  In this paper, we consider finite isospin chiral perturbation theory
including the effects of the axial anomaly (through the Wess-Zumino-Witten
term) in a strong magnetic field. We firstly prove that in a strong external
magnetic field ($H_{\rm ext}$) or more precisely the Schwinger limit, where
photon back-reactions are suppressed, only neutral pions can condense and the
condensation of charged pions is forbidden. Secondly, we find that the
$\pi^{0}$ domain wall is an example of a phase that can exist in a strong
magnetic field and suggest the existence of a new phase transition line from
the normal vacuum state to the $\pi^{0}$ domain wall state. This phase
transition exists for non-zero pion masses if the baryon chemical potential
exceeds a critical value $16\pi f_{\pi}^{2}m_{\pi}/eH_{\rm ext}$. The phase
transition line persists away from the Schwinger limit when the photons can
back-react to the external magnetic field.
