Impeded Growth of Magnetic Flux Bubbles in the Intermediate State Pattern of Type I Superconductors

TL;DR

This study investigates the size and behavior of normal state magnetic flux bubbles in Type I superconductors, revealing that their size is governed by a balance of forces and remains fixed after formation, challenging mean-field predictions.

Contribution

The paper provides a quantitative analysis of flux bubble sizes using a current-loop model, demonstrating the influence of interface energy and magnetic interactions in Type I superconductors.

Findings

Bubble size is nearly independent of long-range interactions.

A master curve describes bubble size scaling.

Bubble sizes are fixed post-formation, opposing mean-field models.

Abstract

Normal state bubble patterns in Type I superconducting Indium and Lead slabs are studied by the high resolution magneto-optical imaging technique. The size of bubbles is found to be almost independent of the long-range interaction between the normal state domains. Under bubble diameter and slab thickness proper scaling, the results gather onto a single master curve. On this basis, in the framework of the "current-loop" model [R.E. Goldstein, D.P. Jackson and A.T. Dorsey, Phys. Rev. Lett. 76, 3818 (1996)], we calculate the equilibrium diameter of an isolated bubble resulting from the competition between the Biot-and-Savart interaction of the Meissner current encircling the bubble and the superconductor-normal interface energy. A good quantitative agreement with the master curve is found over two decades of the magnetic Bond number. The isolation of each bubble in the superconducting matrix and the existence of a positive interface energy are shown to preclude any continuous size variation of the bubbles after their formation, contrary to the prediction of mean-field models.