Vortices are pointlike topological defects in superconductors whose motion dictates superconducting properties and controls device performance. In superconductor-ferromagnet heterostructures, vortices interact with topological defects in the ferromagnet such as linelike domain walls. While in previous heterostructure generations, vortex-domain wall interactions were mediated by stray fields; in new heterostructure families, more important become exchange fields and spin-orbit coupling. However, spin-orbit coupling's role in vortex-domain wall interactions remains unexplored. Here we uncover, via numerical simulations and Ginzburg-Landau theory, that Rashba spin-orbit coupling induces magnetoelectric interactions between vortices and domain walls that crucially depend on the wall's winding direction—its helicity. The wall's helicity controls whether vortices are pushed or dragged by Néel walls, and their gliding direction along Bloch walls. Our work capitalizes on interactions between topological defects from different order parameters and of different dimensionality to engineer enhanced functionality.

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• Domain walls
• Magnetoelectric effect
• Rashba coupling
• Topological defects
• Vortices in superconductors
• Functional materials
• Heterostructures
• Bogoliubov-de Gennes equations
• Landau-Ginzburg theory