  The response to a magnetic flux is considered of the vacuum state of charged
Dirac fermions interacting with a domain wall made of a neutral spinless field
in (3+1) dimensions with the fermion mass having a phase variation across the
wall. It is pointed out that due to simple C parity arguments the spontaneous
magnetization for this system is necessarily zero, thus invalidating some
claims to the contrary in the literature. The cancellation of the spontaneous
magnetization is explicitly demonstrated in a particular class of models. The
same calculation produces a general formula for the electric charge density
induced by the magnetic flux -- an effect previously discussed in the
literature for axionic domain walls. The distribution of the induced charge is
calculated in specific models.
