Possibility of ferromagnetic neutron matter

We study ferromagnetism at high density of neutrons in the QCD hadron phase, by using the simplest chiral effective model incorporating magnetic fields and the chiral anomaly. Under the assumption of spatial homogeneity, we calculate the energy density as a function of neutron density, with a magnetization and a neutral pion condensation a la Dautry and Neyman. We find that at a high density the energy of the ferromagnetic order is lower than that of the ordinary neutron matter, and the reduction effect is enhanced by the anomaly. Compared to the inhomogeneous phase with the alternating layer structure, our ferromagnetic phase turns out to be unfavored. However, once an axial vector meson condensation is taken into account in our simplest model, the ferromagnetic energy density is lowered significantly, which still leaves some room for a possible realization of a QCD ferromagnetic phase and ferromagnetic magnetars.