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By using the Nambu-Jona-Lasinio model with a tensor-type four-pointinteraction between quarks, it is shown that there exists a possibility of aspin polarized phase in quark matter at finite temperature and density. Whenthere exists the spin polarization, the spontaneous magnetization may occur ifthe effect of the anomalous magnetic moment of quark is taken into account. Animplication to the compact star objects with strong magnetic field is discussedwhen the spin polarization occurs.

Quark spin polarization and spontaneous magnetization in high density quark matter