Possibility of a long-range proximity effect in a ferromagnetic nanoparticle

We study the proximity effect in a ferromagnetic nanoparticle having a vortex magnetization pattern. We show that for the axisymmetric system consisting of a circular particle and a magnetic vortex situated at the center of it no long-range superconducting correlations are induced. It means that induced superconductivity is localized in the small area near the superconducting electrode. However, in the real system axial symmetry can be broken by either a shift of the magnetic vortex from the origin or a geometrical anisotropy of the ferromagnetic particle. In this case a long-range proximity effect is possible.