Interference phenomena in Josephson junctions with ferromagnetic bilayers: Spin-triplet correlations and resonances

TL;DR

This paper investigates the Josephson effect in ferromagnetic bilayer junctions, revealing how spin-triplet correlations influence the current-phase relation, with resonances and oscillations depending on magnetic configurations and interface properties.

Contribution

It provides a detailed numerical analysis of spin-triplet correlations and resonance phenomena in $SF_1F_2S$ junctions, highlighting the dominance of long-range triplet components in certain conditions.

Findings

Second harmonic dominated by long-range spin-triplet correlations in noncollinear magnetizations.

Resonances occur at equal ferromagnetic layer thicknesses due to geometric effects.

Oscillations of harmonic amplitudes with ferromagnetic layer thicknesses due to $0- ext{pi}$ transitions.

Abstract

We study the Josephson effect in planar $SF_1F_2S$ junctions that consist of conventional $s$-wave superconductors ($S$) connected by two metallic monodomain ferromagnets ($F_1$ and $F_2$) with arbitrary transparency of interfaces. We solve the scattering problem in the clean limit based on the Bogoliubov-de Gennes equation for both spin-singlet and odd in frequency spin-triplet pairing correlations. We calculate numerically the Josephson current-phase relation $I(\phi)$. While the first harmonic of $I(\phi)$ is completely generated by spin-singlet and short-range spin-triplet superconducting correlations, for noncollinear magnetizations of ferromagnetic layers the second harmonic has an additional long-range spin-triplet component. Therefore, for strong ferromagnetic influence, the long-range spin-triplet contribution to the second harmonic dominates. We find an exception due to the geometric resonance for equal ferromagnetic layers when the first harmonic is strongly enhanced. Both first and second harmonic amplitudes oscillate with ferromagnetic layer thicknesses due to $0-\pi$ transitions. We study the influence of interface transparencies and find additional resonances for finite transparency of interface between ferromagnetic layers.