  In the presence of a chemical potential, the effect of a magnetic field on
chiral symmetry breaking goes beyond the well-known magnetic catalysis. Due to
a subtle interplay with the chemical potential, the magnetic field may work not
only in favor but also against the chirally broken phase. At sufficiently large
coupling, the magnetic field favors the broken phase only for field strengths
beyond any conceivable value in nature. Therefore, in the interior of
magnetars, a possible transition from chirally broken hadronic matter to
chirally symmetric quark matter might occur at smaller densities than
previously thought.
