Josephson current in a superconductor-ferromagnet junction with two non-collinear magnetic domains

TL;DR

This paper analytically investigates how non-collinear magnetic domains in a superconductor-ferromagnet-superconductor junction influence the Josephson current, revealing phase transitions and conditions for 0 and π states.

Contribution

It provides an analytical model for the Josephson effect in SFS junctions with non-collinear magnetic domains, highlighting the impact on phase transitions and critical current behavior.

Findings

Presence of magnetic domains reduces the range of lengths for π phase.

π phase disappears when misorientation angle exceeds π/2.

Domain misorientation influences 0--π transition conditions.

Abstract

We study the Josephson effect in a superconductor--ferromagnet--superconductor (SFS) junction with ferromagnetic domains of non-collinear magnetization. As a model for our study we consider a diffusive junction with two ferromagnetic domains along the junction. The superconductor is assumed to be close to the critical temperature $T_c$, and the linearized Usadel equations predict a sinusoidal current-phase relation. We find analytically the critical current as a function of domain lengths and of the angle between the orientations of their magnetizations. As a function of those parameters, the junction may undergo transitions between 0 and $\pi$ phases. We find that the presence of domains reduces the range of junction lengths at which the $\pi$ phase is observed. For the junction with two domains of the same length, the $\pi$ phase totally disappears as soon as the misorientation angle exceeds $\pi/2$. We further comment on possible implication of our results for experimentally observable 0--$\pi$ transitions in SFS junctions.