Magnetic flux density and the critical field in the intermediate state of type-I superconductors

Abstract

To address unsolved fundamental problems of the intermediate state (IS), the equilibrium magnetic flux structure and the critical field in a high-purity type-I superconductor (indium film) are investigated using magneto-optical imaging with a three-dimensional vector magnet and electrical transport measurements. The least expected observation is that the critical field in the IS can be as small as nearly 40% of the thermodynamic critical field ${H}_{c}$. This indicates that the flux density in the bulk of normal domains can be considerably less than ${H}_{c}$, in apparent contradiction with the long-established paradigm, stating that the normal phase is unstable in fields below ${H}_{c}$. Here we present a theoretical model consistently describing this and all other properties of the IS. Moreover, our model, based on a rigorous thermodynamic treatment of the observed equilibrium flux structure in a tilted field, allows for a quantitative determination of the domain-wall parameter and the coherence length, and provides new insight into the properties of superconductors.