Vortex Lattices in Stripe Domains of Ferromagnet/Superconductor Bilayer

The continuum theory of domain structures in ferromagnetic/superconducting bilayers fails when the equilibrium domain size becomes comparable with effective penetration depth $\Lambda$. Instead, a lattice of discrete vortices must be considered. Here, we report our results on the discrete vortex lattices in stripe domain structures of ferromagnetic/superconducting bilayers. The vortices are assumed to be situated periodically on chains in stripe domains. We study the configurations containing up to three chains per domain, and calculate their equilibrium energies, equilibrium domain size and vortex positions through a method based on London-Maxwell equations. In equilibrium, the vortices in the neighbor domains are half-way shifted while they are next to each other in the same domain. Additionally, more vortex chains per domain appear spontaneously depending on magnetization and domain wall energy.