Interaction between vortices in superconducting films and magnetic dipole arrays

Abstract

The interaction between vortices in planar superconducting films of thickness comparable with the penetration depth and magnetic dipole arrays placed outside the film, and the creation of vortices by the dipole array, are studied in the London limit. This paper starts from the results obtained recently by the author (cond-mat/0308574) for the interaction between an arbitrary distribution of vortex lines, curved and straight, inside the film and a point magnetic dipole placed outside the film, and for the creation of vortices by the dipole. Here these results ere generalized for dipole arrays. The total energy of the vortex–dipole array system is obtained as a functional of the vortex distribution. The vortex configuration generated by the dipole array minimizes the energy functional. Vortex configurations generated by periodic linear chains of dipoles, ordered ferro or anti-ferro magnetically, are studied by minimizing the vortex–dipole array energy functional numerically, using the method introduced in cond-mat/0308574, which is based on the discretization of London theory on a cubic mesh. It is found that the vortex configurations are periodic, with the same period as the vortex chains, consist in general of curved vortex lines, and that chains with anti-ferromagnetic order are more effective in creating vortices than chains with ferromagnetic order.