Vortex pinning in a superconducting film due to in-plane magnetized ferromagnets of different shapes: The London approximation

The London approach is used to study the interaction between a superconducting vortex in a type-II superconducting film (SC) and a ferromagnet (FM) with in-plane magnetization. We calculated numerically the dependence of the pinning behavior on the FM-vortex distance, SC film thickness, and geometry of the magnetic structure and its magnetization. Dual behavior of the interaction energy in terms of the field-polarity-dependent pinning was found. For weak magnetization such that no vortex-antivortex pair is induced by the FM an external vortex will be pinned near the negative pole of the FM. In the presence of a vortex-antivortex pair the external vortex is pinned on the positive (negative) pole of the FM if the magnetization of the FM is below (above) some critical value. Further, we investigated the interaction of a vortex and an in-plane magnetic stripe (wall). Such SC-FM heterostructure is found to be useful in applications where vortex-free superconducting areas are needed. For a more complicated geometry of the FM, i.e., magnets with edge defects, we discuss the breaking of the vortex-FM interaction symmetry which results in different local minima for the energetically favorable vortex position.