  We investigate the Sakai-Sugimoto model at nonzero baryon chemical potential
in a background magnetic field both in the confined phase and in the deconfined
phase with restored chiral symmetry. In this case the 8-brane Chern-Simons term
becomes important. In the confined phase it generates a gradient of the
pseudo-scalar "pion", which carries a non-vanishing baryon charge. Above a
critical value of the chemical potential there is a second order phase
transition to a mixed phase which includes also ordinary baryonic matter.
However, at fixed baryon charge density the matter is purely "pion"-gradient
above a critical magnetic field. In the deconfined chiral-symmetric phase at
nonzero chemical potential the magnetic field induces an axial current. We also
compute the magnetization of the baryonic matter and find that it is
paramagnetic in all three phases but with nonlinear behavior at large magnetic
field.
