sin(2 phi) current-phase relation in SFS junctions with decoherence in the ferromagnet

Abstract

We propose a theoretical description of the sin(2 phi) current-phase relation in SFS junctions at the 0-$π$ cross-over obtained in recent experiments by Sellier et al. [Phys. Rev. Lett. 92, 257005 (2004)] where it was suggested that a strong decoherence in the magnetic alloy can explain the magnitude of the residual supercurrent at the 0-pi cross-over. To describe the interplay between decoherence and elastic scattering in the ferromagnet we use an analogy with crossed Andreev reflection in the presence of disorder. The supercurrent as a function of the length R of the ferromagnet decays exponentially over a length xi, larger than the elastic scattering length $l_d$ in the absence of decoherence, and smaller than the coherence length $l_ϕ$ in the absence of elastic scattering on impurities. The best fit leads to $ξ\simeq ξ_h^{({\rm diff})}/3$, where $ξ_h^{({\rm diff})}$ is exchange length of the diffusive system without decoherence (also equal to $ξ$ in the absence of decoherence). The fit of experiments works well for the amplitude of both the sin(phi) and sin(2 phi) harmonics.