Proximity Induced Vortices and Long-Range Triplet Supercurrents in Ferromagnetic Josephson Junctions and Spin Valves

Abstract

Using a Keldysh formalism, we study supercurrent (SC) transport in several types of diffusive ferromagnet(F)/superconductor(S) configurations. We separate out the even- and odd-frequency components and identify the relative contributions from the singlet and triplet channels. We first consider 1D Josephson structures consisting of a uniform SFFS structure and a trilayer SFFFS configuration. Our results demonstrate that for SCs flowing perpendicular to the FF interfaces, incorporating a conical texture yields the most effective way to observe the signatures of the long-ranged SC. We also consider three different types of finite-sized 2D structures subjected to an applied magnetic field: a uniform SFS junction, and two SFFS configurations with differing FF bilayer arrangements. In one case, the FF interface is parallel with the SF interfaces while in the other case, the FF junction is oriented perpendicular to the SF interfaces. For the uniform SFS junction, we analytically derive the magnetic field induced SC and pair potential, providing insight into the variations of the critical SCs and proximity vortices. Our extensive computations demonstrate that the induced long-range SCs can penetrate deeply into uniform FF bilayers when singlet SCs flow parallel to the FF interfaces which is in stark contrast to configurations where SC flows perpendicular to the FF interfaces. We pinpoint the origin of the induced triplet and singlet correlations through spatial profiles of the decomposed total SCs. We find that the penetration of the long-range SCs associated with SCs flowing parallel to the FF interfaces, are more pronounced when the thickness of the F strips are unequal. Lastly, we show that the corresponding experimentally accessible SFFN spin valve presents an effective platform in which the predicted long-range effects can be effectively generated and probed.