Spin-triplet supercurrent through inhomogeneous ferromagnetic trilayers

Motivated by a recent experiment [J. W. A. Robinson, J. D. S. Witt, and M. G. Blamire, Science 329, 5987 (2010)], we report here the possibility of establishing a long-range spin-triplet supercurrent through an inhomogeneous ferromagnetic region consisting of a Ho vertical bar Co vertical bar Ho trilayer sandwiched between conventional s-wave superconducting leads. We utilize a full numerical solution in the diffusive regime of transport and study the behavior of the supercurrent for various experimentally realistic 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-Co. Moreover, we find a synthesis of 0-pi oscillations with superimposed rapid oscillations when varying the width of the Ho layers symmetrically, which pertain specifically to the spiral magnetization texture in Ho. Although we are not able to reproduce the anomalous sharp peaks in the supercurrent vs Ho-layer thickness observed experimentally in this regime, the results obtained are quite sensitive to the exact magnetization profile in the Ho layers. This might be the reason for the discrepancy between our results 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 vertical bar Co vertical bar Ho case. Furthermore, we propose magnetic Josephson junctions including only a domain-wall ferromagnet and a homogeneous ferromagnetic layer. The hybrid structure not only is simple regarding the magnetization profile but also offers a tunable long-range spin-triplet supercurrent. Finally, we discuss some experimental aspects of our findings.