  The phase diagram of finite isospin, zero temperature QCD with the pions
coupled to photons in a uniform external magnetic field is explored in the low
field, small isospin density regime for which chiral perturbation theory is a
valid description. For realistic pion masses, the system behaves as a type-II
superconductor: a uniform superconducting state is formed at low-enough
magnetic fields, a vortex state for intermediate magnetic fields and finally a
normal state for large magnetic fields. In each these phases (including the
vortex phase), the $\pi^{0}$ remains uncondensed just as in the zero-external
field problem. The critical magnetic field where the phase transition from the
uniform superconducting state to a vortex state occurs was found numerically.
