Equilibrium topology of the intermediate state in type-I superconductors of different shapes

TL;DR

This study uses magneto-optical imaging to analyze flux patterns in various-shaped lead superconductors, revealing how geometry and pinning influence the equilibrium topology of the intermediate state.

Contribution

It demonstrates that flux tubes are the equilibrium structure in reversible samples, while laminar structures occur in samples with magnetic hysteresis, highlighting the role of geometry and pinning.

Findings

Flux tubes dominate in reversible samples without hysteresis.

Laminar structures appear in samples with magnetic hysteresis.

Geometric barriers cause hysteresis in flux penetration and exit.

Abstract

High-resolution magneto-optical technique was used to analyze flux patterns in the intermediate state of bulk Pb samples of various shapes - cones, hemispheres and discs. Combined with the measurements of macroscopic magnetization these results allowed studying the effect of bulk pinning and geometric barrier on the equilibrium structure of the intermediate state. Zero-bulk pinning discs and slabs show hysteretic behavior due to geometric barrier that results in a topological hysteresis -- flux tubes on penetration and lamellae on flux exit. (Hemi)spheres and cones do not have geometric barrier and show no hysteresis with flux tubes dominating the intermediate field region. It is concluded that flux tubes represent the equilibrium topology of the intermediate state in reversible samples, whereas laminar structure appears in samples with magnetic hysteresis (either bulk or geometric). Real-time video is available in http://www.cmpgroup.ameslab.gov/supermaglab/video/Pb.html NOTE: the submitted images were severely downsampled due to Arxiv's limitations of 1 Mb total size.