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Generating superconducting vortices via spin-orbit coupling

Spin-orbit coupling (SOC) is known to play an important role in superconductor/ferromagnet heterostructures. Here we demonstrate that SOC results in the spontaneous generation of vortices in an \textit{s}-wave superconductor placed below a ferromagnetic metal with intrinsic or interfacial SOC. By using the generalized London and Ginzburg-Landau theories, we calculate the supercurrent amplitude in various types of S/F heterostructures at and below the superconducting critical temperature. In particular, we show that even in the limit of weak SOC, vortex-antivortex pairs are stabilized and that an attractive interaction between vortices and SOC act to pin vortices along the S/F interface. We discuss key experiments to investigate these phenomena, which would provide a platform to the creation of Abrikosov vortex memory.