Proximity induced vortices and long-range triplet supercurrents in ferromagnetic Josephson junctions and spin valves

Abstract

Using a spin-parameterized quasiclassical Keldysh-Usadel technique, we theoretically study supercurrent transport in several types of diffusive ferromagnetic(F )/superconducting(S) configurations with differing magnetization textures. We separate out the even-and odd-frequency components of the supercurrent within the low proximity limit and identify the relative contributions from the singlet and triplet channels. We first consider inhomogeneous one-dimensional Josephson structures consisting of a uniform bilayer magnetic S/F /F /S structure and a trilayer S/F /F /F /S configuration, in which case the outer F layers can have either a uniform or conical texture relative to the central uniform F layer. Our results demonstrate that for supercurrents flowing perpendicular to the F /F interfaces, incorporating a conical texture yields the most effective way to observe the signatures of the long-ranged spin-triplet supercurrents. We also consider three different types of finitesized two-dimensional magnetic structures subjected to an applied magnetic field normal to the junction plane: a S/F /S junction with uniform magnetization texture, and two S/F /F /S configurations with differing F /F bilayer arrangements. In one case, the F /F interface is parallel with the S/F junction interfaces while in the other case, the F /F junction is oriented perpendicular to the S/F interfaces. We then discuss the proximity vortices and corresponding spatial maps of currents inside the junctions. For the uniform S/F /S junction, we analytically calculate the magnetic field induced supercurrent and pair potential in both the narrow and wide junction regimes, thus providing insight into the variations in the Fraunhofer diffraction patterns and proximity vortices when transitioning from a wide junction to a narrow one. Our extensive computations demonstrate that the induced long-range spin-triplet supercurrents can deeply penetrate uniform F /F bilayers when spin-singlet supercurrents flow parallel to the F /F interfaces. This is in stark contrast to configurations where a spin-singlet supercurrent flows perpendicular to the F /F interfaces. We pinpoint the origin of the induced triplet and singlet correlations through spatial profiles of the decomposed total supercurrents. We find that the penetration of the long-range spin-triplet supercurrents associated with supercurrents flowing parallel to the F /F interfaces, are more pronounced when the thickness of the F strips are unequal. Lastly, if one of the S terminals is replaced with a finite-sized normal metal, we demonstrate that the corresponding experimentally accessible S/F /F /N spin valve presents an effective platform in which the predicted long-range effects can be effectively generated and probed.

Two-dimensional Josephson vortex lattice and anomalously slow decay of the Fraunhofer oscillations in a ballistic SNS junction with a warped Fermi surface

“…Two-dimensional vortex lattices are well established for Abrikosov vortices in a bulk superconductor [1], but Josephson vortices in an SNS junction were only known to arrange as a one-dimensional chain [13,14,16]. Our key conceptual finding is that the 2D arrangement is hidden by angular averaging over the Fermi surface.…”

“…It is known that the linear arrangement of the vortices along the superconducting interface is modified by insulating boundaries [9][10][11][12], in a junction of lateral width W comparable to the separation L of the interfaces. But in wide junctions (W L), when boundary effects are irrelevant, only linear arrangements of Josephson vortices are known [13][14][15][16][17].…”

Zero-energy peak and triplet correlations in nanoscale superconductor/ferromagnet/ferromagnet spin valves

“…This is consistent with f 1 triplet generation being optimal for highly asymmetric ferromagnetic layer widths. 33 It is notable that the periodic occurrence of peaks in f 1 when varying D F 1 , evolves into a single maximum as h is reduced further.…”

“…This behavior was qualitatively explained in terms of the longrange penetration of proximity-induced spin-1 triplet pairings due to the helical structure of the magnetization. 33 In practice however, simpler structures involving SF hybrids with uniform exchange fields are often preferable from both an experimental and theoretical perspective. 14,16,17,[24][25][26][27][28][29] Therefore, the primary aim of this work is the determination of experimentally optimal parameters for probing odd-frequency spin-1 triplet correlations with DOS signatures in nanoscale SF F spin valves.…”

Effects of spin-orbit coupling and spatial symmetries on the Josephson current in SNS junctions

“…Including all these ingredients makes it very challenging to obtain analytic insights, and usually one has to revert to numerics in order to produce quantitative or qualitative results. Numerical results based on a Keldysh-Usadel approach were used to study the supercurrent in diffusive junctions, with an asymmetric design or inhomogeneous exchange field [25,26]. There it was found that an anomalous supercurrent can also be caused by device asymmetries.…”