Role of interface transparency and spin-dependent scattering in diffusive ferromagnet/superconductor heterostructures

Abstract

We present a numerical study of the density of states in a ferromagnet/superconductor junction and the Josephson current in a superconductor/ferromagnet/superconductor junction in the diffusive limit by solving the Usadel equation with Nazarov's boundary conditions. Our calculations are valid for an arbitrary interface transparency and an arbitrary spin-dependent scattering rate, which allows us to explore the entire proximity-effect regime. We first investigate how the proximity-induced anomalous Green's function affects the density of states in the ferromagnet for three magnitudes of the exchange field $h$ compared to the superconducting gap $\ensuremath{\Delta}$: (i) $h\ensuremath{\lesssim}\ensuremath{\Delta}$, (ii) $h\ensuremath{\gtrsim}\ensuremath{\Delta}$, and (iii) $h⪢\ensuremath{\Delta}$. In each case, we consider the effect of the barrier transparency and allow for various concentrations of magnetic impurities. We clarify features that may be expected in the various parameter regimes accessible for the ferromagnetic film, with regard to thickness and exchange field. In particular, we address how the zero-energy peak and minigap observed in experiments may be understood in terms of the interplay between the singlet and the triplet anomalous Green's functions and their dependence on the concentration of magnetic impurities. Our results should serve as a useful tool for the quantitative analysis of experimental data. We also investigate the role of the barrier transparency and spin-flip scattering in a superconductor/ferromagnet/superconductor junction. We suggest that such diffusive Josephson junctions with large residual values of the supercurrent at the $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition, where the first harmonic term in the current vanishes, may be used as efficient supercurrent-switching devices. We numerically solve for the Josephson current in such a junction to clarify to what extent this idea may be realized in an experimental setup. It is also found that uniaxial spin-flip scattering has a very different effect on the $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition points depending on whether one considers the width or the temperature dependence of the current. Our theory takes into account vital elements that are necessary to obtain quantitative predictions of the supercurrent in such junctions.