Long-range spin-triplet proximity effect in Josephson junctions with multilayered ferromagnets

TL;DR

This paper investigates the long-range spin-triplet proximity effect in Josephson junctions with multilayered ferromagnets, revealing how the triplet current depends on layer thickness and magnetization orientation, aligning with recent experimental findings.

Contribution

It provides a comprehensive numerical analysis of the triplet proximity effect in multilayered ferromagnetic Josephson junctions with arbitrary layer thicknesses and magnetization angles, extending understanding beyond previous studies.

Findings

Triplet Josephson current peaks at specific ferromagnetic layer thicknesses.

Triplet proximity effect is similar in AF and F structures under moderate disorder.

Results qualitatively agree with recent experimental observations.

Abstract

We study the proximity effect in SF'(AF)F'S and SF'(F)F'S planar junctions, where S is a clean conventional (s-wave) superconductor, while F' and middle layers are clean or moderately diffusive ferromagnets. Middle layers consist of two equal ferromagnets with antiparallel (AF) or parallel (F) magnetizations that are not collinear with magnetizations in the neighboring F' layers. We use fully self-consistent numerical solutions of the Eilenberger equations to calculate the superconducting pair amplitudes and the Josephson current for arbitrary thickness of ferromagnetic layers and the angle between in-plane magnetisations. For moderate disorder in ferromagnets the triplet proximity effect is practically the same for AF and F structures, like in the dirty limit. Triplet Josephson current is dominant for $d'\approx\hbar v_F/2h'$, where $d'$ is the F' layer thickness and $h'$ is the exchange energy. Our results are in a qualitative agreement with the recent experimental observations [T. S. Khaire, M. A. Khasawneh, W. P. Pratt, and N. O. Birge, Phys. Rev. Lett. \textbf{104}, 137002 (2010)].