The spin-triplet correlations in superconducting spin valve structures arising in the presence of noncollinear textures of magnetic moment are shown to enhance strongly the electromagnetic proximity effect, i. e. the long-range leakage of the magnetic field from the ferromagnet (F) to the superconducting (S) layer. Both the dirty and clean limits are studied on the basis of the Usadel and Eilenberger theory, correspondingly. Our results suggest a natural explanation for the puzzling enhancement of the spontaneous magnetic fields induced by the noncollinear magnetic structures observed by the muon spin rotation techniques in a wide class of layered S/F systems. We show that the electromagnetic proximity effect causes the shift of the Fraunhofer dependence of the critical current on the external magnetic field in the Josephson junction with one superconducting electrode covered by the ferromagnetic layer. This provides an alternative way to measure both the magnitude and the direction of the spontaneous magnetic field induced in the superconductor. We also demonstrate the possibility of the long ranged superconductivity control of the magnetic state in F$_1$/S/F$_2$ structures.
We report magnetic and superconducting properties of the modified spin valve system CoOx/Fe1/Cu/Fe2/Cu/Pb. Introduction of a Cu interlayer between Fe2 and Pb layers prevents material interdiffusion process, increases the Fe2/Pb interface transparency, stabilizes and enhances properties of the system. This allowed us to perform a comprehensive study of such heterostructures and to present theoretical description of the superconducting spin valve effect and of the manifestation of the long-range triplet component of the superconducting condensate.
We demonstrate that contrary to the common belief the critical temperature Tc of clean F1/S/F2 spin valves can depend non-monotonically on the angle between the magnetic moments of the ferromagnetic F1 and F2 layers. Depending on the system parameters the minimum of Tc may correspond to parallel, antiparallel or non-collinear mutual orientation of magnetic moments. Such anomalous behavior can reveal itself only provided the ferromagnetic layers differ from each other and it completely disappears in the dirty limit.
The trilayer and pentalayer spin valve structures are revisited to determine the behavior of pair correlations and Josephson current when the magnetic layers are canted at arbitrary angle. The two systems display markedly different behaviors in the center magnetic layer. While the trilayer generates a triplet component that is weakly affected by canting, the pentalayer tunes in singlet pair correlations depending heavily on canting. We also show that a minimum with depleted $m=\pm1$ triplet components, rather than a $0-π$ transition, may be observed in the current profile $I_c(d_F)$ of a trila…
Interface engineering of spin triplet Cooper pairs for spin-valve implementation
School of Physical Sciences, National Institute of Science Education and Research (NISER)（国家科学教育与研究学院物理科学学院）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
The difference in the density of states for up- and down-spin electrons in a ferromagnet (F) results in spin-dependent scattering of electrons at a ferromagnet / nonmagnetic (F/N) interface. In a F/N/F spin-valve, this causes a current-independent difference in resistance ($ΔR$) between antiparallel (AP) and parallel (P) magnetization states. Giant magnetoresistance (GMR), $ΔR = R(AP) - R(P)$, is positive due to increased scattering of majority and minority spin-electrons in the AP-state. If N is substituted for a superconductor (S), there exists a competition between GMR and the superconducti…
We theoretically study a finite size $SF_1NF_2$ spin valve, where a normal metal ($N$) insert separates a thin standard ferromagnet ($F_1$) and a thick half-metallic ferromagnet ($F_2$). For sufficiently thin superconductor ($S$) widths close to the coherence length $ξ_0$, we find that changes to the relative magnetization orientations in the ferromagnets can result in substantial variations in the transition temperature $T_c$, consistent with experiment [Singh et al., Phys. Rev. X 5, 021019 (2015)]. Our results demonstrate that, in good agreement with the experiment, the variations are larges…
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 $ΔT_c$ in the dependence of the Py2-layer thickness $d_{Py2}$. We determined the value of $d_{Py2}$ at which $ΔT_c$ caused by the ordinary spin-valve effect (th…
It has been predicted theoretically that an unconventional odd-frequency spin-triplet component of superconducting order parameter can be induced in multilayered ferromagnetic structures with non-collinear magnetization. In this work we study experimentally nano-scale devices, in which a ferromagnetic spin valve is embedded into a Josephson junction. We demonstrate two ways of in-situ analysis of such Josephson spin valves: via magnetoresistance measurements and via in-situ magnetometry based on flux quantization in the junction. We observe that supercurrent through the device depends on the r…
The theory of superconductor-ferromagnet (S-F) heterostructures with two ferromagnetic layers predicts the generation of a long-range, odd-in-frequency triplet pairing at non-collinear alignment (NCA) of the magnetizations of the F-layers. This triplet pairing has been detected in a Nb/Cu41Ni59/nc-Nb/Co/CoOx spin-valve type proximity effect heterostructure, in which a very thin Nb film between the F-layers serves as a normal conducting (nc) spacer. The resistance of the sample as a function of an external magnetic field shows that for not too high fields the system is superconducting at a coll…
Ferromagnets can sustain supercurrents through the formation of equal spin triplet Cooper pairs and the mechanism of odd-frequency pairing. Since such pairs are not broken by the exchange energy of the ferromagnet, superconducting triplet correlations are long-ranged and spin-polarized, with promises for superconducting spintronics devices. The main challenge is to understand how triplets are generated at the superconductor (S)/ ferromagnet (F) interface. Here we use the concept of a so-called triplet spin valve (TSV) to investigate the conversion of singlets in a conventional superconductor t…
We have studied the dependence of the superconducting (SC) transition temperature on the mutual orientation of magnetizations of Fe1 and Fe2 layers in the spin valve system CoO_x/Fe1/Cu/Fe2/Pb. We find that this dependence is nonmonotonic when passing from the parallel to the antiparallel case and reveals a distinct minimum near the orthogonal configuration. The analysis of the data in the framework of the SC triplet spin valve theory gives direct evidence for the long-range triplet superconductivity arising due to noncollinearity of the two magnetizations.
We study experimentally nanoscale Josephson junctions and Josephson spin-valves containing strong Ni ferromagnets. We observe that in contrast to junctions, spin valves with the same geometry exhibit anomalous Ic(H) patterns with two peaks separated by a dip. We develop several techniques for in-situ characterization of micromagnetic states in our nano-devices, including magnetoresistance, absolute Josephson fluxometry and First-Order-Reversal-Curves analysis. They reveal a clear correlation of the dip in supercurrent with the antiparallel state of a spin-valve and the peaks with two noncollin…
We report the superconducting properties of the Co$_2$Cr$_{1-x}$Fe$_x$Al$_y$/Cu/Ni/Cu/Pb spin-valve structure which magnetic part comprises the Heusler alloy layer HA = Co$_2$Cr$_{1-x}$Fe$_x$Al$_y$ with a high degree of spin polarization (DSP) of the conduction band and the Ni layer of variable thickness. We obtained that the separation between the superconducting transition curves measured for the parallel ($α= 0^\circ$) and perpendicular ($α= 90^\circ$) orientation of the magnetizations of the HA and Ni layers reaches up to 0.5 K ($α$ is an angle between the magnetization of two ferromagneti…
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 $φ_0$-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 …
Superconducting correlations which are long-ranged in magnetic systems have attracted much attention due to their spin-polarization properties and potential use in spintronic devices. Whereas experiments have demonstrated the slow decay of such correlations, it has proven more difficult to obtain a smoking gun signature of their odd-frequency character which is responsible, e.g. for their gapless behavior. We here demonstrate that the magnetic susceptibility response of a normal metal in contact with a superconducting spin-valve provides precisely this signature, namely in form of an anomalous…
A detailed investigation of a superconducting spin-triplet valve is presented. This spin-valve consists of a superconducting film covering a metal with an intrinsic spiral magnetic order, which could result from competing isotropic exchanges or, if the crystal lattice breaks central symmetry, from asymmetric Dzyaloshinskii-Moriya exchange. Depending on the anisotropy, such a metal may change its magnetization either from a spiral to uniform order, as seen in Ho and Er, or in the direction of the spiral itself, as in crystals of the B20-type structure (such as MnSi, (Fe,Co)Si, FeGe, etc.). The …
Spin-singlet Cooper pairs consisting of two electrons with opposite spins cannot directly penetrate from a superconductor to a half-metal (fully spin polarized ferromagnets) which blocks the superconducting proximity effect between these materials. In this paper we demonstrate that, nevertheless, two half-metallic layers electrically coupled to the superconducting film substantially affect its critical temperature and produce the spin valve effect. Within the tight-binding model for the atomically thin multilayered spin valves we show that depending on the details of the electron energy spectr…
We propose a superconducting spin-triplet valve, which consists of a superconductor and an itinerant magnetic material, with the magnet showing an intrinsic non-collinear order characterized by a wave vector that may be aligned in a few equivalent preferred directions under control of a weak external magnetic field. Re-orienting the spiral direction allows one to controllably modify long-range spin-triplet superconducting correlations, leading to spin-valve switching behavior. Our results indicate that the spin-valve effect may be noticeable. This bilayer may be used as a magnetic memory eleme…
We investigate SFF structures (S-superconductor, F feromagnetic metal) with noncollinear magnetizations of F films with arbitrary transparency of FF interface. We show the existence of phase slips both at SF and FF interfaces which manifest themselves in the anomalous dependence of the spin-triplet correlations on misorientation angle between magnetization vectors in the F-layers. We discuss how these effects can be observed in experiments with Josephson $π$-junctions.
We present a model for fully developed triplet proximity effect in superconductor-ferromagnet heterostructures. Within the circuit-theory approximation, we evaluate the Green's functions, the density of states, and the Josephson current that depend essentially on the magnetization configuration.
Coupling a conventional s-wave superconductor to a ferromagnet allows, via the proximity effect, to generate superconducting triplet correlations. This feature can be employed to achieve a superconducting triplet spin-valve effect in superconductor-ferromagnet (SF) hybrid structures, for example by switching the magnetizations of the ferromagnets between parallel and antiparallel configurations in F1SF2 and SF1F2 trilayers, or in SF bilayers with both Rashba and Dresselhaus SOC. It was recently reported that geometric curvature can control the generation of long ranged triplets. We use this pr…
Heterostructures consisting of a cuprate superconductor YBa2Cu3O7x and a ruthenate/manganite (SrRuO3/La0.7Sr0.3MnO3) spin valve have been studied by SQUID magnetometry, ferromagnetic resonances and neutron reflectometry. It was shown that due to the influence of magnetic proximity effect a magnetic moment is induced in the superconducting part of heterostructure and at the same time the magnetic moment is suppressed in the ferromagnetic spin valve. The experimental value of magnetization induced in the superconductor has the same order of magnitude with the calculations based on the induced ma…
Transport measurements are presented on thin-film superconducting spin-valve systems, where the controlled non-collinear arrangement of two ferromagnetic Co layers can be used to influence the superconducting state of Nb. We observe a very clear oscillation of the superconducting transition temperature with the relative orientation of the two ferromagnetic layers. Our measurements allow us to distinguish between the competing influences of domain averaging, stray dipolar fields and the formation of superconducting spin triplets. Domain averaging is shown to lead to a weak enhancement of transi…
We study the critical temperature T_c of SFF trilayers (S is a singlet superconductor, F is a ferromagnetic metal), where the long-range triplet superconducting component is generated at noncollinear magnetizations of the F layers. We demonstrate that T_c can be a nonmonotonic function of the angle αbetween the magnetizations of the two F layers. The minimum is achieved at an intermediate α, lying between the parallel (P, α=0) and antiparallel (AP, α=π) cases. This implies a possibility of a "triplet" spin-valve effect: at temperatures above the minimum T_c^{Tr} but below T_c^{P} and T_c^{AP},…
Using a self-consistent Bogoliubov-de Gennes approach, we theoretically study the proximity-induced density of states (DOS) in clean SFF spin-valves with noncollinear exchange fields. Our results clearly demonstrate a direct correlation between the presence of a zero energy peak (ZEP) in the DOS spectrum and the persistence of spin-1 triplet pair correlations. By systematically varying the geometrical and material parameters governing the spin-valve, we point out to experimentally optimal system configurations where the ZEPs are most pronounced, and which can be effectively probed via scanning…
We have measured the transport properties of Ferromagnet - Superconductor nanostructures, where two superconducting aluminum (Al) electrodes are connected through two ferromagnetic iron (Fe) ellipsoids in parallel. We find that, below the superconducting critical temperature of Al, the resistance depends on the relative alignment of the ferromagnets' magnetization. This spin-valve effect is analyzed in terms of spin accumulation in the superconducting electrode submitted to inverse proximity effect.
We investigate inverse proximity effects in a spin-triplet superconductor (TSC) interfaced with a ferromagnet (FM), assuming different types of magnetic profiles and chiral or helical pairings. The region of the coexistence of spin-triplet superconductivity and magnetism is significantly influenced by the orientation and spatial extension of the magnetization with respect to the spin configuration of the Cooper pairs, resulting into clearcut anisotropy signatures. A characteristic mark of the inverse proximity effect arises in the induced spin-polarization at the TSC interface. This is unexpec…
The discovery of noncentrosymmetric superconductors, such as CePt$_3$Si, and chiral superconductors, such as Sr$_2$RuO$_4$, calls for experimental methods to identify the presence of spin-triplet pairing. We here demonstrate a method which accomplishes this in an appealingly simple manner: a spin-sensitive proximity effect in a ferromagnet$\mid$triplet superconductor bilayer. It is shown how the orientation of the field can be used to unambiguously distinguish between different spin-triplet states. Moreover, the proximity effect becomes long-ranged in spite of the presence of an exchange field…
Thin film junctions and bilayers of the doped topological insulator $\rm Bi_2Se_3$ and the s-wave superconductor NbN were found to exhibit conductance spectra with prominent zero bias and coherence peaks. Various tunneling models with different pair potentials have failed to fit our data, except for the triplet $p_x+ip_y$ pair potential, which breaks time reversal symmetry, but yielded reasonably good fits. This provides evidence for proximity induced triplet superconductivity in the $\rm Bi_2Se_3$ layer near the interface with the NbN film.
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 STM-measurements. Motivated by recent experiments on S$\mid$N$\mid$S graphene Josephson junctions, we also study the spectrum of Andreev-bound states formed i…
We study the impact of the long-range spin-triplet proximity effect on the density of states (DOS) in planar SF1F2S Josephson junctions that consist of conventional superconductors (S) connected by two metallic monodomain ferromagnets (F1 and F2) with transparent interfaces. We determine the electronic DOS in F layers and the Josephson current for arbitrary orientation of the magnetizations using the solutions of Eilenberger equations in the clean limit and for a moderate disorder in ferromagnets. We find that fully developed long-range proximity effect can occur in highly asymmetric ferromagn…
Considerable evidence for proximity-induced triplet superconductivity on the ferromagnetic side of a superconductor-ferromagnet (S-F) interface now exists; however, the corresponding effect on the superconductor side has hardly been addressed. We have performed scanning tunneling spectroscopy measurements on NbN superconducting thin films proximity coupled to the half-metallic ferromagnet La2/3Ca1/3MnO3 (LCMO) as a function of magnetic field. We have found that at zero and low applied magnetic fields the tunneling spectra on NbN typically show an anomalous gap structure with suppressed coheren…
In diffusive Josephson junctions the phase-difference $ϕ$ between the superconductors strongly influences the spectroscopic features of the layer separating them. The observation of a uniform minigap and its phase modulation were only recently experimentally reported, demonstrating agreement with theoretical predictions up to now - a vanishing minigap at $ϕ=π$. Remarkably, we find that in the presence of intrinsic spin-orbit coupling a giant proximity effect due to spin-triplet Cooper pairs can develop at $ϕ=π$, in complete contrast to the suppressed proximity effect without spin-orbit couplin…
We study spin switching effects in finite-size superconducting multivalve structures. We examine $\rm F_1F_2SF_3$ and $\rm F_1F_2SF_3F_4$ hybrids where a singlet superconductor ($\rm S$) layer is sandwiched among ferromagnet ($\rm F$) layers with differing thicknesses and magnetization orientations. Our results reveal a considerable number of experimentally viable spin valve configurations that lead to on-off switching of the superconducting state. For $\rm S$ widths on the order of the superconducting coherence length $ξ_0$, non-collinear magnetization orientations in adjacent $\rm F$ layers …
Superconductor/ferromagnet (S/F) spin valve effect theories based on the S/F proximity phenomenon assume that the superconducting transition temperature Tc of F1/F2/S or F1/S/F2 trilayers for parallel magnetizations of the F1- and F2-layers (TcP) are smaller than for the antiparallel orientations (TcAP). Here, we report for CoOx/Fe1/Cu/Fe2/In multilayered systems with varying Fe2-layer thickness the sign-changing oscillating behavior of the spin valve effect ΔTc=TcAP-TcP. Our measurements revealed the full direct spin valve effect with TcAP>TcP for Fe2-layer thickness dFe2<1 nm and the full in…
Scanning tunneling spectroscopy measurements conducted on epitaxially grown bilayers of half-metallic ferromagnetic La2/3Ca1/3MnO3 (LCMO) on superconducting (SC) (100)YBa2Cu3O7-delta (YBCO) reveal long-range penetration of superconducting order into the LCMO. This anomalous proximity effect manifests itself in the tunneling spectra measured on the LCMO layer as gaps and zero bias conductance peaks. Remarkably, these proximity-induced spectral features were observed for bilayers with LCMO thickness of up to 30 nm, an order of magnitude larger than the expected ferromagnetic coherence length in …
In this paper, we study the quantum transport at the Ferromagnet$|$Noncentrosymmetric Superconductor (F$|$NCSC) interface of an F$|$S$|$F spin valve. In this context, we investigate the tunneling conductance and its dependence on Rashba Spin-Orbit Coupling (RSOC) considering different barrier strength and a significant Fermi Wave-vector Mismatch (FWM) at the ferromagnetic and superconducting regions. The study is carried out for different magnetization orientations and its strength. We developed Bogoliubov de Gennes (BdG) Hamiltonian introducing RSOC and exchange interaction for such an hybrid…
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) junction 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 calcula…
We show that the peculiarities of the electron band structure strongly affect the spin-valve effect in heterostructures consisting of a superconductor (S) and two ferromagnetic layers F1 and F2. For the S/F1/F2 systems the energy shift between the electron bands in the S and F2 layers determines wether the critical temperature $T_c$ of the superconductor increases or decreases as a function of the angle $θ$ between the magnetic moments in the ferromagnets. In the case of half-metallic F2 layer the type of the spin-valve effect becomes dependent on the position of the only occupied spin-band an…
Competition between superconducting and ferromagnetic ordering at interfaces between ferromagnets (F) and superconductors (S) gives rise to several proximity effects such as odd-triplet superconductivity and spin-polarized supercurrents. A prominent example of an S/F proximity effect is the spin switch effect (SSE) observed in S/F/N/F superconducting spin-valve multilayers, in which the superconducting transition temperature T$_c$ is controlled by the angle $ϕ$ between the magnetic moments of the F layers separated by a nonmagnetic metallic spacer N. Here we present an experimental study of SS…
We report measurements of the superconducting transition temperature, $T_c$, in CoO/Co/Cu/Co/Nb multilayers as a function of the angle $α$ between the magnetic moments of the Co layers. Our measurements reveal that $T_c(α)$ is a nonmonotonic function, with a minimum near $α=π/{2}$. Numerical self-consistent solutions of the Bogoliubov - de Gennes equations quantitatively and accurately describe the behavior of $T_c$ as a function of $α$ and layer thicknesses in these superconductor / spin-valve heterostructures. We show that experimental data and theoretical evidence agree in relating $T_c(α)$…
We study the proximity effect in SF'(AF)F'S and SF'(F)F'S planar junctions, where S is a clean conventional (s-wave) superconductor, while F' 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 F' 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 be…
Superconducting spin valves based on the superconductor/ferromagnet (S/F) proximity effect are considered to be a key element in the emerging field of superconducting spintronics. Here, we demonstrate the crucial role of the morphology of the superconducting layer in the operation of a multilayer S/F1/F2 spin valve. We study two types of superconducting spin valve heterostructures, with rough and with smooth superconducting layers, using transmission electron microscopy in combination with transport and magnetic characterization. We find that the quality of the S/F interface is not critical fo…
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. I…
Applying the linearized Usadel equations, we consider the nucleation of superconductivity in multiply connected mesoscopic superconductor/ferromagnet (S/F) hybrids such as a thin superconducting ring on a ferromagnet with a uniform in-plane magnetization M and a spin-active S/F interface. We demonstrate that the exchange field in F provokes a switching between superconducting states with different vorticities which may increase the critical temperature ( Tc ) of the superconductor in a magnetic field. We study the interplay between oscillations in Tc due to the Little--Parks effect and oscilla…
Spin-valve structures in which a change of magnetic configuration is responsible for magnetoresistance have enabled impressive advances in spintronics, focusing on magnetically storing and sensing information. However, this mature technology also offers versatile control of the underlying fringing fields and entirely different applications by realizing topologically-nontrivial states. Together with proximity-induced superconductivity in a two-dimensional electron gas, these fringing fields realized in commercially-available spin valves could control Majorana bound states (MBS). Detailed suppor…
Ferromagnetic spin valves offer the key building blocks to integrate giant- and tunneling-magnetoresistance effects into spintronics devices. Starting from a generalized Blonder-Tinkham-Klapwijk approach, we theoretically investigate the impact of interfacial Rashba and Dresselhaus spin-orbit couplings on the tunneling conductance, and thereby the magnetoresistance characteristics, of ferromagnet/superconductor/ferromagnet spin-valve junctions embedding thin superconducting spacers between the either parallel or antiparallel magnetized ferromagnets. We focus on the unique interplay between usu…
Electronic transport and magnetization measurements were performed on La$_{0.7}$Ca$_{0.3}$MnO$_3$/YBa$_2$Cu$_3$O$_{7-δ}$ (LCMO/YBCO) bilayers below the superconducting transition temperature in order to study the interaction between magnetism and superconductivity. This study shows that a substantial number of weakly pinned vortices are induced in the YBCO layer by the large out-of-plane stray field in the domain walls. Their motion gives rise to large dissipation peaks at the coercive field. The angular dependent magnetoresistance (MR) data reveal the interaction between the stripe domain str…
In the traditional view, the magnetic moment appearing in the superconducting region is induced by equal-spin triplet superconducting correlations in superconductor ($S$) ferromagnet ($F$) heterostructure with noncollinear magnetization. In this paper, we represent that in $NSF_1F_2$ ($N$--normal-metal) spin-valve structure the induced magnetic moment emerging in both the $S$ and $N$ regions can also be generated by Cooper pair splitting: one electron coherently tunnels from the $S$ layer into the $F_1$ layer, and the other one stays in the $S$ layer or tunnels into the $N$ layer. Two electron…
Superconductor/ferromagnet/superconductor heterostructures exhibit a so-called long-range proximity effect provided some layers of conical magnet Holmium are included in the respective interface regions. The Ho layers lead to a spin-flip process at the interface generating equal-spin spin-triplet pairing correlations in the ferromagnet. These equal-spin spin-triplet pairing correlations penetrate much further into the heterostructure compared to the spin-singlet and unequal-spin spin-triplet correlations which occur in the absence of Ho. Here we present calculations of this effect based on the…
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 superc…
At the interface between a superconductor and a ferromagnetic metal spin-singlet Cooper pairs can penetrate into the ferromagnetic part of the heterostructure with an oscillating and decaying spin-singlet Cooper pair density. However, if the interface allows for a spin-mixing effect, equal-spin spin-triplet Cooper pairs can be generated that can penetrate much further into the ferromagnetic part of the heterostructure, known as the long-range proximity effect. Here, we present results of spin-mixing based on self-consistent solutions of the microscopic Bogoliubov-de Gennes equations incorporat…
