Evidence for a $\pi $-junction in Nb/F/Nb' trilayers from superfluid density measurements

Two-coil measurements of the sheet superfluid density of Nb/NiV/Nb' trilayers reveal the transition temperatures and volume superfluid densities of both Nb layers, as functions of the thickness, $d_{F}$, of the intervening ferromagnetic (F) Ni$_{\mathrm{0.96}}$V$_{\mathrm{0.04}}$ layer. The upper transition occurs when the thicker Nb layer goes superconducting and superfluid first appears. Fitting the high-temperature superfluid density to an appropriate functional form reveals the presence of a lower ``transition'' where additional superfluid appears. This event is really a crossover, but the difference is irrelevant here. There is a surprising minimum in superfluid densities of both Nb layers at $d_{F} \quad \approx $ 30 {\AA}, followed by a slow rise. This behavior suggests that a $\pi $ phase difference between the Nb layers develops at $d_{F} \quad \approx $ 30 {\AA} and continues to larger F thickness.