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Ferromagnetic neutron stars: axial anomaly, dense neutron matter, and pionic wall

We show that a chiral nonlinear sigma model coupled to degenerate neutrons exhibits a ferromagnetic phase at high density. The magnetization is due to the axial anomaly acting on the parallel layers of neutral pion domain walls spontaneously formed at high density. The emergent magnetic field would reach the QCD scale ~ 10^19 [G], which suggests that the quantum anomaly can be a microscopic origin of the magnetars (highly magnetized neutron stars).