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.