Ferromagnetism of axion domain wall

We show that axion domain wall is ferromagnetic in the universe with nonvanishing baryon number or lepton number. It is caused by protons and electrons bounded to the domain wall with their spins aligned. These bound states arise due to attractive potentials generated through pseudo-vector couplings between the fermions and the axion. Using a model of hadronic axions we predict existence of a primordial magnetic field with strength 10−13 Gauss at recombination.