Abstract
We investigate the proximity effect in diffusive superconducting hybrid structures with a spin-orbit (SO) coupling. Our study is focused on the singlet-triplet conversion and the generation of long-range superconducting correlations in ferromagnetic elements. We derive the quasiclassical equations for the Green's functions including the SO coupling terms in form of a background SU(2) field. With the help of these equations, we first present a complete analogy between the spin diffusion process in normal metals and the generation of the triplet components of the condensate in a diffusive superconducting structure in the presence of SO coupling. From this analogy it turns out naturally that the SO coupling is an additional source of the long-range triplet component (LRTC) besides the magnetic inhomogeneities studied in the past. We demonstrate an explicit connection between an inhomogeneous exchange field and SO coupling mechanisms for the generation of the LRTC and establish the conditions for the appearance of the LRTC in different geometries. We also consider a S/F bilayer in contact with normal metal with SO coupling and show that the latter can be used as a source for the LRTC. Our work gives a global description of the singlet-triplet conversion in hybrids structures in terms of generic spin-fields and our results are particularly important for the understanding of the physics underlying spintronics devices with superconductor elements.
Highlights
It is common knowledge that the interaction between conventional superconductivity and ferromagnetism in superconductor-ferromagnet (S/F) hybrids leads to a new type of superconducting correlations in a triplet state [1,2]
With the help of these equations, we first present an interesting complete analogy between the spin diffusion process in normal metals and the generation of the triplet components of the condensate in a diffusive superconducting structure in the presence of SO coupling. From this analogy it turns out naturally that the SO coupling is an additional source of the long-range triplet component (LRTC) besides the magnetic inhomogeneities studied in the past
It is important to emphasize that this condition for triplet generation is more restrictive than in the lateral geometry studied in the previous section, in which a pure Rashba SO coupling at the S/F interface and arbitrary magnetization orientation are enough for the LRTC to exist
Summary
It is common knowledge that the interaction between conventional superconductivity and ferromagnetism in superconductor-ferromagnet (S/F) hybrids leads to a new type of superconducting correlations in a triplet state [1,2]. It is commonly believed that singlet-long-range triplet (in short singlet-triplet) conversion happens only in the presence of magnetic inhomogeneities, as for example magnetic domain walls [1,25,26,27,28], ferromagnetic multilayers with different magnetization orientations [29,30,31], or interfaces with magnetic disorder [32,33]. The main goal of the present paper is twofold: First, we present a complete analogy between the diffusion of a spin density in a normal metal and the singlet-triplet conversion in superconducting hybrids. This analogy opens a different view of the singlet-triplet conversion that helps in the understanding of the proximity effect in more complex hybrid structures. We present some discussions and a summary of results in our concluding section
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