Odd spin-triplet superconductivity in a multilayered superconductor-ferromagnet Josephson junction

TL;DR

This paper investigates the Josephson effect in multilayered superconductor-ferromagnet structures, revealing the coexistence of short-range singlet/triplet and long-range triplet superconducting components and their dependence on magnetic configurations.

Contribution

It provides a theoretical analysis of the Josephson critical current considering arbitrary layer thicknesses and magnetic orientations, highlighting the presence of odd spin-triplet superconductivity in multilayered structures.

Findings

Short-range components decay over length scale ξ_H.

Long-range triplet component persists over length scale ξ_N.

Results agree with experimental observations.

Abstract

We study the dc Josephson effect in a diffusive multilayered SF'FF'S structure, where S is a superconductor and F,F' are different ferromagnets. We assume that the exchange energies in the F' and F layers are different ($% h $ and $H$, respectively) and the middle F layer consists of two layers with parallel or antiparallel magnetization vectors $M$. The $M$ vectors in the left and right F' layers are generally not collinear to those in the F layer. In the limit of a weak proximity effect we use a linearized Usadel equation. Solving this equation, we calculate the Josephson critical current for arbitrary temperatures, arbitrary thicknesses of the F' and F layers ($% L_{h}$ and $L_{H}$) in the case of parallel and antiparallel $M$ orientations in the F layer. The part of the critical current $I_{cSR}$ formed by the short-range (SRC) singlet and S=0 triplet condensate components decays on a short length $\xi_{H}=\sqrt{D/H}$, whereas the part $% I_{cLR}$ due to the long-range triplet $|S|=1$ component (LRTC) decreases with increasing $L_{H}$ on the length $\xi_{N}=\sqrt{D/\pi T}$. Our results are in agreement with the experiment \cite{Birge}.