Josephson effect in S$_{\rm F}$XS$_{\rm F}$ junctions

TL;DR

This paper explores the Josephson effect in ferromagnetic-superconductor junctions, revealing how exchange fields influence supercurrent and drawing analogies with voltage effects in tunnel junctions, including AC phenomena.

Contribution

It introduces the impact of exchange fields on supercurrent enhancement and establishes a correspondence between exchange field differences and voltage in tunnel junctions, including AC effects.

Findings

Critical current increases with antiparallel exchange fields under certain conditions.

Exchange field difference relates to voltage difference in analogous SIS junctions.

Identifies a singularity in critical current at specific exchange field differences.

Abstract

We investigate the Josephson effect in S$_{\rm F}$XS$_{\rm F}$ junctions, where S$_{\rm F}$ is a superconducting material with a ferromagnetic exchange field, and X a weak link. The critical current $I_c$ increases with the (antiparallel) exchange fields if the distribution of transmission eigenvalues of the X-layer has its maximum weight at small values. This exchange field enhancement of the supercurrent does not exist if X is a diffusive normal metal. At low temperatures, there is a correspondence between the critical current in an S$_{\rm F}$IS$_{\rm F}$ junction with collinear orientations of the two exchange fields, and the AC supercurrent amplitude in an SIS tunnel junction. The difference of the exchange fields $h_1-h_2$ in an S$_{\rm F}$IS$_{\rm F}$ junction corresponds to the potential difference $V_1-V_2$ in an SIS junction; i.e., the singularity in $I_c$ [in an S$_{\rm F}$IS$_{\rm F}$ junction] at $|h_1-h_2|=\Delta_1+\Delta_2$ is the analogue of the Riedel peak. We also discuss the AC Josephson effect in S$_{\rm F}$IS$_{\rm F}$ junctions.