Magneto-optical study of the intermediate state in type-I superconductors: Effects of sample shape and applied current

The magnetic flux structures in the intermediate state of bulk, pinning-free Type-I superconductors are studied using a high resolution magneto-optical imaging technique. Unlike most previous studies, this work focuses on the pattern formation of the coexisting normal and superconducting phases in the intermediate state. The influence of various parameters such as sample shape, structure defects (pinning) and applied current are discussed in relation to two distinct topologies: flux tubes (closed topology) and laminar (open topology). Imaging and magnetization measurements performed on samples of different shapes (cones, hemispheres and slabs), show that contrary to previous beliefs, the tubular structure is the equilibrium topology, but it is unstable toward defects and flux motion. Moreover, the application of current into a sample with the geometric barrier can replace an established laminar structure with flux tubes. At very high currents, however, there exists a laminar 'stripe pattern.' Quantitative analysis of the mean tube diameter is shown to be in good agreement with the prediction proposed by Goren and Tinkham. This is the first time that this model has been confirmed experimentally. Further research into the flux tube phase shows a direct correlation with the current loop model proposed in the 1990's by Goldstein, Jackson and Dorsey. There also appears a range of flux tube density that results in a suprafroth structure, a well-formed polygonal mesh, which behaves according to the physics of foams, following standard statistical laws such as von Neumann and Lewis. The reaction of flux structures to a fast-ramped magnetic field was also studied. This provided an alignment of the structure not normally observed at slow ramp rates.