Dipolar Interactions in Superconductor-Ferromagnet Heterostructures

We consider a simple model for a superlattice composed of a thin magnetic film placed between two bulk superconductors. The magnetic film is modelled by a planar but otherwise arbitrary distribution of magnetic dipoles and the superconductors are treated in the London approximation. Due to the linearity of the problem, we are able to compute the magnetic energy of the film in the presence of the superconductors. We show that in the case of small wavenumbers compared to the inverse London penetration depth, the magnetic energy resembles the energy of a distribution of magnetisation in a two dimensional space. Possible experimental applications of these results are discussed.