Triplet Proximity Effect Research Articles

Andreev Conductance in Disordered SF Junctions with Spin-Orbit Scattering

We calculate the conductance of a junction between a disordered superconductor and a very strong half-metallic ferromagnet admitting electrons with only one spin projection. A usual mechanism of Andreev reflection is strongly suppressed in this case since Cooper pairs are composed of electrons with opposite spins. However, this obstacle can be overcome if we take into account spin-orbit scattering inside the superconductor. Spin-orbit scattering induces a fluctuational (zero on average) spin-triplet component of the superconducting condensate, which is enough to establish Andreev transport into a strong ferromagnet. This remarkably simple mechanism is quite versatile and can explain long-range triplet proximity effect in a number of experimental setups. One particular application of the suggested effect is to measure the spin-orbit scattering time τSO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _{\ ext {SO}}$$\\end{document} in disordered superconducting materials. The value of Andreev conductance strongly depends on the parameter ΔτSO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \ au _\ ext {SO}$$\\end{document} and can be noticeable even in very disordered but relatively light metals like granular aluminum.

Enhanced controllable triplet proximity effect in superconducting spin–orbit coupled spin valves with modified superconductor/ferromagnet interfaces

In a superconductor/ferromagnet hybrid, a magnetically controlled singlet-to-triplet Cooper pair conversion can modulate the superconducting critical temperature. In these triplet superconducting spin valves, such control usually requires inhomogeneous magnetism. However, in the presence of spin–orbit coupling from an interfacial heavy metal layer, the singlet/triplet conversion rate and, thus, critical temperature can be controlled via the magnetization direction of a single homogeneous ferromagnet. Here, we report significantly enhanced controllable pair conversion to a triplet state in a Nb/Pt/Co/Pt superconducting spin valve in which Pt/Co/Pt is homogenously magnetized and proximity-coupled to a superconducting layer of Nb. The Co/Pt interface furthest away from Nb is modified by a sub-nanometer-thick layer of Cu or Au. We argue that the enhancement is most likely associated from an improvement of the Co/Pt interface due to the insertion of Cu and Au layers. Additionally, the higher normalized orbital moments in Au measured using x-ray magnetic circular dichroism shows that increasing spin–orbit coupling enhances the triplet proximity effect—an observation supported by our theoretical calculations. Our results provide a pathway to enhancing triplet pair creation by interface engineering for device development in superspintronics.

Unconventional long range triplet proximity effect in planar YBa2Cu3O7/La0.7Sr0.3MnO3/YBa2Cu3O7 Josephson junctions

The proximity effect between superconductors and ferromagnets may become long range due to the generation of triplet pairs. The recent finding of a long, one micron-range unconventional Josephson effect between YBa2Cu3O7 high Tc cuprates separated by a half metallic La0.7Sr0.3MnO3 manganite ferromagnet has uncovered a novel unconventional triplet proximity effect. In this paper, we examine the temperature dependence of the critical current in planar Josephson junctions. We find that the critical current—normal resistance product follows the predictions of traditional superconductor-normal metal-superconductor junctions, which implies that triplet pairs in a ferromagnet are transported in the diffusive limit similarly to singlet pairs in a normal metal. This result calls for theoretical studies of the new triplet Josephson effect and underlines its potential in future superconducting spintronics.

Effect of spin-triplet correlations on Josephson transport in atomically thin superconductor/half-metal/superconductor structures

We study the effect of the triplet proximity effect on Josephson transport in superconductor/half-metal/superconductor structures of atomic thickness beyond the quasiclassical approximation. Using the combination of microscopic ${\mathrm{Gor}}^{\ensuremath{'}}\mathrm{kov}$ formalism and tight-binding model we show that the full spin polarization inside the half-metal give rise to nonmonotonic temperature dependence of the critical current in S/HM/S Josephson junction with two spin active S/HM interfaces. We also calculate the magnetic moment inside the ${\mathrm{S}}_{2}$ layer in ${\mathrm{S}}_{1}/\mathrm{HM}/{\mathrm{S}}_{2}$ structure with spin-active ${\mathrm{S}}_{1}/\mathrm{HM}$ interface, which is induced by the spin-triplet superconducting correlations. Finally, we analyze the second-harmonic generation in ${\mathrm{S}}_{1}/\mathrm{HM}/{\mathrm{S}}_{2}$ structure with one spin-active interface.

Triplet Cooper pairs induced in diffusive s-wave superconductors interfaced with strongly spin-polarized magnetic insulators or half-metallic ferromagnets

Interfacing superconductors with strongly spin-polarized magnetic materials opens the possibility to discover new spintronic devices in which spin-triplet Cooper pairs play a key role. Motivated by the recent derivation of spin-polarized quasiclassical boundary conditions capable of describing such a scenario in the diffusive limit, we consider the emergent physics in hybrid structures comprised of a conventional s-wave superconductor (e.g. Nb, Al) and either strongly spin-polarized ferromagnetic insulators (e.g. EuO, GdN) or halfmetallic ferromagnets (e.g. CrO2, LCMO). In contrast to most previous works, we focus on how the superconductor itself is influenced by the proximity effect, and how the generated triplet Cooper pairs manifest themselves in the self-consistently computed density of states (DOS) and the superconducting critical temperature Tc. We provide a comprehensive treatment of how the superconductor and its properties are affected by the triplet pairs, demonstrating that our theory can reproduce the recent observation of an unusually large zero-energy peak in a superconductor interfaced with a half-metal, which even exceeds the normal-state DOS. We also discuss the recent observation of a large superconducting spin-valve effect with a Tc change ~1 K in superconductor/half-metal structures, in which case our results indicate that the experiment cannot be explained fully by a long-ranged triplet proximity effect.

Triplet proximity effect in superconducting heterostructures with a half-metallic layer

We present the Usadel theory describing the superconducting proximity effect in heterostructures with a half-metallic layer. It is shown that the full spin polarization inside the half-metals gives rise to the giant triplet spin-valve effect in superconductor (S) - ferromagnet (F) - half-metal (HM) trilayers as well as to the $\varphi_0$-junction formation in the S/F/HM/F/S systems. In addition, we consider the exactly solvable model of the S/F/HM trilayers of atomic thickness and demonstrate that it reproduces the main features of the spin-valve effect found within the Usadel approach. Our results are shown to be in a qualitative agreement with the recent experimental data on the spin-valve effect in ${\rm MoGe/Cu/Ni/CrO_2}$ hybrids [A. Singh et al., Phys. Rev. X 5, 021019 (2015)].

Triplet superconductivity and proximity effect induced by Bloch and Néel domain walls

Noncollinear magnetic interfaces introduced in superconductor (SC)/ferromagnet/SC heterostructures allow for spin-flipping processes and are able to generate equal-spin spin-triplet pairing correlations within the ferromagnetic region. This leads to the occurrence of the so-called long-range proximity effect. Particular examples of noncollinear magnetic interfaces include Bloch and Néel domain walls. Here, we present results for heterostructures containing Bloch and Néel domain walls based on self-consistent solutions of the spin-dependent Bogoliubov–de Gennes equations in the clean limit. In particular, we investigate the thickness dependence of Bloch and Néel domain walls on induced spin-triplet pairing correlations and compare with other experimental and theoretical results, including conical magnetic layers as noncollinear magnetic interfaces. It is shown that both Bloch and Néel domain walls lead to the generation of unequal-spin spin-triplet pairing correlations of similar strength as for conical magnetic layers. However, for the particular heterostructure geometries investigated, only Bloch domain walls lead to the generation of equal-spin spin-triplet pairing correlations. They are stronger than those generated by an equivalent thickness of conical magnetic layers. In order for Néel domain walls to induce equal-spin spin-triplet pairing correlations, they have to be oriented such that the noncollinearity appears within the plane parallel to the interface region.

Giant triplet proximity effect in superconducting pseudo spin valves with engineered anisotropy

The proximity coupling of a thin superconducting layer and an inhomogeneous ferromagnet can lead to a significant reduction of the critical temperature due to the generation of spin-polarized triplet Cooper pairs. We report critical temperature measurements of Co/Cu/NiFe(Py)/Cu/Nb superconducting pseudo spin valves (PSVs) in which the magnetization of the soft layer (Py) can be independently rotated in-plane with a magnetic field to create an angle (\ensuremath{\theta}) between it and the magnetization of Co. Here we observe results consistent with spin-triplet theory and demonstrate large changes in $\ensuremath{\Delta}{T}_{C}$ up to \ensuremath{-}120 mK as the Py layer is rotated from 0\ifmmode^\circ\else\textdegree\fi{} (Co and Py are parallel) to 90\ifmmode^\circ\else\textdegree\fi{} (Co and Py are orthogonal), which offers the potential for active control of the superconducting state. The key to this achievement is engineered magnetic anisotropy in Py, which enables well-defined control over the magnetization configuration of the PSV.

Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures

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.

The influence of an external magnetic field on the triplet proximity effect in ferromagnet/superconductor trilayers

The properties of the ferromagnet/superconductor (FS) system are theoretically studied in an external magnetic field. We consider the boundary value problem for the Usadel-like equations in the case of the so-called ‘dirty’ limit. Based on a fit of theoretical and known experimental data for the real symmetrical CuNi/Nb/CuNi trilayer, we expand upon numerical predictions on the asymmetrical F1SF2 and F1F2S systems. It is shown that the asymmetry essentially influences the critical properties of both the trilayers. The appearance of peculiar solitary re-entrant superconductivity caused by an external magnetic field is predicted for the F1F2S system.

Andreev spectroscopy of CrO2 thin films on TiO2 and Al2O3

Here we analyse the spectroscopic information gathered at a number of single CrO2/Pb interfaces. We examine thin films requiring additional interfacial layers to generate long-range spin triplet proximity effect superconductivity (CrO2/TiO2) or not (CrO2/Al2O3). We analyse the data using two theoretical models and explore the use of a parameter-free method to determine the agreement between the models and experimental observations, showing the necessary temperature range that would be required to make a definitive statement. The use of the excess current as a further tool to distinguish between models is also examined. The analysis of the spectra demonstrates that the temperature dependence of the normalised zero-bias conductance is independent of the substrate onto which the films are grown. This result has important implications for the engineering of interfaces required for the long-range spin triplet proximity effect.

Supercurrent enhancement in Bloch domain walls

Conventional spin-singlet Cooper pairs convert into spin-triplet pairs in ferromagnetic Josephson junctions in which the superconductor/ferromagnet interfaces (S/F) are magnetically inhomogeneous. Although much of the theoretical work describing this triplet proximity effect has considered ideal junctions with magnetic domain walls (DW) at the interfaces, in practice it is not easily possible to isolate a DW and propagate a supercurrent through it. The rare-earth magnet Gd can form a field-tuneable in-plane Bloch DW if grown between non-co-linearly aligned ferromagnets. Here we report supercurrents through magnetic Ni-Gd-Ni nanopillars: by field annealing at room temperature, we are able to modify the low temperature DW-state in Gd and this result has a striking effect on the junction supercurrent at 4.2 K. We argue that this result can only be explained in terms of the interconversion of triplet and singlet pairs, the efficiency of which depends on the magnetic helicity of the structure.

Observation of Andreev Bound States at Spin-active Interfaces

We report on high-resolution differential conductance experiments on nanoscale superconductor-ferromagnet tunnel junctions with ultrathin oxide tunnel barriers. We observe subgap conductance features that are symmetric with respect to bias and shift according to the Zeeman energy with an applied magnetic field. These features can be explained by resonant transport via Andreev bound states induced by spin-active scattering at the interface. From the energy and Zeeman shift of the bound states, both the magnitude and sign of the spin-dependent interfacial phase shifts between spin-up and spin-down electrons can be determined. These results contribute to the microscopic insight into the triplet proximity effect at spin-active interfaces.

Signature of the long range triplet proximity effect in the density of states

We study the impact of the long range spin-triplet proximity effect on the density of states (DOS) in planar SF${}_{1}$F${}_{2}$S Josephson junctions that consist of conventional superconductors (S) connected by two metallic monodomain ferromagnets (F${}_{1}$ and F${}_{2}$) with transparent interfaces. We determine the electronic DOS in F layers for arbitrary orientation of the magnetizations using the solutions of Eilenberger equations in the clean limit and for a moderate concentration of impurities in ferromagnets. We find that a fully developed long range proximity effect occurs in Josephson junctions with a highly asymmetric ferromagnetic bilayer. For orthogonal magnetizations, the effect manifests itself as an enhancement in DOS and as a dominant second harmonic in the Josephson current-phase relation. Distinctive variation of DOS in ferromagnets with the angle between magnetizations is experimentally observable by tunneling spectroscopy. This can provide an unambiguous signature of the long range spin-triplet proximity effect.

Domain walls and long-range triplet correlations in SFS Josephson junctions

We study the contribution of domain walls to the Josephson current through a ferromagnetic metal both in clean and diffusive limits. Our consideration of these limits is based on the quasiclassical version of the Bogoliubov--de Gennes equations and the Usadel theory, correspondingly. In the clean limit, the domain walls connecting superconducting leads are shown to be responsible for strong enhancement of the Josephson current, even for a domain structure with collinear magnetic moments. In the dirty limit, a noticeable increase in the critical current appears only for a system with noncollinear magnetic moments. We demonstrate that a thin domain wall in this case may serve as an efficient source of the long-range triplet proximity effect.

Response to comment on “Controlled injection of spin triplet supercurrents into a strong ferromagnet”

The comment by Lin He proposes that at the interface between holmium and cobalt an interesting magnetic proximity effect occurs in which the spiral magnetic wavelength ( λ ) of holmium is enhanced to 5.4 nm. Consequently, the optimum holmium layer thickness for the superconductor spin triplet proximity effect to occur in Nb/Ho/Co/Ho/Nb Josephson junctions of ≈4.5 and ≈10 nm would then correspond to the presence of ≈ λ / 2 and ≈ 3 λ / 2 spiral wavelengths. Although intriguing, this idea seems to be at odds with the conventional micromagnetics of either thin film (polycrystalline) holmium or single-crystal Ho at low temperatures (10 K). Although an increase in λ in Ho/metal multilayer thin films with epitaxially matched interfaces has been reported, the possibility of such an effect in a polycrystalline system seems unlikely.

Triplet proximity effect and odd-frequency pairing in graphene

We study the interplay between proximity-induced superconductivity and ferromagnetism in graphene by self-consistently solving the Bogoliubov de Gennes equations on the honeycomb lattice. We find that a strong triplet proximity effect is generated in graphene, leading to odd-frequency pairing correlations. These odd-frequency correlations are clearly manifested in the local density of states of the graphene sheet, which can be probed via scanning tunnel microscope measurements. Motivated by recent experiments on $\text{S}|\text{N}|\text{S}$ graphene Josephson junctions, we also study the spectrum of Andreev bound states formed in the normal region due to the proximity effect. Our results may be useful for interpreting spectroscopic data and can also serve as a guideline for future experiments.

Long-range spin-triplet proximity effect in Josephson junctions with multilayered ferromagnets

We study the proximity effect in ${\text{SF}}^{\ensuremath{'}}(\text{AF}){\text{F}}^{\ensuremath{'}}\text{S}$ and ${\text{SF}}^{\ensuremath{'}}(\text{F}){\text{F}}^{\ensuremath{'}}\text{S}$ planar junctions, where S is a clean conventional ($s$-wave) superconductor, while ${\text{F}}^{\ensuremath{'}}$ and middle layers are clean or moderately diffusive ferromagnets. Middle layers consist of two equal ferromagnets with antiparallel (AF) or parallel (F) magnetizations that are not collinear with magnetizations in the neighboring ${\text{F}}^{\ensuremath{'}}$ layers. We use fully self-consistent numerical solutions of the Eilenberger equations to calculate the superconducting pair amplitudes and the Josephson current for arbitrary thickness of ferromagnetic layers and the angle between in-plane magnetizations. For moderate disorder in ferromagnets, the triplet proximity effect is practically the same for AF and F structures, like in the dirty limit. Triplet Josephson current is dominant for ${d}^{\ensuremath{'}}\ensuremath{\approx}\ensuremath{\hbar}{v}_{F}/2{h}^{\ensuremath{'}}$, where ${d}^{\ensuremath{'}}$ is the ${\text{F}}^{\ensuremath{'}}$ layer thickness and ${h}^{\ensuremath{'}}$ is the exchange energy. Our results are in a qualitative agreement with the recent experimental observations [T. S. Khaire, M. A. Khasawneh, W. P. Pratt, and N. O. Birge, Phys. Rev. Lett. 104, 137002 (2010)].

Enhanced triplet Andreev reflection off a domain wall in a lateral geometry

We find that the triplet Andreev reflection amplitude at the interface between a half-metal and an s-wave superconductor in the presence of a domain wall is significantly enhanced if the half metal is a thin film, rather than an extended magnet. The enhancement is by a factor $l_{\rm d}/d$, where $l_{\rm d}$ is the width of the domain wall and $d$ the film thickness. We conclude that in a lateral geometry, domain walls can be an effective source of the triplet proximity effect.

Quantum limit of the triplet proximity effect in half-metal–superconductor junctions

We apply the scattering matrix approach to the triplet proximity effect in superconductor--half-metal structures. We find that for junctions that do not mix different orbital modes, the zero-bias Andreev conductance vanishes, while the zero-bias Josephson current is nonzero. We illustrate this finding on a ballistic half-metal--superconductor (HS) and superconductor--half-metal--superconductor (SHS) junctions with translation invariance along the interfaces and on HS and SHS systems where transport through the half-metallic region takes place through a single conducting channel. Our calculations for these physically single-mode setups---single-mode point contacts and chaotic quantum dots with single-mode contacts---illustrate the main strength of the scattering matrix approach. It allows for studying systems in the quantum mechanical limit, which is inaccessible for the quasiclassical Green's function methods, the main theoretical tool in previous works on the triplet proximity effect.