Ferromagnetism in quark matter and origin of the magnetic field in compact stars

So far, many studies have been devoted to understand high-density and/or high-temperature QCD. In this talk we are concentrated on magnetic aspects of quark matter. We shall discuss the possibility of ferromagnetism and spin density wave in quark matter. These magnetic properties of quark matter should be closely related to phenomena observed in relativistic heavy-ion collisions or compact stars. Actually our study has been stimulated by the recent discovery of magnetars [ 1], which have huge magnetic field of 10G and come into a new class of compact stars. It has been first estimated by P − Ṗ curve for pulsars and more recently suggested by observation of the cyclotron absorption lines. The origin of the magnetic field in compact stars has been a long-standing problem since the first discovery of pulsars in early seventies. Instead of asking for the origin, many people have taken a simple working hypothesis, conservation of magnetic flux during the stellar evolution. However, if we apply this hypothesis to explain the magnetic field of magnetars, we immediately have a contradiction that their radius should be much less than the Scwartzschild radius. Thus, the discovery of magnetars seems to give a chance to reconsider the origin of the magnetic field in compact stars. Since there is widely developed hadronic matter inside compact stars, we consider the spin-polarization in hadronic matter as a microscopic origin of the magnetic field in compact stars.