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}, the system is superconducting only in the vicinity of the collinear orientations. At certain parameters, we predict a reentrant T_c(α) behavior. At the same time, considering only the P and AP orientations, we find that both the "standard" (T_c^{P} < T_c^{AP}) and "inverse" (T_c^{P} > T_c^{AP}) switching effects are possible depending on parameters of the system.
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…
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.
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…
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…
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…
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.
A superconductor with a spin-split excitation spectrum behaves as an ideal ferromagnetic spin-injector in a tunneling junction. It was theoretical predicted that the combination of two such spin-split superconductors with independently tunable magnetizations, may be used as an ideal $absolute$ spin-valve. Here we report on the first switchable superconducting spin-valve based on two EuS/Al bilayers coupled through an aluminum oxide tunnel barrier. The spin-valve shows a relative resistance change between the parallel and antiparallel configuration of the EuS layers up to 900% that demonstrates…
A superconducting double spin valve device is proposed. Its operation takes advantage of the interplay between the spin-filtering effect of ferromagnetic insulators and superconductivity-induced out-of-equilibrium transport. Depending on the degree of nonequilibrium, extraordinary large tunnel magnetoresistance as large as 10^2...10^6% can be obtained for realistic material parameters, and it can be tuned over several orders of magnitude under proper voltage biasing and temperature. The relevance of this setup for low-temperature applications is further discussed.
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）
A hybrid ferromagnet-superconductor spin valve is proposed. Its operation relies on the interplay between nonequilibrium transport and proximity-induced exchange coupling in superconductors. Huge tunnel magnetoresistance values as large as some 10^6% can be achieved in suitable ferromagnet-superconductor combinations under proper voltage biasing. The controllable spin-filter nature of the structure combined with its intrinsic simplicity make this setup attractive for low-temperature spintronic applications where reduced power dissipation is an additional requirement.
Electrons in a quantum-dot spin valve, consisting of a single-level quantum dot coupled to two ferromagnetic leads with magnetizations pointing in arbitrary directions, experience an exchange field that is induced on the dot by the interplay of Coulomb interaction and quantum fluctuations. We show that a third, superconducting lead with large superconducting gap attached to the dot probes this exchange field very sensitively. In particular, we find striking signatures of the exchange field in the symmetric component of the supercurrent with respect to the bias voltage applied between the ferro…
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 investigated CuNi/Nb/CuNi trilayers, as have been recently used as the core structure of a spin-valve like device [J. Y. Gu et al., Phys. Rev. Lett. 89, 267001 (2002)] to study the effect of magnetic configurations of the CuNi layers on the critical temperature, Tc, of the superconducting Nb. After reproducing a Tc shift of a few mK, we have gone on to explore the performance limits of the structure. The results showed the Tc shift we found to be quite close to the basic limits of this particular materials system. The ratio between the thickness and the coherence length of the supercon…
The spin valve effect for the superconducting current based on the superconductor/ferromagnet proximity effect has been studied for a CoO_x/Fe1/Cu/Fe2/Cu/Pb multilayer. The magnitude of the effect $ΔT_c$ = T_c^{AP} - T_c^{P}, where T_c^{P} and T_c^{AP} are the superconducting transition temperatures for the parallel (P) and antiparallel (AP) orientation of magnetizations, respectively, has been measured for different thicknesses of the Fe1 layer d_{Fe1}. The obtained dependence of the effect on d_{Fe1} reveals that $ΔT_c$ can be increased in comparison with the case of a half-infinite Fe1 laye…
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…
Here, we present a study on Si(111)/\-Ta($150$Å)/\-IrMn($150$Å)/\-NiFe($50$Å)/\-Nb($x$)/\-NiFe($50$Å)/\-Ta($50$Å) and Si(111)/\-Ta($150$Å)/\-NiFe($50$Å)/\-Nb($x$)/\-NiFe($50$Å)/\-IrMn($150$Å)/\-Ta($50$Å) spin-valves with $x=100$ to $500$Å. For both sample families, above a specific critical thickness of the Nb-layer and below $T_c$, the superconducting Nb-layer contributes strongly to the magnetization. These systems show an anomalous hysteresis loop in the magnetization of the superconducting layer; the hysteresis loop is similar to what is generally expected from hard superconductors and man…
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…
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 m…
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 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…
The resistance of a ferromagnet/superconductor/ferromagnet (F/S/F) spin valve near its superconducting transition temperature, $T_c$, depends on the state of magnetization of the F layers. This phenomenon, known as spin switch effect (SSE), manifests itself as a resistance difference between parallel ($R_P$) and antiparallel ($R_{AP}$) configurations of the F layers. Both standard ($R_{P}>R_{AP}$) and inverse ($R_{P}<R_{AP}$) SSE have been observed in different superconducting spin valve systems, but the origin of the inverse SSE was not understood. Here we report observation of a coexistence …
We report a comparative analysis and theoretical description of the superconducting properties of two spin-valve-valve structures containing the Heusler alloy Co$_2$Cr$_{1-x}$Fe$_x$Al$_{y}$ as one of two ferromagnetic (F1 or F2) layers of the F1/F2/S structure, where S stands for the superconducting Pb layer. In our experiments we used the Heusler alloy layer in two roles: as a weak ferromagnet on the place of the F2 layer and as a half-metal on the place of the F1 layer. In the first case, we obtained a large ordinary superconducting spin-valve effect $ΔT_c$ assisted by the triplet supercondu…
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…
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 …
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 …
Using a Keldysh formalism, we study supercurrent (SC) transport in several types of diffusive ferromagnet(F)/superconductor(S) configurations. We separate out the even- and odd-frequency components and identify the relative contributions from the singlet and triplet channels. We first consider 1D Josephson structures consisting of a uniform SFFS structure and a trilayer SFFFS configuration. Our results demonstrate that for SCs flowing perpendicular to the FF interfaces, incorporating a conical texture yields the most effective way to observe the signatures of the long-ranged SC. We also consid…
We consider the non-local quantum transport properties of a graphene superconducting spin-valve. It is shown that one may create a spin-switch effect between perfect elastic co-tunneling (CT) and perfect crossed Andreev-reflection (CAR) for all bias voltages in the low-energy regime by reversing the magnetization direction in one of the ferromagnetic layers. This opportunity arises due the possibility of tuning the local Fermi-level in graphene to values equivalent to a weak, magnetic exchange splitting, thus reducing the Fermi surface for minority spins to a single point and rendering graphen…
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.
Spin-valve structures are usually associated with the ability to modify the resistance of electrical currents. We here demonstrate a profoundly different effect of a spin-valve. In combination with a topological insulator and superconducting materials, we show that a spin-valve can be used to toggle quantum vortices in and out of existence. In the antiparallel configuration, the spin-valve causes superconducting vortex nucleation. In the parallel configuration, however, no vortices appear. This switching effect suggests a new way to control quantum vortices.
We have studied superconducting properties of the spin-valve thin layer heterostructures CoO$_x$/F1/Cu/F2/Cu/Pb where the ferromagnetic F1 layer was standardly made of Permalloy whereas for the F2 layer we have taken a specially prepared film of the Heusler alloy Co$_2$Cr$_{1-x}$Fe$_x$Al with a small degree of spin polarization of the conduction band. The heterostructures demonstrate a significant superconducting spin-valve effect, i.e. a complete switching on and off of the superconducting current flowing through the system by manipulating the mutual orientations of the magnetization of the F…
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.
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…
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…
The article considers the simulation of the formation of a multilayer nanocomposite, the combination of elements of which gives rise to the effect of a spin valve. The relevance and importance of the effects in the field of spintronics and related materials and devices are described. The composition and atomic structure of individual layers of the multilayer nanocomposite, as well as the composition and morphology of the interface of the nanocomposite layers are the object of research. A sample with a periodic superconductor - ferromagnetic structure consisting of more than 20 alternating laye…
We study the spin-transfer torque and magnetoresistance of a ferromagnet$\mid$superconductor$\mid$ferromagnet spin-valve, allowing for an arbitrary magnetization misorientation and treating both s-wave and d-wave symmetries of the superconductor. We take fully into account Andreev reflection and also the spin-triplet correlations that are generated when the magnetizations are non-collinear. It is found that the torque and magnetoresistance are both strongly enhanced when topological zero-energy states are present at the interfaces, which is the case for d-wave superconductors with a crystallog…
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…
We establish that Majorana fermions on the boundary of topological superconductors have only spin-triplet superconducting correlations independent of whether the bulk superconducting gap is spin singlet or triplet. This is universal for time-reversal broken (respected) topological superconductors (TSCs) with an odd number of (pairs of) Majorana fermions on the boundary. Consequently, resonant Andreev reflection induced by Majorana fermions only occurs in spin-triplet channels and always injects spin-triplet Cooper pairs into the leads. This spin-triplet condensate results in a spin-orbit coupl…
We study graphene ferromagnet/superconductor/ferromagnet (F/S/F) nanostructures via a microscopic self-consistent Dirac Bogoliubov-de Gennes formalism. We show that as a result of proximity effects, experimentally accessible spin switching phenomena can occur as one tunes the Fermi level $μ_F$ of the F regions or varies the angle $θ$ between exchange field orientations. Superconductivity can then be switched on and off by varying either $θ$ or $μ_F$ (a spin-controlled superconducting graphene switch). The induced equal-spin triplet correlations in S can be controlled by tuning $μ_F$, effective…
The Andreev current and the subgap conductance in a superconductor/ insulator/ ferromagnet (SIF) structure in the presence of a small spin-splitting field show novel interesting features (A. Ozaeta et al., Phys. Rev. B 86, 060509(R), 2012). For example, the Andreev current at zero temperature can be enhanced by a spin-splitting field h, smaller than the superconducting gap, as has been recently reported by the authors. Also at finite temperatures the Andreev current has a peak for values of the spin-splitting field close to the superconducting gap. Finally, the differential subgap conductance …
Superconducting spintronics has emerged in the last decade as a promising new field that seeks to open a new dimension for nanoelectronics by utilizing the internal spin structure of the superconducting Cooper pair as a new degree of freedom. Its basic building blocks are spin-triplet Cooper pairs with equally aligned spins, which are promoted by proximity of a conventional superconductor to a ferromagnetic material with inhomogeneous macroscopic magnetization. Using low-energy muon spin rotation experiments, we find an entirely unexpected novel effect: the appearance of a magnetization in a t…
Superconductivity and ferromagnetism are antagonistic forms of order, and rarely coexist. Many interesting new phenomena occur, however, in hybrid superconducting/ferromagnetic systems. For example, a Josephson junction containing a ferromagnetic material can exhibit an intrinsic phase shift of pi in its ground state for certain thicknesses of the material. Such "pi-junctions" were first realized experimentally in 2001, and have been proposed as circuit elements for both high-speed classical superconducting computing and for quantum computing. Here we demonstrate experimentally that the phase …
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…
Valley Valves at Domain Walls in Symmetry-Broken Rhombohedral Graphene
Florida State University（佛罗里达州立大学）；National High Magnetic Field Laboratory（国家高磁场实验室）；Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（马德里材料科学研究所，西班牙国家研究委员会）；IMDEA Nanoscience（IMDEA纳米科学研究所）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；University of Pennsylvania（宾夕法尼亚大学）
