The long-range proximity effect in superconductor/ferromagnet (S/F) hybrid nano-structures is observed if singlet Cooper pairs from the superconductor are converted into triplet pairs which can diffuse into the fer- romagnet over large distances. It is commonly believed that this happens only in the presence of magnetic inhomogeneities. We show that there are other sources of the long-range triplet component (LRTC) of the con- densate and establish general conditions for their occurrence. As a prototypical example we consider first a system where the exchange field and spin-orbit coupling can be treated as time and space components of an effective SU(2) potential. We derive a SU(2) covariant diffusive equation for the condensate and demonstrate that an effective SU(2) electric field is responsible for the long-range proximity effect. Finally, we extend our analysis to a generic ferromagnet and establish a universal condition for the LRTC. Our results open a new avenue in the search for such correlations in S/F structures and make a hitherto unknown connection between the LRTC and Yang-Mills electrostatics.
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 Greens 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.
We have studied the proximity-induced superconducting triplet pairing in CoO$_x$/Py1/Cu/Py2/Cu/Pb spin-valve structure (where Py = Ni$_{0.81}$Fe$_{0.19}$). By optimizing the parameters of this structure we found a triplet channel assisted full switching between the normal and superconducting states. To observe an isolated triplet spin-valve effect we exploited the oscillatory feature of the magnitude of the ordinary spin-valve effect $Delta T_c$ in the dependence of the Py2-layer thickness $d_{Py2}$. We determined the value of $d_{Py2}$ at which $Delta T_c$ caused by the ordinary spin-valve effect (the difference in the superconducting transition temperature $T_c$ between the antiparallel and parallel mutual orientation of magnetizations of the Py1 and Py2 layers) is suppressed. For such a sample a pure triplet spin-valve effect which causes the minimum in $T_c$ at the orthogonal configuration of magnetizations has been observed.
Measurements of the polar Kerr effect using a zero-area-loop Sagnac magnetometer on Pb/Ni and Al/(Co-Pd) proximity-effect bilayers show unambiguous evidence for the inverse proximity effect, in which the ferromagnet (F) induces a finite magnetization in the superconducting (S) layer. To avoid probing the magnetic effects in the ferromagnet, the superconducting layer was prepared much thicker than the lights optical penetration depth. The sign and size of the effect, as well as its temperature dependence agree with recent predictions by Bergeret et al..
The magnetization in a superconductor induced due to the inverse proximity effect is investigated in hybrid bilayers containing a superconductor and a ferromagnetic insulator or a strongly spin-polarized ferromagnetic metal. The study is performed within a quasiclassical Green function framework, wherein Usadel equations are solved with boundary conditions appropriate for strongly spin-polarized ferromagnetic materials. A comparison with recent experimental data is presented. The singlet to triplet conversion of the superconducting correlations as a result of the proximity effect with a ferromagnet is studied.
We study the physical properties of a ballistic heterostructure made of a ferromagnet (FM) and a spin-triplet superconductor (TSC) with a layered structure stacking along the direction perpendicular to the planes where a chiral px+ipy pairing occurs and assuming spin dependent processes at the interface. We use a self-consistent Bogoliubov-de Gennes approach on a three-dimensional lattice to obtain the spatial profiles of the pairing amplitude and the magnetization. We find that, depending on the strength of the ferromagnetic exchange field, the ground state of the system can have two distinct configurations with a parallel or anti-parallel collinearity between the magnetic moments in the bulk and at the interface. We demonstrate that a magnetic state having non coplanar interface, bulk and Cooper pairs spins may be stabilized if the bulk magnetization is assumed to be fixed along a given direction. The study of the density of states reveals that the modification of the electronic spectrum in the FM plays an important role in the setting of the optimal magnetic configuration. Finally, we find the existence of induced spin-polarized pair correlations in the FM-TSC system.
F. S. Bergeret
,I. Tokatly
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(2012)
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"Singlet-triplet conversion and the long-range proximity effect in superconductor-ferromagnet structures with generic spin dependent fields"
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F. S. Bergeret
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