Josephson current in diffusive multilayer superconductor/ferromagnet/superconductor junctions

TL;DR

This paper investigates the Josephson current in diffusive superconductor/ferromagnet/superconductor junctions with multilayer ferromagnetic regions, analyzing how magnetic misorientation and temperature influence 0-$ ext{pi}$ oscillations and critical current enhancement.

Contribution

It provides a detailed analysis of 0-$ ext{pi}$ oscillations in multilayer ferromagnetic junctions, including effects of non-ideal interfaces, spin-flip scattering, and magnetization misorientation.

Findings

Critical angle for $ ext{pi}$ state vanishing depends on temperature.

Significant critical current enhancement possible via magnetization switching.

Phase diagrams illustrate conditions for 0-$ ext{pi}$ oscillations.

Abstract

We calculate the Josephson current in a diffusive superconductor/ferromagnet/superconductor junction, where the ferromagnetic region contains multiple layers (or domains). In particular, we study a configuration where there are two layers with an arbitrary relative in-plane magnetization orientation, and also include non-ideal interfaces and arbitrary spin-flip scattering. We study the 0-$\pi$ oscillations of the critical current for varying junction width $d$, and find that the $\pi$ state vanishes entirely when the magnetic misorientation angle of the two layers exceeds a critical angle $\phi_c$. While $\phi_c \to \pi/2$ in the limit of high temperatures, we find that $\phi_c$ becomes smaller than $\pi/2$ at low temperatures compared to $T_c$. 0-$\pi$ oscillations are also found when varying the temperature or the misorientation angle for fixed values of $d$, and we present phase diagrams that show qualitatively the conditions for the appearance of such oscillations. We also point out how one may obtain significant enhancement of the critical current in such a system by switching the magnetization for selected values of the junction width $d$, and comment on the necessary conditions for establishing a long range triplet Josephson effect.