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 3D vect
or 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 textit{bulk} of normal domains can be textit{considerably} less than $H_c$, in apparent contradiction with the long established paradigm, stating that the normal phase is unstable below $H_c$. Here we present a novel theoretical model consistently describing this and textit{all} other properties of the IS. Moreover, our model, based the rigorous thermodynamic treatment of observed laminar flux structure in a tilted field, allows for a textit{quantitative} determination of the domain-wall parameter and the coherence length, and provides new insight into the properties of all superconductors.
Polarized neutron reflectometry (PNR) provides evidence that nonlocal electrodynamics governs the magnetic field penetration in an extreme low-k superconductor. The sample is an indium film with a large elastic mean free path (11 mkm) deposited on a
silicon oxide wafer. It is shown that PNR can resolve the difference between the reflected neutron spin asymmetries predicted by the local and nonlocal theories of superconductivity. The experimental data support the nonlocal theory, which predicts a nonmonotonic decay of the magnetic field.
