Flux-line lattice and surface barrier in a Nb/Al multilayer

The interaction of the flux line and the surface in a Nb/Al multilayer was studied with DC magnetization measurements for a magnetic field applied nearly parallel to the film surface and with a Gibbs free-energy calculation. Peaks were observed in the M-H curves above the lower critical field, and a free-energy minimization calculation showed that the peak positions matched well with flux-line transitions of 1 row to 2 rows and 2 rows to 3 rows. When the field is applied at a small angle to the surface, an extra peak at small field, that was missed for a parallel field, was observed. With the free-energy calculation, we found that the extra peak corresponded to the lower critical field for flux-lines running parallel to the surface (Hc1). We point out that the flux lines in a thin-film superconductor follow the field applied with a sightly titled angle to the surface for Hc1 < HsinΘ and HcosΘ < Hc1, and rotate to be parallel to the surface at HcosΘ = Hc1