This examine 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. Using the simulations based mostly on time-dependent Ginzburg–Landau coupled with Maxwell’s equations, we reveal the evolution of curved vortex buildings that exhibit creep-like deformation earlier than stabilizing. The interaction between vortices and currents confined inside the superconducting nanoelement offers rise to unconventional stationary vortex preparations, which evolve steadily with rising magnetic discipline energy—a conduct absent in homogeneous fields. Our numerical outcomes illustrate how the ferromagnetic ingredient can management vortex configurations through a stray magnetic discipline—insights which can be tough to entry experimentally or analytically. We show that the superconducting nanoelement can stabilize into distinct vortex states in response to even small system perturbations. This highlights the intense sensitivity of the system and the richness of its dynamic behaviour, revealing advanced pinning mechanisms and offering helpful insights into the optimisation of nanoscale superconducting programs.
