Spin-triplet Supercurrent through Inhomogeneous Ferromagnetic Trilayers

TL;DR

This paper investigates the generation of long-range spin-triplet supercurrents in inhomogeneous ferromagnetic trilayers, using numerical methods to match experimental observations and proposing new junction designs with tunable supercurrents.

Contribution

The study provides a detailed numerical analysis of supercurrents in Ho|Co|Ho trilayers, compares results with experiments, and introduces a novel magnetic Josephson junction design with tunable supercurrent.

Findings

Qualitative agreement with experimental supercurrent behavior.

Identification of 0-$ ext{pi}$ oscillations and rapid oscillations due to spiral magnetization.

Proposal of a new tunable magnetic Josephson junction design.

Abstract

Motivated by a recent experiment [J. W. A. Robinson, J. D. S. Witt and M. G. Blamire, Science, \textbf{329}, 5987 (2010)], we here study the possibility of establishing a long-range spin-triplet supercurrent through an inhomogeneous ferromagnetic region consisting of a Ho$\mid$Co$\mid$Ho trilayer sandwiched between two conventional s-wave superconductors. We utilize a full numerical solution in the diffusive regime of transport and study the behavior of the supercurrent for various experimentally relevant configurations of the ferromagnetic trilayer. We obtain qualitatively very good agreement with experimental data regarding the behavior of the supercurrent as a function of the width of the Co-layer, $L_\text{Co}$. Moreover, we find a synthesis of 0-$\pi$ oscillations with superimposed rapid oscillations when varying the width of the Ho-layer which pertain specifically to the spiral magnetization texture in Ho. We are not able to reproduce the anomalous peaks in the supercurrent observed experimentally in this regime, but note that the results obtained are quite sensitive to the exact magnetization profile in the Ho-layers, which could be the reason for the discrepancy between our model and the experimental reported data for this particular aspect. We also investigate the supercurrent in a system where the intrinsically inhomogeneous Ho ferromagnets are replaced with domain-wall ferromagnets, and find similar behavior as in the Ho$\mid$Co$\mid$Ho case. Furthermore, we propose a novel type of magnetic Josephson junction including only a domain-wall ferromagnet and a homogeneous ferromagnetic layer, which in addition to simplicity regarding the magnetization profile also offers a tunable long-range spin-triplet supercurrent. Finally, we discuss some experimental aspects of our findings.