Josephson current in a superconductor -- ferromagnet -- superconductor junction with in-plane ferromagnetic domains

TL;DR

This paper investigates how in-plane ferromagnetic domains in a superconductor-ferromagnet-superconductor junction influence the Josephson effect, revealing domain size-dependent transitions and local current inhomogeneities.

Contribution

It introduces a detailed analysis of the impact of ferromagnetic domain size and domain walls on the Josephson current in SFS junctions near the critical temperature.

Findings

Large domains induce 0-$\pi$ transitions similar to single-domain junctions.

Small domains lead to a zero state due to effective magnetization averaging.

Domain walls cause local variations in current direction near the transition points.

Abstract

We study a diffusive superconductor--ferromagnet--superconductor (SFS) junction with in-plane ferromagnetic domains. Close to the superconducting transition temperature, we describe the proximity effect in the junction with the linearized Usadel equations. We find that properties of such a junction depend on the size of the domains relative to the magnetic coherence length. In the case of large domains, the junction exhibits transitions to the $\pi$ state, similarly to a single-domain SFS junction. In the case of small domains, the magnetization effectively averages out, and the junction is always in the zero state, similarly to a superconductor--normal metal--superconductor (SNS) junction. In both those regimes, the influence of domain walls may be approximately described as an effective spin-flip scattering. We also study the inhomogeneous distribution of the local current density in the junction. Close to the 0--$\pi$ transitions, the directions of the critical current may be opposite in the vicinity of the domain wall and in the middle of the domains.