Flux motion in thin superconductors with inhomogeneous pinning

The penetration and exit of magnetic flux in thin superconductors in a perpendicular applied field is investigated in detail. Flux-density pictures and profiles are obtained by magneto-optics; magnetization curves are measured by torque magnetometry; theoretical space- and time-dependent flux-density and current-density profiles are calculated from Maxwell's equations in a planar approximation assuming a highly nonlinear current-voltage law E∼(J/Jc)n (n1, E=electric field, J=sheet current) with a critical sheet current Jc(B,r) in general depending on the position and on the perpendicular flux density B. Our experiments and calculations show that for inhomogeneous pinning the additional nontrivial condition Jc= for B=0 is appropriate. Our specimens are high-Tc superconductors in the form of platelets, strips, or rings. In two platelets, an inhomogeneous Jc was produced by heavy-ion irradiation of the edge zone or by thinning down the central part by sputtering. In all cases good qualitative agreement is found between the experimental and theoretical results. In particular, our time-dependent theory reproduces the recently derived static Bean-model profiles in perpendicular geometry, which we also confirm experimentally; field and current profiles in the ring are as predicted for a current-carrying strip in perpendicular field; in the platelet with enhanced edge pinning, when flux starts to leak into the central weak pinning zone the flux lines are driven immediately to the sample center and pile up there; for weaker inhomogeneity of Jc(r), when the flux front arrives from the edges at the central weak-pinning zone the flux lines jump to an intermediate position from where they fill the central zone gradually. Our experiments also confirm the predicted "uphill motion" of flux lines against the flux-density gradient and the occurrence of overcritical current densities in the flux-free regions.