Using the nonlinear Ginzburg-Landau theory we study vortex configurations in a superconducting thin film with a square array of pillars in the presence of a uniform applied magnetic field. The presence of the pillars changes the vortex structures in the superconducting film considerably: a transition between triangular and square vortex lattices takes place with increasing size and/or height of the pillars and vortex lines and vortex clusters can be obtained for particular applied magnetic fields. All of these findings are summarized into an equilibrium vortex phase diagram, which shows the transition between different ground-state vortex configurations as a function of the radius and periodicity of pillars. For larger radius of the pillars vortices start to penetrate the pillars and order in vortex shell structures both inside and around the pillars. The theoretical results are complemented by an experimental study of the vortex configurations in single-crystal based Nb pillars with radius $R\sim 0.5–2\mu \mathrm{m}$. Using Bitter decoration, concentric shells of vortices are revealed inside the pillars and shell-like structures are found at the interstitial sites, in accordance with the theoretical results. In addition, the observed distortion of the vortex shell structures by weak pinning centers present in our Nb samples is investigated by molecular dynamics simulations. We also show that the transition between predicted vortex states can be obtained from the temperature dependence of local magnetization measurements.

• Received 18 July 2007

DOI:https://doi.org/10.1103/PhysRevB.77.024526