  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.
