Complex conductivity of proximity-superconducting Nb/Cu bilayers

The effective complex conductivity σᵉᶠᶠ=σ₁ᵉᶠᶠ-iσ₂ᵉᶠᶠ of proximity-coupled Nb/Cu bilayer films at 11.7 GHz is examined. The peak in the real part σ₁(T) just below Tc in bare Nb films gives way to a broader, shallower peak in σ₁ᵉᶠᶠ(T) as the Cu layer thickness increases, consistent with the existence of coherence effects in proximity-superconducting Cu. The imaginary part σ₂ᵉᶠᶠ(T) changes curvature from concave down to concave up as the Cu thickness dN increases. We extract proximity-induced penetration depth in Cu in the range 320 {} {≤}λN(0,0){≤}580 {}, with λN(0,0) increasing slightly with increasing dN, and an order-parameter decay length in Cu of K^-1(4.6 K)=225 {}±{}60 {}. The temperature dependence of K^-1(T) is consistent with K^-1(T){~}T^-2. Our results suggest that the single-frequency approximation of Werthamer and de Gennes does not adequately describe the behavior of very thin proximity-coupled Cu layers, in which the exact near-interface profile of the induced order parameter in Cu plays an important role. {} 1996 The American Physical Society.