Vortex-antivortex nucleation in superconducting films with arrays of in-plane dipoles

Using the phenomenological Ginzburg-Landau (GL) theory, we investigate the superconducting (SC) state of a thin SC film under a square array of rectangular ferromagnets (FM) with in-plane magnetization. The equilibrium vortex states consist of vortex-antivortex (VAV) pairs formed under the poles of each magnet due to their specific inhomogeneous magnetic field which makes the total flux penetrating the SC equal zero. Even for a weakly magnetized FM, the nucleation of VAV structures can be stimulated by applying electric current perpendicular to the FM-moment. When the sample is exposed to an additional homogeneous magnetic field H, the presence of VAV pairs results in an even j c(H) characteristic, with maximal critical current achieved at H ±H max ≠ 0, where H max can be temperature dependent