Quantitative analysis of proximity effect in $Nb/Co_{60}Fe_{40}$, Nb/Ni, and $Nb/Cu_{40}Ni_{60}$ bilayers

TL;DR

This study investigates how the superconducting critical temperature varies with ferromagnetic layer thickness in Nb-based bilayers, revealing non-monotonic behavior and comparing experimental results with theoretical predictions using Usadel formalism.

Contribution

It provides a detailed quantitative analysis of Tc behavior in Nb/ferromagnet bilayers, highlighting agreements and discrepancies with Usadel theory and discussing the effects of thin ferromagnetic layers.

Findings

Tc exhibits non-monotonic dependence on ferromagnetic layer thickness.

Nb/CoFe bilayers match theoretical predictions across all thicknesses.

Ni and CuNi layers show higher Tc than theory predicts at small thicknesses.

Abstract

We have studied the behavior of the superconducting critical temperature Tc in $Nb/Co_{60}Fe_{40}$, Nb/Ni, and $Nb/Cu_{40}Ni_{60}$ bilayers as a function of the thickness of each ferromagnetic metal layer. The Tc s of three sets of bilayers exhibit non-monotonic behavior as a function of each ferromagnetic metal thickness. Employing the quantitative analysis based on Usadel formalism of the effect of the exchange energy, we observed that the Tc behavior of $Nb/Co_{60}Fe_{40}$ bilayers is in good agreement with the theoretical values over the entire range of the data. On the other hand, the Tc s of Nb/Ni and $Nb/Cu_{40}Ni_{60}$ bilayers show a higher value in the small thickness regime than the theoretical prediction obtained from the calculation, which matches the dip position and the saturation value of Tc in the large thickness limit. This discrepancy is probably due to the weakened magnetic properties of Ni and $Cu_{40}Ni_{60}$ when they are thin. We discuss the values of our fitting parameters and its implication on the validity of the current Usadel formalism of the effect of the exchange energy.