Numerical modeling of the singlet proximity effect in a superconductor-ferromagnet trilayer

We investigate superconductor-insulator-ferromagnet-superconductor Josephson junctions using the quasiclassical Green's functional theory in the “dirty limit,” where the elastic scattering length ℓ is much shorter than the characteristic decay length in the ferromagnet. We manipulate the governing Usadel equations for entry into numerical analysis and develop a numerical model to explore the behavior of the superconducting Green's functions in the trilayer, avoiding the linearizing approximation usually found in the literature. We then review the results of the numerical calculation for the behavior of the Green's function under the variation of the ferromagnet thickness df, the ferromagnet's internal magnetization strength h, the strength of the proximity effect γ, and the interface transparency γBi. These results are compared to analytical, numerical, and experimental results in the existing literature. We close with suggestions for future research