Thermodynamics of the Domain Structure and Determination of the Transition Fields in Type-1 Superconductors

A detailed electromagnetic and thermodynamical theory of the intermediate state in type-1 superconductors is worked out in the Landau laminar geometry. It is shown that the Landau s domain bounded by a convex wall where the magnetic field very nearly approaches the critical value is likely to be near the most stable configuration. The analysis of the field distribution in the n laminas provides a qualitative explanation of the experimentally observed small importance of the branching that Landau first suggested. Explicit analytical expressions of the various contributions to the free energy are derived as functions of the applied magnetic field and of the superconductive fraction. This allows the exact formulation of the equations yielding the transition fields at the ends of the intermediate range. At the lowest order, the departure of the field from the ideal value varies predominantly as (Δl)1/3 at the diamagnetic intermediate-phase transition and as (Δl)1/2 at the intermediate normal-phase transition, Δ being the surface energy and l the thickness of the sample.