  We show a possibility that there exists a color ferromagnetic state in quark
matter, in which a color magnetic field is spontaneously generated. The state
arises between the hadronic state and the color superconducting state when the
density of quarks is varied.Although the state (Savvidy state) has been known
to involve unstablemodes of gluons, we show that the modes compose a quantum
Hall state to stabilize the ferromagnetic state. Such a quantum Hall statecan
arise only when quarks matter is present. We also show that the order of the
phase transition between the state andthe quark gluon plasma is of the first
order.
