Vortex-antivortex molecules induced by a magnetic disk on top of a superconducting film--influence of the magnet geometry

Using the nonlinear Ginzburg-Landau (GL) theory, we investigate the equilibrium vortex configurations in a thin superconducting film (SC) with a magnetic disk (MD) on top of it, for two magnet geometries: (i) circular, and (ii) square MD. We study the critical parameters for the nucleation of vortex-antivortex pairs under the edge of the magnet due to its specific inhomogeneous magnetic field which makes the total flux penetrating the SC equal zero. For the case of a circular magnetic disk, a shell (anti)vortex structure is found, and the exact vortex configuration depends on the size and magnetization of the magnetic disk and the properties of the SC. For square MDs, the energetically favorable vortex-antivortex configurations are additionally influenced by the magnet geometry