Vortex-antivortex states in nanostructured superconductor-ferromagnet hybrids

The formation of vortex-antivortex states in a superconducting film with a square array of magnetic dipoles magnetized perpendicularly to the film is investigated in the framework of the time-dependent Ginzburg-Landau equations. It is shown that a possible route to obtain equilibrium states is obtained following an experimentally realizable field-cooling procedure. The states thus obtained demonstrate a rich variety of phases, depending on magnetic moment intensity and dipole array-to-superconducting film distance. For instance, in the region of the phase diagram where each dipoles is able to generate N = 2 vortex-antivortex pairs, the antivortices induced by the negative stray fields of the dipoles undergo two transitions before ultimately merging into doubly-quantized giant antivortices. For N = 4, a state consisting on a three-quanta giant vortex below each dipole and an interstitial vortex-antivortex molecule was observed. Such state is thermodynamically stable and is induced by the fourfold symmetry of the dipole array, similar to symmetry-induced vortex-antivortex molecules found in mesoscopic superconductors.