Equilibrium Properties of the Mixed State in Superconducting Niobium in a Transverse Magnetic Field: Experiment and Theoretical Model

Equilibrium magnetic properties of the mixed state in type II superconductors were studied on high-purity film and single-crystal niobium samples with different Ginzburg-Landau parameters in perpendicular and parallel magnetic fields using dc magnetometry and scanning Hall-probe microscopy. The magnetization curve for samples with unity demagnetizing factor (slabs in perpendicular field) was obtained for the first time. It was found that none of the existing theories is consistent with these new data. To address this problem, a theoretical model is developed and comprehensively validated. The new model describes the mixed state in an averaged limit, i.e., without detailing the samples’ magnetic structure and therefore ignoring the surface current and interactions between the structural units (vortices). At low values of the Ginzburg-Landau parameter, it converts to the model of Peierls and London for the intermediate state in type I superconductors. The model quantitatively describes the magnetization curve for the perpendicular field and provides new insights into the properties of the mixed state, including properties of individual vortices. In particular, it suggests that description of the vortex matter in superconductors of the transverse geometry as a “gas-like” system of non-interacting vortices is more appropriate than the frequently used solid-like scenarios.