Meissner Currents Induced by Topological Magnetic Textures in Hybrid Superconductor/Ferromagnet Structures

Topological spin configurations in proximity to a superconductor have recently attracted great interest due to the potential application of the former in spintronics and also as another platform for realizing non-trivial topological superconductors. Their application in these areas requires precise knowledge of the existing exchange fields and/or the stray-fields which are therefore essential for the study of these systems. Here, we determine the effective stray-field and the Meissner currents in a Superconductor/Ferromagnet/Superconductor (S/F/S) junction produced by various nonhomogenous magnetic textures in the F. The inhomogeneity arises either due to a periodic structure with flat domain walls (DW) or is caused by an isolated chiral magnetic skyrmion (Sk). We consider both Bloch- and N\'{e}el-type Sk and also analyze in detail the periodic structures of different types of DW's-- that is Bloch-type DW (BDW) and N\'{e}el-type DW (NDW) of finite width with in- and out-of-plane magnetization vector. The spatial dependence of the fields and Meissner currents are shown to be qualitatively different for the case of Bloch- and N\'{e}el-type magnetic textures. While the spatial distributions in the upper and lower S are identical for Bloch-type Sk and DW's they are asymmetric for the case of N\'{e}el-type magnetic textures. The depairing factor, which determines the critical temperature and which is related to vector potential of the stray-field, can have its maximum at the center of a magnetic domain but also, as we show, above the DW. For Sk's the maximum is located at a finite distance within the Sk radius. Based on this, we study the nucleation of superconductivity in the presence of DW's. Because of the asymmetry for N\'{e}el-type structures, the critical temperature in the upper and lower S is expected to be different. The obtained results can also be applied to S/F bilayers.