Ferromagnetic condensation in high density hadronic matter

We investigate the occurrence of a ferromagnetic phase transition in high density hadronic matter (e.g., in the interior of a neutron star). This could be induced by a four fermion interaction analogous to the one which is responsible for chiral symmetry breaking in the Nambu-Jona-Lasinio model, to which it is related through a Fierz transformation. Flavor SU(2) and flavor SU(3) quark matter are considered. A second order phase transition is predicted at densities about 5 times the normal nuclear matter density, a magnetization of the order of $10^{16}$ gauss being expected. It is also found that in flavor SU(3) quark matter, a first order transition from the so-called 2 flavor super-conducting (2SC) phase to the ferromagnetic phase arises. The color-flavor-locked (CFL) phase may be completely hidden by the ferromagnetic phase.