Phenomenological theory of superconductivity near domain walls in ferromagnets

We develop a phenomenological model of superconductivity near a domain wall in a ferromagnet. In addition to the electromagnetic interaction of the order parameter with the ferromagnetic magnetization, we take into account the possibility of a local enhancement or suppression of superconducting pairing in the vicinity of the wall, and also a non-perfect transparency of the wall to electrons. It is found that the critical temperature of superconductivity near the domain wall might be substantially higher than in the bulk.