We show that a supercurrent carried by spinless singlet Cooper pairs can induce a spin accumulation in the normal metal interlayer of a Josephson junction. This phenomenon occurs when a nonequilibrium spin-energy mode is excited in the normal metal, for instance by an applied temperature gradient between ferromagnetic electrodes. Without supercurrent, the spin accumulation vanishes in the Josephson junction. With supercurrent, a spatially antisymmetric spin accumulation is generated that can be measured by tunneling to a polarized detector electrode. We explain the physical origin of the induced spin accumulation by the combined effect of a Doppler shift induced by a flow of singlet Cooper pairs, and the spin-energy mode excited in the normal metal. This effect shows that spin control is possible even with singlet Cooper pairs in conventional superconductors, a finding which could open new perspectives in superconducting spintronics.
The lengthscale over which supercurrent from conventional BCS, $s$-wave, superconductors ($S$) can penetrate an adjacent ferromagnetic ($F$) layer depends on the ability to convert singlet Cooper pairs into triplet Cooper pairs. Spin aligned triplet Cooper pairs are not dephased by the ferromagnetic exchange interaction, and can thus penetrate an $F$ layer over much longer distances than singlet Cooper pairs. These triplet Cooper pairs carry a dissipationless spin current and are the fundamental building block for the fledgling field of superspintronics. Singlet-triplet conversion by inhomogen…
We study the supercurrent in a superconductor-ferromagnet-superconductor heterostructure containing a noncollinear magnetic domain in the ferromagnetic region. It is demonstrated that the magnetic domain can lead to a spin-flip process, which can reverse the spin orientations of the singlet Cooper pair propagating through the magnetic domain region. If the ferromagnetic layers on both sides of magnetic domain have the same features, the long-range proximity effect will take place. That is because the singlet Cooper pair will create an exact phase-cancellation effect and gets an additional $π$ …
Employing a spin-parameterized Kleldysh-Usadel technique for the diffusive regime, we demonstrate that even in the low proximity limit, considerable long-ranged triplet supercurrents can be effectively generated by spin-singlet supercurrents flowing \textit{parallel} to the interfaces of uniform double ferromagnet interlayers with noncollinear exchange fields "{\it independent}" of actual junction geometry. The triplet supercurrents are found to be most pronounced when the thicknesses of the ferromagnet strips are unequal. To experimentally verify this generic phenomenon, we propose an accessi…
Josephson junctions with s-wave superconductors (S) and multiple ferromagnetic (F) layers carry spin-triplet supercurrents in the presence of magnetically inhomogeneous spin-mixer interfaces. Here, we report magnetic Josephson junctions with exchange-spring and double exchange-spring ("spin-mixer") Co/Py interfaces. At the Co/Py interface, exchange coupling is strong with respect to the magnetic anisotropy of Py and so, depending on the direction and magnitude of an external magnetic field, a non-collinear magnetic structure forms in Py creating the necessary magnetic inhomogeneity for singlet…
We study the Josephson effect in a triplet superconductor--ferromagnet--singlet superconductor junction. We show that the interaction of tunneling Cooper pairs with the interface magnetization can permit a Josephson current at the lowest order of a tunneling Hamiltonian perturbation theory. Two conditions must be satisfied for this to occur: the magnetization of the ferromagnet has a component parallel to the ${\bf d}$-vector of the triplet superconductor, and the gaps of the superconductors have the same parity with respect to the interface momentum. The resulting charge current displays an u…
We study the Andreev bound states in a Josephson junction between a singlet and a triplet superconductors. Because of the mismatch in the spin symmetries of pairing, the energies of the spin up and down quasiparticles are generally different. This results in imbalance of spin populations and net spin accumulation at the junction in equilibrium. This effect can be detected using probes of local magnetic field, such as the scanning SQUID, Hall, and Kerr probes. It may help to identify potential triplet pairing in $\rm(TMTSF)_2X$, $\rm Sr_2RuO_4$, and oxypnictides.
A magnetic adatom chain, proximity coupled to a conventional superconductor with spin-orbit coupling, exhibits locally an odd-parity, spin-triplet pairing amplitude. We show that the singlet-triplet junction, thus formed, leads to a net spin accumulation in the near vicinity of the chain. The accumulated spins are polarized along the direction of the local $\mathbf{d}$-vector for triplet pairing and generate an enhanced persistent current flowing around the chain. The spin polarization and the "supercurrent" reverse their directions beyond a critical exchange coupling strength at which the sin…
We study spin-polarized quasiparticle transport in a mesoscopic superconductor with a spin- splitting field in the presence of co-flowing supercurrent. In such a system, the nonequilibrium state is characterized by charge, spin, energy and spin energy modes. Here we show that in the presence of both spin splitting and supercurrent, all these modes are mutually coupled. As a result, the supercurrent can convert charge imbalance, that in the presence of spin splitting decays on a relatively short scale, to a long-range spin accumulation decaying only via inelastic scattering. This effect enables…
We study a quantum dot Josephson junction inside an Aharonov-Bohm environment. The geometry is modeled by an Anderson impurity coupled to two directly-linked BCS leads. We illustrate that the well-established picture of the low-energy physics being governed by an interplay of two distinct (singlet and doublet) phases is still valid for this interferometric setup. The phase boundary depends, however, non-monotonically on the coupling strength between the superconductors, causing the system to exhibit re-entrance behavior and multiple phase transitions. We compute the zero-temperature Josephson …
A useful experimental signature of the ordinary spin Hall effect is the spin accumulation it produces at the sample edges. The superspin Hall current [Phys. Rev. B 96, 094512 (2017)] is a transverse equilibrium spin current which is induced by a charge supercurrent. We study the superspin Hall current numerically, and find that it does not give rise to a similar edge magnetization. We also predict and numerically confirm the existence of the inverse superspin Hall effect, which produces a transverse charge supercurrent in response to an equilibrium spin current. We verify the existence of the …
We show that all the singlet even-frequency, singlet odd-frequency, triplet even-frequency and triplet odd-frequency pairings, and together with the corresponding order parameters (gaps) can be realized in InSb (110) spin-orbit-coupled quantum well in proximity to s-wave superconductor in Fulde-Ferrell-Larkin-Ovchinnikov phase or with a supercurrent. It is revealed that with the singlet even-frequency order parameter induced by the proximity effect, triplet even-frequency pairing is induced due to the broken spin-rotational symmetry by the spin-orbit coupling. Since the translational symmetry …
We study heterostructures of singlet superconductors (SC) and strongly spin-polarized ferromagnets (sFM) and show that a relative phase arises between the superconducting proximity amplitudes in the two ferromagnetic spin bands. We find a tunable pure spin supercurrent in a sFM contacted with only one SC electrode. We show that Josephson junctions are most effective for a spin polarization $P\sim 0.3$, and that critical currents for positive and negative bias differ for a high transmission Josephson junction, due to a relative phase between single and double pair transmission.
We theoretically demonstrate that the vortex supercurrent can be reversed by odd-frequency Cooper pairs accompanied by surface Andreev bound states. The surface of a three-dimensional superconductor pierced by a flux quantum is considered. We compare the vortex supercurrents near the surface of the spin-singlet $s$-wave and spin-triplet $p_z$-wave superconductors using quasiclassical Eilenberger theory, where the surface is perpendicular to the $z$ direction. We demonstrate that the vortex supercurrent near the surface of a $p_z$-wave superconductor is reversed compared to those far from the s…
Magnetic inhomogeneity at a superconductor (S)/ferromagnet (F) interface converts spin-singlet Cooper pairs into spin-one triplet pairs. These pairs are immune to the pair-breaking exchange field in F and support a long-range proximity effect. Although recent experiments have confirmed the existence of spin-polarised triplet supercurrents in S-F-S Josephson junctions, reversible control of the supercurrent has been impossible because of the robust pre-configured nature of the inhomogeneity. Here we use a barrier comprising three F layers whose relative magnetic orientation, and hence the inter…
In general, conventional superconductivity should not occur in a ferromagnet, though it has been seen in iron under pressure. Moreover, theory predicts that the current is always carried by pairs of electrons in a spin singlet state, so conventional superconductivity decays very rapidly when in contact with a ferromagnet, which normally prohibits the existence of singlet pairs. It has been predicted that this rapid spatial decay would not occur when spin triplet superconductivity could be induced in the ferromagnet. Here we report a Josephson supercurrent through the strong ferromagnet CrO2, f…
An inhomogeneous magnetic exchange field at a superconductor/ferromagnet interface converts spin-singlet Cooper pairs to a spin-aligned (i.e. spin-polarized) triplet state. Although the decay envelope of such triplet pairs within ferromagnetic materials is well studied, little is known about their decay in non-magnetic metals and superconductors, and in particular in the presence of spin-orbit coupling (SOC). Here we investigate devices in which triplet supercurrents are injected into the s-wave superconductor Nb. In the normal state of Nb, triplet supercurrents decay over a distance of 5 nm, …
Enhancement of Josephson Supercurrent in a $π$-Junction state by Chiral Antiferromagnetism
Hefei National Laboratory（合肥国家实验室）；Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Intense Laser Application Technology, and College of Engineering Physics, Shenzhen Technology University（深圳技术大学超快激光与先进材料技术重点实验室、强激光应用技术中心及工程物理学院）；Institute for Theoretical Physics and Astrophysics, University of Würzburg（维尔茨堡大学理论物理与天体物理研究所）；Würzburg-Dresden Cluster of Excellence ct.qmat（维尔茨堡-德累斯顿卓越集群ct.qmat）；School of Emerging Technology, University of Science and Technology of China（中国科学技术大学新兴技术学院）
By now it is known that in an s-wave superconductor-ferromagnet-superconductor ($SFS$) structure the supercurrent induced by spin singlet pairs can only transmit a short distance of the order of magnetic coherence length. The long-range supercurrent, taking place on the length scale of the normal metal coherence length, will be maintained by equal-spin triplet pairs, which can be generated by magnetic inhomogeneities in the system. In this paper, we show an unusual long-range supercurrent, which can take place in clean $SF_1F_2S$ junction with non-parallel orientation of magnetic moments. The …
We propose a mechanism whereby spin supercurrents can be manipulated in superconductor/ferromagnet proximity systems via nonequilibrium spin injection. We find that if a spin supercurrent exists in equilibrium, a nonequilibrium spin accumulation will exert a torque on the spins transported by this current. This interaction causes a new spin supercurrent contribution to manifest out of equilibrium, which is proportional to and polarized perpendicularly to both the injected spins and equilibrium spin current. This is interesting for several reasons: as a fundamental physical effect; due to possi…
The experimental achievements during the past year in demonstrating the existence of long-ranged spin-triplet supercurrents in ferromagnets proximity coupled to singlet superconductors open up the possibility for new interesting physics and applications [for a review, see M. Eschrig, Phys. Today 64(1), 43 (2011)]. Our group reported the injection of triplet supercurrents into a magnetically uniform ferromagnet (Co) by sandwiching it between two helimagnet/superconductor (Ho/Nb) bilayers to form a Nb/Ho/Co/Ho/Nb-type Josephson device. In the function of the Ho layer thicknesses, the supercurren…
We consider a Josephson junction with an arbitrary transmission coefficient $\mathcal{D}$ between a singlet and a triplet superconductor with the latter order parameter characterized by a d-vector of the form ($k_x\hat{y}-k_y\hat{x}$). Various quantities such as the tunnelling current, spin accumulation, and spin current are calculated via the quasiclassical Green's functions. We also present a symmetry argument on the existence of these quantities and their dependencies on the phase difference across the junction. A physical picture is also given in terms of the Andreev states near the juncti…
The Josephson current through a long s-wave superconductor/weak ferromagnet/s-wave superconductor weak link is studied theoretically in the regime of nonequilibrium spin-dependent occupation of electron states in the ferromagnetic intelayer. While under the considered nonequilibrium conditions the standard supercurrent, carried by the singlet part of current-carrying density of states, practically is not modified, the additional supercurrent flowing via the triplet part of the current-carrying density of states appears. Depending on voltage, controlling the particular form of spin-dependent no…
We predict that long-range triplet correlations (LRTC) in superconductor/ferromagnet (S/F) hybrids with extrinsic impurity spin-orbit coupling (SOC) can be generated and manipulated by supercurrent flowing in the superconducting leads along the S/F interfaces. The LRTC appear via two basic mechanisms. The essence of the first one is the generation of triplets by the superconducting spin Hall effect. These pairs are long-range in the ferromagnet under the appropriate mutual orientation of the condensate momentum and the ferromagnet magnetization. The second mechanism is based on the singlet-tri…
By converting conventional spin-singlet Cooper pairs to polarized spin-triplet pairs, it is possible to sustain long-ranged spin-polarized supercurrents flowing through strongly polarized ferromagnets. Obtaining such a conversion via spin-orbit interactions, rather than magnetic inhomogeneities, has recently been explored in the literature. A challenging aspect with regard to experimental detection has been that in order for Rashba spin-orbit interactions, present e.g. at interfaces due to inversion symmetry breaking, to generate such long-ranged supercurrents, an out-of-plane component of the…
Josephson junctions containing three ferromagnetic layers with non-collinear magnetizations between adjacent layers carry spin-triplet supercurrent under certain conditions. The signature of the spin-triplet supercurrent is a relatively slow decay of the maximum supercurrent as a function of the thickness of the middle ferromagnetic layer. In this work we focus on junctions where the middle magnetic layer is a [Co/Pd]$_N$ multilayer with perpendicular magnetic anisotropy (PMA), while the outer two layers have in-plane anisotropy. We compare junctions where the middle PMA layer is or is not con…
Spin-Polarized Josephson Supercurrent in Nodeless Altermagnets
Zhejiang University（浙江大学）；Hefei National Laboratory（合肥国家实验室）；University of Science and Technology of China（中国科学技术大学）；University of Chinese Academy of Sciences（中国科学院大学）
We present measurements of Josephson junctions containing three magnetic layers with noncolinear magnetizations. The junctions are of the form $S/F^{\prime}/N/F/N/F^{\prime \prime}/S$, where $S$ is superconducting Nb, $F^\prime$ is either a thin Ni or Permalloy layer with in-plane magnetization, $N$ is the normal metal Cu, $F$ is a synthetic antiferromagnet (SAF) with magnetization perpendicular to the plane, composed of Pd/Co multilayers on either side of a thin Ru spacer, and $F^{\prime \prime}$ is a thin Ni layer with in-plane magnetization. The supercurrent in these junctions decays more s…
Serial double quantum dots created in semiconductor nanostructures provide a versatile platform for investigating two-electron spin quantum states, which can be tuned by electrostatic gating and an external magnetic field. In this work, we directly measure the supercurrent reversal between adjacent charge states of an InAs nanowire double quantum dot with superconducting leads, in good agreement with theoretical models. In the even charge parity sector, we observe a supercurrent blockade with increasing magnetic field, corresponding to the spin singlet to triplet transition. Our results demons…
The Josephson current through a long s-wave superconductor/weak ferromagnet/s-wave superconductor weak link is studied theoretically in the regime of nonequilibrium spin-dependent occupation of electron states in the ferromagnetic intelayer. While under the considered nonequilibrium condition the standard supercurrent, carried by the singlet part of current-carrying density of states, is not modified, the additional supercurrent flowing via the triplet part of the current-carrying density of states appears. Depending on voltage, controlling the particular form of spin-dependent nonequilibrium …
Interfaces between materials with differently ordered phases present unique opportunities to study fundamental problems in physics. One example is the interface between a singlet superconductor and a half-metallic ferromagnet, where Cooper pairing occurs between electrons with opposite spin on one side, while the other displays 100% spin polarisation. The recent surprising observation of a supercurrent through half-metallic CrO_2 therefore requires a mechanism for conversion between unpolarised and completely spin polarised supercurrents. Here we suggest a conversion mechanism based on electro…
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…
Breaking of time-reversal and point-group spatial symmetries can have a profound impact on superconductivity. One of the most extraordinary effects, due to the application of a magnetic field, is represented by the Abrikosov vortices with charged supercurrents circulating around their cores. Whether a similar phenomenon can be obtained by exploiting spatial symmetry breaking, e.g. through electric fields or mechanical strain, is a fundamentally relevant but not yet fully settled problem. Here, we show that in two-dimensional spin-singlet superconductors with unusually low degree of spatial sym…
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…
Cooper pairs in superconductors are normally spin singlet. Nevertheless, recent studies suggest that spin-triplet Cooper pairs can be created at carefully engineered superconductor-ferromagnet interfaces. If Cooper pairs are spin-polarized they would transport not only charge but also a net spin component, but without dissipation, and therefore minimize the heating effects associated with spintronic devices. Although it is now established that triplet supercurrents exist, their most interesting property - spin - is only inferred indirectly from transport measurements. In conventional spintroni…
Controlling magnetic domain walls with supercurrents
University of Jyväskylä（于韦斯屈莱大学）；Centro de Física de Materiales (CFM-MPC) Centro Mixto CSIC-UPV/EHU（材料物理中心（CFM-MPC）CSIC-UPV/EHU联合中心）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
We study the spatial distribution of supercurrent circulated around an Abrikosov vortex in an SF bilayer in perpendicular magnetic field. Within the dirty limit regime and circular cell approximation for the vortex lattice, we derive the conditions when the Usadel equations the F layer can be solved analytically. Using the obtained solutions, we demonstrate the possibility of reversal of direction of proximity induced supercurrents around the vortex in the F layer compared to that in the S-layer. The direction of currents can be controlled either by varying transparency of the SF interface or …
Finite-momentum mixed singlet-triplet pairing in chiral antiferromagnets induced by even-parity spin texture
Hefei National Laboratory（合肥国家实验室）；International Center for Quantum Design of Functional Materials (ICQD), University of Science and Technology of China（中国科学技术大学量子功能材料国际设计中心）；Center for Correlated Matter and School of Physics, Zhejiang University（浙江大学关联物质中心与物理学院）；Department of Applied Physics, Aalto University School of Science（阿尔托大学理学院应用物理系）
Local spins coupled to superconductors give rise to several emerging phenomena directly linked to the competition between Cooper pair formation and magnetic exchange. These effects are generally scrutinized using a spectroscopic approach which relies on detecting the in-gap bound modes arising from Cooper pair breaking, the so-called Yu-Shiba-Rusinov (YSR) states. However, the impact of local magnetic impurities on the superconducting order parameter remains largely unexplored. Here, we use scanning Josephson spectroscopy to directly visualize the effect of magnetic perturbations on Cooper pai…
We extend the standard effective model of d-wave superconductivity of a single band tight-binding Hamiltonian with nearest-neighbor attraction to include finite range periodically modulated pair-hopping. The pair-hopping is characterized by a fixed wave number $\pmb{\mathcal{Q}}=\mathcal{Q}\hat{x}$ breaking lattice rotational symmetry. Within self-consistent BCS theory we study the general variational state consisting of two incommensurate singlet pair amplitudes $Δ_{{\bf Q}_1}$ and $Δ_{{\bf Q}_2}$ and find two types of near degenerate ground states; of the Larkin-Ovchnnikov (LO) or pair-densi…
Altermagnetic spin textures coupled to superconductors: Domain wall spin-triplet superconductivity and supercurrent-induced torques
Hearne Institute of Theoretical Physics, Department of Physics & Astronomy, Louisiana State University（路易斯安那州立大学物理与天文学系赫恩理论物理研究所）；Institute for Theoretical Physics III, University of Stuttgart（斯图加特大学理论物理第三研究所）
研究与传统 s 波超导体耦合的交变磁体中库珀对形式，考虑交变磁序参量空间不均匀性，发现超导性受交变磁畴影响，有三重态热点等，还存在超电流与交变磁序的相互作用，为相关研究提供独特机会。
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 theoretically study spin and charge currents through finite-size two-dimensional $s$-wave superconductor/uniform ferromagnet/s-wave superconductor (SFS) junctions with intrinsic spin-orbit interactions (ISOIs) using a quasiclassical approach. Considering experimentally realistic parameters, we demonstrate that the combination of spontaneously broken time-reversal symmetry and lack of inversion symmetry can result in spontaneously accumulated spin currents at the edges of finite-size two-dimensional magnetic SF hybrids. Due to the spontaneous edge spin accumulation, the corners of the F wire…
Spin-polarized supercurrents can be generated with magnetic inhomogeneity at a ferromagnet/spin-singlet-superconductor interface. In such systems, complex magnetic inhomogeneity makes it difficult to functionalise the spin-polarized supercurrents. However, spin-polarized supercurrents in ferromagnet/spin-triplet-superconductor junctions can be controlled by angle between magnetization and spin of Copper pairs ($d$-vector), that can effectively be utilized in developing of a field of research known as superconducting spintronics. Recently, we found induction of spin-triplet correlation into a f…
We study theoretically the simultaneous influence of spin accumulation potential $eV_\uparrow-eV_\downarrow$ and the Zeeman exchange field on singlet superconductivity. It is shown that the pair-breaking effect of the Zeeman field can be fully compensated by creation of the appropriate spin accumulation potential in the superconductor. Moreover, superconductivity can be recovered for exchange fields well exceeding the Pauli limiting field. It is proposed that the effect can be experimentally realized on the basis of voltage biased junction consisting of a thin superconducting film sandwiched b…
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）
