Josephson current through a ferromagnetic bilayer: Beyond the quasiclassical approximation

Abstract

Based on the Bogoliubov-de Gennes equations, we provide an exact numerical solution for the critical current of Josephson junctions with a composite ferromagnetic bilayer. We demonstrate that for the antiparallel orientation of the magnetic moments of the bilayer, the presence of a potential barrier at the bilayer interface results in large oscillations of the critical current as a function of ferromagnet thickness and/or exchange field. Because of this, and remarkably, in the range of small exchange field and thicknesses, the magnetism leads to the increase of the critical current. This effect is well pronounced at low temperature but disappears near Tc. If the potential barrier is replaced by a spin-active barrier at the bilayer interface the conventional 0-π transition, similar to the case of an uniform ferromagnetic Josephson junction, is observed. Strikingly, for a parallel orientation of the magnetic moments of the bilayer, the presence of the spin-active barrier restores the anomalous behavior-potential barrier in the antiparallel case. These behaviors result from the resonant tunneling of Cooper pairs across the composite barrier-an effect related to the spindependent Fermi vector in the presence of the ferromagnets' exchange field.

Magnetoelectric effects in Josephson junctions

“…Theoretical description of the φ 0 -junctions is significantly more challenging than that of the 0 and π-junctions. To obtain the anomalous phase shift one has to include the magnetoelectric coupling which is beyond the standard quasiclassical approximation [64,66,68,71,96,98,116,118,126,[144][145][146][147][148][149][150][151][152]. For Rashba-type SOC described by the hamiltonian H R = α[p × n]σ in the ballistic regime and for large Rashba constant α, the anomalous phase shift is given by [92]:…”

Anomalous supercurrent modulated by interfacial magnetizations in Josephson junctions with ferromagnetic bilayers

“…However, the applicability of these methods assumes that the exchange field h in the ferromagnet should be much smaller than the Fermi energy h ≪ E F and the use of the Usadel equations implies even more restrictive conditions hτ ≪ 1, where τ is the electrons scattering time [2]. As a result, since the transport properties of the majority and minority electrons in the F layers are very different, the quasiclassical approaches lose their effectiveness, and some subtle qualitative effects may be missed, see, for example, [30,33,69,70]. Moreover, a lot of experimental activities with the S/F heterostructures deal with strong ferromagnets (or even half-metals [63,71,72]) for which the quasiclassical approximation cannot provide an adequate quantitative description.…”

Interference phenomena in clean Josephson junctions with ferromagnetic bilayers: Spin-triplet correlations and resonances

“…A simple realization of the Josephson junction with inhomogeneous ferromagnet is SF 1 F 2 S heterostructure with two monodomain ferromagnets having noncollinear in-plane magnetizations [19][20][21][22][23][24][25][26][27][28][29][30]. However, in such proximity structures the long-range spin-triplet component of the supercurrent is consisted only of even harmonic amplitudes [22][23][24][25].…”