In the classic description of the thin-film spin-paramagnetic transition one assumes that the film thickness is much less than the coherence length of the superconductor. In this limit the parallel critical field is entirely mediated by the Zeeman coupling. If, however, the thin-film condition is marginally relaxed so as to introduce a characteristic orbital energy that is of the same order as the Zeeman energy, then the phase diagram of the system is fundamentally changed. As was pointed out by Peter Fulde and coworkers more that 30 years ago ,it becomes possible for the parallel field behavior to become reentrant.

In the plot on the left note that the parallel critical field of this 6 nm thick Al film has a local maximum. This plot is effectively a phase diagram and should be compared to that of a thinner film in which there is a negligible orbital response, see Spin-Paramagnetic page. Note that in the field range of 3.32 to 3.35 T the superconducting transition is reentrant!

On the left we show a quasi-reversible reentrant superconducting transition obtained by taking a cut though the above phase diagram as dipicted by the dashed arrow.

As we will discuss on the next page, the reentrance and the anomalous critical field behavior are associated with a hyper-entropic phase in which the entropy of the superconductor is higher than that on the paramagnetic normal state.