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![Zero energy density of states at x = d in a S/F/I structure, in terms of [(N (0)/N0) − 1]/γ 2 t as a function of d/ξF , for γt ≪ 1 and different values of γ φ (full lines). The dotted lines show 4[(N (0)/N0) − 1]/γ 2 t at x = d in a semiinfinite S/F structure with the same values of γt and γ φ . The inset shows the DOS at x = d as a function of γ φ for the S/F/I structure.](profile/Audrey-Cottet-2/publication/235451228/figure/fig1/AS:393346817249284@1470792597312/Zero-energy-density-of-states-at-x-d-in-a-S-F-I-structure-in-terms-of-N-0-N0.png)
Zero energy density of states at x = d in a S/F/I structure, in terms of [(N (0)/N0) − 1]/γ 2 t as a function of d/ξF , for γt ≪ 1 and different values of γ φ (full lines). The dotted lines show 4[(N (0)/N0) − 1]/γ 2 t at x = d in a semiinfinite S/F structure with the same values of γt and γ φ . The inset shows the DOS at x = d as a function of γ φ for the S/F/I structure.
Source publication
We reconsider the problem of the superconducting proximity effect in a diffusive ferromagnet bounded by tunneling interfaces, using spin-dependent boundary conditions. This introduces for each interface a phase-shifting conductance Gϕ which results from the spin dependence of the phase shifts acquired by electrons upon scattering on the interface....
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Citations
... For example, in Al, G S i ≈ 0.13. The polarization cloud enhances the total spin magnetic moment and g factor by G S i , which can be observed via the imaginary part of the spin-mixing conductance (effective field) at ferromagnet|normal metal interfaces [47] or spin-dependent interfacial phase shifts at ferromagnet| superconductor interfaces [48]. ...
Dilute alloys of rare earths have played a vital role in understanding magnetic phenomena. Here, we model the ground state of dilute 4f rare-earth impurities in light metals. When the 4f subshells are open (but not half-filled), the spin-orbit coupling imprints a rotational charge current of conduction electrons around rare-earth atoms. The sign and amplitude of the current oscillate similar to the Ruderman-Kittel-Kasuya-Yosida (RKKY) spin polarization. We compute the observable effect, namely, the Ørsted field generated by the current vortices and the Knight shift.
... For example, in Al, G S i ≈ 0.13. The polarization cloud enhances the total spin magnetic moment and g-factor by G S i , which can be observed via the imaginary part of the spin-mixing conductance (effective field) at ferromagnet|normal metal interfaces [47] or spin-dependent interfacial phase shifts at ferromagnet| superconductor interfaces [48]. ...
Dilute alloys of rare earths have played a vital role in understanding magnetic phenomena. Here, we model the ground state of dilute 4f rare-earth impurities in light metals. When the 4f subshells are open (but not half-filled), the spin-orbit coupling imprints a rotational charge current of conduction electrons around rare-earth atoms. The sign and amplitude of the current oscillate similar to the RKKY spin polarization. We compute the observable effect, namely the Oersted field generated by the current vortices and the Knight shift.
... In this theory, which is analogous to that of classic electric circuits, a mesoscopic layout is separated into easily characterisable units, e.g., terminals, connectors, and finite-element nodes, where the only di↵erence between them is that we know a priori the equilibrium Green functions in the terminals and yet it has to be determined on the node [77]. This method has been developed individually for S/N [75], F/N [78], and subsequently applied to S/F heterostructures [79][80][81][82][83]. ...
BCS superconductivity and ferromagnetism rarely coexist in bulk materials due to their mutually antagonistic spin orderings. Many exciting new phenomena taht are not present in each system alone, however, could occur in proximity-coupled superconductor/ferromagnet (S/F) heterostructures. The goal of this dissertation is to theoretically present a variety of fascinating but still not experimentally reported phenomena occurring in magnetic superconducting hybrid devices, which in addition to serving as a platform for novel fundamental spin physics, could become essential building blocks in superconducting spintronics.
One of the key concepts in quantum transport is the controlled creation and interaction of charge and spin in nanoscale hybrid structures. Conventional S is composed of singlet Cooper pairs that carry no net spin. Achieving exotic superconducting phases as well as exploiting zero-dissipation supercurrents for switching magnetic memories, for example, requires equal-spin triplet Cooper pairs which are challenging to obtain due to their elusive nature. We will demonstrate a minimal and experimentally achievable setup of a four-terminal S/F hybrid that allows for the generation, control, and detection of these pairs. In particular, we propose a detection scheme based on charge current measurements and show that equal-spin triplet correlations establish a tunable spin current flow into the magnets.
A very large thermopower is not directly obtainable in conventional S due to the presence of an almost perfect spin-dependent electron-hole symmetry around the Fermi energy. However, a thin S with a spin-split density of states, could break this symmetry and thereby provides a giant thermoelectric effect. We will show that spinflip scattering could strongly enhance the thermoelectric response of an S/F bilayer via creating a sizeable figure of merit at low values of temperature and spin-splitting. The scattering rate shifts the maximum of the thermopower from a higher to a weaker magnetic field, which turns out to be of crucial importance for reducing the necessary spin-splitting in these structures and thereby avoiding additional detrimental effects related to external magnetic fields.
Inducing a spin-splitting field in an adjacent S usually has been achieved via employing ferromagnets or externally applied magnetic fields. However, using ferromagnets in these designs is marred with numerous detrimental and parasitic effects which lower the practical feasibility of the proposed models. Deriving the interfacial self-energy, we will confirm that an insulating antiferromagnet in proximity to a thin S layer, can indeed more conveniently, be used to induce a sizeable, and disorder resistant spin-splitting in the S than ferromagnets or applied magnetic fields. This prediction is a promising step towards eliminating the limiting impacts of ferromagnets employed to this end and allows realizing several concepts involving spin-split superconductors.
... While the absolute phases are usually irrelevant, the relative phase shift θ s between electron waves of spin up and spin down can lead to observable consequences. θ s is called the spin-mixing angle [24] or the spin dependence of interfacial phase shifts (SDIPS) [25]. Interfaces with non-zero θ s are called spin active (or magnetically active). ...
... The singlet and m z = 0 triplet can propagate into a ferromagnetic metal, where they oscillate as a function of the distance from the interface [45,46]. Determining the phase of these oscillations [47,48] as a function of the thickness of the ferromagnetic film may therefore also provide insight into spin-dependent phase shifts [25]. ...
Andreev bound states are ubiquitous in superconducting hybrid structures. They are formed near impurities, in Josephson junctions, in vortex cores and at interfaces. At spin-active superconductor–ferromagnet interfaces, Andreev bound states are formed due to spin-dependent scattering phases. Spin-dependent phase shifts are an important ingredient for the generation of triplet Cooper pairs in superconductor–ferromagnet hybrid structures. Spectroscopy of Andreev bound states is a powerful probe of superconducting order parameter symmetry, as well as spin-dependent interface scattering and the triplet proximity effect.
This article is part of the theme issue ‘Andreev bound states’.
... Here, the reflected spin-up wave trails that of the spindown wave, and the effect increases when V ↑ − E F approaches zero. The phase ϑ = ϑ ↑ − ϑ ↓ of the parameter r ↑ r * ↓ = |r ↑ r ↓ | e iϑ is called spin-mixing angle [79], or spin-dependent scattering phase shift [80]. It is an important parameter for superconducting spintronics. ...
Andreev bound states are an expression of quantum coherence between particles
and holes in hybrid structures composed of superconducting and
non-superconducting metallic parts. Their spectrum carries important
information on the nature of the pairing, and determines the current in
Josephson devices. Here I give a short review on Andreev bound states in
systems involving superconductors and ferromagnets with strong
spin-polarization. I show how the processes of spin-dependent scattering phase
shifts and of triplet rotation influence Andreev point contact spectra, and
provide a general framework for non-local Andreev phenomena in such structures
in terms of coherence functions. Finally, I demonstrate how the concept of
coherence functions cross-links wave-function and Green-function based
theories, by showing that coherence functions fulfilling the equations of
motion for quasiclassical Green functions can be used to derive a set of
generalised Andreev equations.
... Looking at the formulation of the problem by de Gennes (see also [17]) from the modern point of view, an alternative approach to the FI/S/FI spin valve operating physics can be drawn considering FI/S interface as spin-active one [18][19][20]. The concept of the spin-active interface implies that electrons acquire spin-dependent phase shifts when reflecting from an interface with ferromagnetic insulator (for the pictorial view see [21], Fig. 7). ...
The short review is devoted to the state of the art of a booming field of research in spintronics – superconducting spintronics. The spin-valve properties of hybrid structures consisting of alternating layers of superconductor (S) and ferromagnetic (F) of nanoscale thicknesses and superconducting due to the proximity effect are considered in detail. The experimental data for the weak and strong ferromagnetic materials are analyzed; the role of the domain structure of the ferromagnet and the scattering of electrons with spin flip at the S-F interfaces in the magnitude of the valve effect is considered. Theoretical works describing the effects of the spin valve for diffusive and clean limits are analyzed. The necessity of consideration of the multiplicity of configurations of the superconducting order parameter in multilayer SF heterostructures is underlined.
... The triplet type of superconductivity occurs when the exchange field is inhomogeneous 3,4,[15][16][17][18][19][20] . This can be realized in SF multilayers with noncolinear magnetizations in different F layers 11,12,16,[21][22][23][24] , in the presence of domain walls [25][26][27] or a spin-active interface 10,28 . ...
A possible explanation for the long-range proximity effect observed in single-crystalline cobalt nanowires sandwiched between two tungsten superconducting electrodes [Wang, M. et al. Nat. Phys. 6, 389 (2010)] is proposed. The theoretical model uses properties of a ferromagnet band structure. Specifically, to connect the exchange field with the momentum of quasiparticles the distinction between the effective masses in majority and minority spin-subbands and the Fermi surface anisotropy are considered. The derived Eilenberger-like equations allowed us to obtain a renormalized exchange interaction that is completely compensated for some crystallographic directions under certain conditions. The proposed theoretical model is compared with previous approaches.
... [86] Interface phenomena at superconducting junctions constitutes an active research field both theoretically and experimentally. [93][94][95][96][97][98][99][100] Intense theoretical efforts [93,94,[96][97][98][101][102][103][104][105][106][107][108][109][110][111] have been devoted to explaining experimental observations [112][113][114][115] in terms of interface phenomena. The interface of a hybrid superconducting junction can operate as a spin-polarizer when it is coated by an ultrathin uniform F layer, for example. ...
... [86] Interface phenomena at superconducting junctions constitutes an active research field both theoretically and experimentally. [93][94][95][96][97][98][99][100] Intense theoretical efforts [93,94,[96][97][98][101][102][103][104][105][106][107][108][109][110][111] have been devoted to explaining experimental observations [112][113][114][115] in terms of interface phenomena. The interface of a hybrid superconducting junction can operate as a spin-polarizer when it is coated by an ultrathin uniform F layer, for example. ...
... In order to theoretically account for spin-polarization and spin-dependent phase shifts that an electron experiences upon transmitting across such spin-active interfaces, spin-boundary conditions were introduced. [101] Motivated by recent experimental and theoretical advancements in the context of superconducting hybrids with spin-active interfaces [93][94][95][96][97][98][99][100][101][102][103][104][105][106][107][108][109][110][111] and intrinsic spinorbit coupled hybrids [19-27, 64, 77, 81], we study here finite sized two-dimensional spin-orbit coupled swave superconductor/normal-metal/s-wave superconductor (S/N /S) heterojunctions with one spin-active interface in the diffusive regime. We utilize a spin-parameterized twodimensional Keldysh-Usadel technique [81] in the presence of ISOIs. ...
Utilizing a SU(2) gauge symmetry technique in the quasiclassical diffusive
regime, we theoretically study finite-sized two-dimensional intrinsic
spin-orbit coupled superconductor/normal-metal/superconductor (S/N/S) hybrid
structures with a single spin-active interface. We consider intrinsic
spin-orbit interactions (ISOIs) that are confined within the N wire and absent
in the s-wave superconducting electrodes (S). Using experimentally feasible
parameters, we demonstrate that the coupling of the ISOIs and spin moment of
the spin-active interface results in maximum singlet-triplet conversion and
accumulation of spin current density at the corners of the N wire nearest the
spin-active interface. By solely modulating the superconducting phase
difference, we show how the opposing parities of the charge and spin currents
provide an effective venue to experimentally examine pure edge spin currents
not accompanied by charge currents. These effects occur in the absence of
externally imposed fields, and moreover are insensitive to the arbitrary
orientations of the interface spin moment. The experimental implementation of
these robust edge phenomena are also discussed.
... We start by analyzing the appropriate Bogoliubovde Gennes (BdG) Hamiltonian and develop a generalized Blonder-Tinkham-Klapwijk (BTK) [58] formalism to calculate the current-voltage characteristics for our general setup. We phenomenologically model what we call the spin-orbit-active interface as a generalization of a spin-active interface [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74], which itself is a generalization of a single Z parameter used in the original BTK approach. We find that the rich physics emanating from non-uniform SOC and/or spin-orbit-active interface is not only of fundamental interest but also highly relevent for interpreting the results of experiments. ...
... The original BTK model adopts one parameter Z 0 τ z ⊗ 1 to describe barrier effects from an oxide layer or local disorder [58]. For ferromagnetsuperconductor heterostructures, H I can be modeled as a Zeeman form 1 ⊗ Z h (n · σ) with unit directionn = (sin θ cos φ, sin θ sin φ, cos θ), which accounts for various spin-active processes such as spin-flip scattering, spindependent phase shift, and spin-related Andreev reflection [61][62][63][64][65][66][67][68][69][70][71][72][73][74]. In our case, we expect that the discontinuity of the bulk SOC and the interfacial SOC itself would play an active role in the transport. ...
Electronic spin-orbit coupling (SOC) is essential for various newly
discovered phenomena in condensed-matter systems. In particular,
one-dimensional topological heterostructures with SOC have been widely
investigated in both theory and experiment for their distinct transport
signatures indicating the presence of emergent Majorana fermions. However, a
general framework for the SOC-affected transport in superconducting
heterostructures, especially with the consideration of interfacial effects, has
not been developed even regardless of the topological aspects. We hereby
provide one for an effectively one-dimensional superconductor-normal
heterostructure with nonuniform magnitude and direction of both Rashba and
Dresselhaus SOC as well as a spin-orbit-active interface. We extend the
Blonder-Tinkham-Klapwijk treatment to analyze the current-voltage relation and
obtain a rich range of transport behaviors. Our work provides a basis for
characterizing fundamental physics arising from spin-orbit interactions in
heterostructures and its implications for topological systems, spintronic
applications, and a whole variety of experimental setups.
... Here, we propose an alternative way to observe spin imbalance, which does not require a magnetic field. Our idea relies on the possibility of fabricating spin-active interfaces [9][10][11][12][13][14][15][16][17]. A superconductor coated with a spinactive layer hosts a pair of interface bound Andreev states, whose properties are controlled by parameters of the interface [11,12]. ...
We consider a heterostructure consisting of a normal metal and a superconductor separated by a spin-active interface. At finite-bias voltages, spin-filtering and spin-mixing effects at the interface allow for an induced magnetization (spin imbalance) on the superconducting side of the junction, which relaxes to zero in the bulk. Such interfaces are also known to host a pair of in-gap Andreev bound states which were recently observed experimentally. We show that these states are responsible for the dominant contribution to the induced spin imbalance close to the interface. Motivated by recent experiments on spin-charge density separation in superconducting aluminum wires, we propose an alternative way to observe spin imbalance without applying an external magnetic field. We also suggest that the peculiar dependence of the spin imbalance on the applied bias voltage permits an indirect bound-state spectroscopy.
