We study the superconducting response induced by a Néel domain wall in a thin superconducting film proximity-coupled to a ferromagnetic layer in the presence of interfacial Rashba spin-orbit coupling. The combined action of the magnetic texture and broken inversion symmetry generates a magnetoelectric coupling that induces spontaneous equilibrium currents. To establish the basic response to a continuously rotating magnetic texture, we first consider a periodic harmonic cycloid as an analytically tractable reference problem. Near $T_c$, this reference problem illustrates how the magnetoelectric coupling modifies the superconducting order parameter, while below $T_c$ it provides a simple setting for describing the phase response, Pearl screening, and the interaction with a vortex. We then turn to the main problem of this work, a single Néel domain wall, and derive analytical expressions for its equilibrium phase profile, spontaneous current, magnetic field, and vortex-wall interaction energy. We show that the Néel wall acts as an extended magnetoelectric source and produces a vorticity-selective pinning landscape controlled by the competition between the wall width and the effective screening length. We further demonstrate that sufficiently strong magnetoelectric coupling can render a bound vortex-antivortex pair energetically favorable relative to the vortex-free state, even in the absence of an applied magnetic field. Our results provide an analytical framework for understanding magnetoelectric vortex pinning and vortex-antivortex nucleation by Néel domain walls in spin-orbit coupled superconducting films.

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• Domain walls
• Flux pinning
• Magnetoelectric effect
• Rashba coupling
• Vortices in superconductors
• Heterostructures
• Landau-Ginzburg theory
• London theory