Scattering by magnetic and spin-orbit impurities and the Josephson current in superconductor-ferromagnet-superconductor junctions

TL;DR

This paper derives an analytical formula for the Josephson current in superconductor-ferromagnet-superconductor junctions considering magnetic, non-magnetic, and spin-orbit impurities, covering a broad impurity concentration range.

Contribution

It provides a new analytical expression for the Josephson critical current applicable across various impurity regimes, including intermediate concentrations.

Findings

Analytical expression valid for broad impurity range

Includes effects of magnetic and spin-orbit impurities

Bridges gap between clean and dirty limits

Abstract

We analyze the Josephson current in a junction consisting of two superconductors (S) and a ferromagnetic layer (F) for arbitrary impurity concentration. In addition to non-magnetic impurities, we consider also magnetic ones and spin-orbit scattering. In the limit of weak proximity effect we solve the linearized Eilenberger equation and derive an analytical expression for the Josephson critical current valid in a broad range of parameters. This expression enables us to obtain not only known results in the dirty and clean limits but also in a intermediate region of the impurity concentration, which may be very important for comparison with experimental data.