
