Odd triplet superconductivity in clean and moderately disordered SFFS junctions

TL;DR

This paper investigates the Josephson effect and pairing correlations in SFFS junctions with ferromagnetic layers, revealing how magnetization orientation and disorder influence the decay and behavior of singlet and triplet superconducting correlations.

Contribution

It provides a detailed analysis of how magnetization misorientation and moderate disorder affect triplet and singlet pairing amplitudes and Josephson current in SFFS junctions, extending understanding beyond the dirty limit.

Findings

Both singlet and triplet pair amplitudes decay oscillatory with distance in the ferromagnets.

Triplet amplitude $f_{t1}$ penetrates into superconductors and decays over the coherence length.

Magnetization misorientation influences Josephson current independently of triplet correlations.

Abstract

We study the Josephson effect and pairing correlations in SFFS junctions that consist of conventional superconductors (S) connected through two metallic monodomain ferromagnets (F) with transparent and spin inactive interfaces. We solve the Eilenberger equations for arbitrary relative orientation of magnetizations of the two F layers in the clean limit and for moderate disorder in ferromagnets. Spatial variation of pair amplitudes, singlet $f_s$, and odd in frequency triplet $f_{t0}$ and $f_{t1}$, with 0 and $\pm1$ spin projections, as well as the Josephson current-phase relations are calculated for different values of the ferromagnetic layers thickness and angle $\alpha$ between in-plane magnetizations. In contrast to the dirty limit case, we find that for $0<\alpha<\pi$ both spin singlet and triplet pair amplitudes in F layers power-law decay in the same oscillatory manner with distance from the FS interfaces. This decay gets faster as the impurity-scattering rate in ferromagnets is increased. The computed triplet amplitude $f_{t1}$ has opposite signs in the two magnet regions, penetrates into the superconductors and monotonically decays over the same distance, which is the superconducting coherence length, as the singlet amplitude $f_s$ saturates to the bulk value. We point out that influence of misorientation of magnetizations on the Josephson current can not be attributed directly to the appearance of odd triplet correlations.