Crossover from intravalley to intervalley vortex motion in type-II superconductors with a periodic pinning array

Abstract

We have determined the transition from intravalley vortex motion (Campbell regime) to intervalley motion (critical state regime) in Pb thin films with and without a square array of holes (antidots) by means of ac susceptibility $\ensuremath{\chi}(T,H)$ measurements. The Campbell regime is characterized by a maximum dissipation ${\ensuremath{\chi}}_{\mathrm{max}}^{\ensuremath{''}}$ dependent on the ac excitation $h$ but nearly temperature independent. In contrast, in the critical state regime, the height of the dissipation peak remains constant, whereas its position shifts to lower temperatures with increasing $h$. We introduce an alternative way for determining the temperature dependence of the ac onset of the Bean critical state by analyzing the critical current density $J(T)$ extracted from the ${\ensuremath{\chi}}^{\ensuremath{'}}(T)$ data at several $h$. We demonstrate that the presence of a periodic pinning array strongly affects the extension of the crossover area in the $h\ensuremath{-}T$ diagram between these regimes. We show that this effect can be ascribed to the lower dispersion of the pinning energy together with the higher topological order for the antidot sample.