  Magnetic properties of quark matter are discussed. The possibility of
ferromagnetic transition is studied by using the one-gluon-exchange
interaction. Magnetic susceptibility is evaluated within Landau Fermi liquid
theory, and the important roles of the screening for the gluon propagation are
elucidated. Static screening for the longitudinal gluons improves the infrared
singularities, while the transverse gluons receive only dynamic screening. The
latter property gives rise to a novel non-Fermi-liquid behaviour in the
magnetic susceptibility. The critical density is estimated to be around the
nuclear density and the Curie temperature several tens MeV. The spin density
wave is also discussed at moderate densities, where chiral transition becomes
important. Pseudoscalar condensate as well as scalar one takes a spatially
non-uniform form in a chirally invariant way. Accordingly magnetization
oscillates like spin density wave. These results should have some implications
on compact star phenomena.
