Spontaneous spin polarization is studied in quark matter. Fock exchange interaction of OGE gives rise to it at high densities within the zero-range approximation. We figure out the interesting features of the ferromagnetic phase. Effects of quark mass dependence,charge neutrality, chemical equilibrium or finite rangeness are then addressed in a self-consistent way. By extending the analysis to the finite temperature case, we can estimate the Curie temperature below which quark matter is in the ferromagnetic phase and write a magnetic phase diagram in the density-temperature plane. Coexistence with color superconductivity is also discussed. Using these results we present a scenario that quark matter may give a strong magnetic field observed in compact stars and discuss some implications on recent magnetars. [1] T. Tatsumi et al.,Prog. Theor. Phys. Suppl. 153(2004); hep-ph/0312351;0502201. [2] E. Nakano et al., Phys. Rev. D68(2003)105001. [3] T. Tatsumi, Phys. lett. B489(2000)280.