Nucleation and arrangement of Abrikosov vortices in hybrid superconductor–ferromagnet nanostructures

Abstract

This study investigates the nucleation, dynamics, and stationary configurations of Abrikosov vortices in hybrid superconductor–ferromagnet nanostructures subjected to inhomogeneous magnetic fields generated by a ferromagnetic nanodot. Employing the simulations based on time-dependent Ginzburg–Landau coupled with Maxwell's equations, we reveal the evolution of curved vortex structures that exhibit creep-like deformation before stabilizing. The interplay between vortices and currents confined within the superconducting nanoelement gives rise to unconventional stationary vortex arrangements, which evolve gradually with increasing magnetic field strength—a behavior absent in homogeneous fields. Our numerical results illustrate how the ferromagnetic element can control vortex configurations via a stray magnetic field—insights that are difficult to access experimentally or analytically. We demonstrate that the superconducting nanoelement can stabilize into distinct vortex states in response to even small system perturbations. This highlights the extreme sensitivity of the system and the richness of its dynamic behaviour, revealing complex pinning mechanisms and providing valuable insights into the optimisation of nanoscale superconducting systems.