Orientational phase transitions of a lattice of magnetic dots embedded in a London-type superconductor

In recent experiments, structured arrays of ferromagnetic nanoparticles in the bulk of a superconductor have been fabricated. We present the theory of orientational phase transitions in a planar regular lattice of nanoscale ferromagnetic particles embedded in a superconductor. In the London approximation, we show that the interactions between ferromagnetic particles can lead to either a parallel or antiparallel spin alignment depending on the ratio of the interparticle distance, the London penetration depth and the temperature. The extension of the results to systems of ferromagnetic nanoparticles with more complicated geometries is discussed.