Use of a Sigmoid Function to Describe Second Peak in Magnetization Loops

Order-disorder transitions of a vortex lattice transfer type-II superconductors from a low critical current state to a high one. The similar transition between different current states can be caused by electromagnetic granularity. A sigmoid curve is proposed to describe the corresponding peak in a field dependence of the macroscopic critical density. Using the extended critical state model, analytic expressions are obtained for the field dependencies of the local critical current density, the depth of equilibrium surface region, and the macroscopic critical current density. The expressions are well fit to published data.