Phase-field simulation of superconductor vortex clustering in the vicinity of ferromagnetic domain bifurcations

Superconductors and ferromagnets are highly non-compatible materials due to the natures of their respective electronic states. But when artificially brought together, they develop interesting characteristics, one of which, vortex clustering, is discussed here in this paper. Phase-field and micromagnetic simulations are performed to investigate the superconductor and ferromagnet bilayer, respectively. The ferromagnet with uniaxial anisotropy is observed to develop the maze domain, whereas the superconductor subjected to the influence of the ferromagnetic stray field displays a vortex pattern. Clustered vortices in superconductors at certain locations are observed to be precisely located over magnetic domain bifurcations. The enhanced out-of-plane stray field at bifurcations around the curved domain walls and the convergent Lorentz force due to screening currents in superconductor are attributed to the formation of clusters at bifurcation sites. Segregation of the inter-vortex spacing between straight and bifurcated domain is clearly observed. More importantly, inter-vortex spacing is predicted to serve as a precise tool to map local ferromagnet domain shapes.