Coexistance and tuning of spin-triplet superconductivity in spin-filter Josephson junctions*

The Josephson effect in ferromagnetic Josephson junctions (SFS JJs) is a powerful tool to investigate intriguing processes occurring because of the interplay between the competition superconducting and ferromagnetic order parameters. Among these physical phenomena, the possibility to generate dissipationless spin-triplet supercurrents captured the attention of the spintronics and superconductivity research community, and a strong effort has been given to discuss the motivations and the conditions for which spin-triplet supercurrents are induced. We here propose a novel complementary study of unconventional spin-triplet mechanisms in high-quality tunnel-SFS JJs, made of an insulating ferromagnetic (FI) barrier (GdN) between two S-wave NbN electrodes, which involves the use of a microscopic theoretical approach. The goal is to give a detailed study of the unconventional thermal behavior of the critical current Ic in JJs with different FI barrier thicknesses, reported in previous works, and for the first time in presence of an external magnetic field. We report the demonstration of competition between spin-singlet and spin-triplet transport mechanisms, we discuss the physical mechanisms involved in the spin-triplet generation and we propose a technique to estimate the relative weight between spin-singlet and triplet correlation functions, which disentangles from the more standard study of the IcRN product of the JJ as a function of the interlayer thickness. Finally, we experimentally demonstrate how to tune the amount of spin-triplet supercurrents through weak external magnetic fields, thus giving a fundamental step to use such high-quality spin-filter JJs in superconducting spintronics devices.