Width of the $0-\pi$ phase transition in diffusive magnetic Josephson junctions

TL;DR

This study explores how insulating barriers and additional normal metal layers in diffusive magnetic Josephson junctions influence the width of the 0-$pi$ phase transition, revealing conditions that enhance transition detectability.

Contribution

It provides a detailed phase diagram for complex F$_{c}$ structures, showing how barriers and layers affect the 0-$pi$ transition width compared to simple SFS junctions.

Findings

Insulating barriers increase the transition width.

Additional N layers further enlarge the transition interval.

Symmetric F$_{c}$ structures maximize the transition width.

Abstract

We investigate the Josephson current between two superconductors (S) which are connected through a diffusive magnetic junction with a complex structure (F$_{c}$). Using the quantum circuit theory, we obtain the phase diagram of 0 and $\pi$ Josephson couplings for F$_{c}$ being a IFI (insulator-ferromagnet-insulator) double barrier junction or a IFNFI structure (where N indicates a normal metal layer). Compared to a simple SFS structure, we find that the width of the transition, defined by the interval of exchange fields in which a $0-\pi$ transition is possible, is increased by insulating barriers at the interfaces and also by the presence of the additional N layer. The widest transition is found for symmetric F$_{c}$ structures. The symmetric SIFNFIS presents the most favorable condition to detect the temperature induced $0-\pi$ transition with a relative width, which is five times larger than that of the corresponding simple SFS structure.