A spin triplet supercurrent through the half-metallic ferromagnet CrO2

Universal Spin Superconducting Diode Effect from Spin-Orbit Coupling

We propose a universal spin superconducting diode effect (SDE) induced by spin-orbit coupling (SOC) in systems with spin-triplet correlations, where the critical spin supercurrents in opposite directions are unequal. By analysis from both the Ginzburg-Landau theory and energy band analysis, we show that the spin-↑↑ and spin-↓↓ Cooper pairs possess opposite phase gradients and opposite momenta from the SOC, which leads to the spin SDE. Two superconductors with SOC, a p-wave superconductor as a toy model and a practical superconducting nanowire, are numerically studied and they both exhibit spin SDE. In addition, our theory also provides a unified picture for both spin and charge SDEs.

Exceptional behavior of a high-temperature superconductor in proximity to a ferromagnet in a bilayer film, La0.67Sr0.33MnO3/YBa2Cu3O7

We studied the electronic properties of a high-temperature superconductor in proximity to a ferromagnetic material in a bilayer film of La0.67Sr0.33MnO3 (LSMO)/YBa2Cu3O7 (YBCO). High-quality single-crystalline films of YBCO and LSMO/YBCO were grown epitaxially on an SrTiO3 (001) surface. Magnetization data of the LSMO/YBCO bilayer exhibit ferromagnetic transition at about 255 K, which is much smaller than the Curie temperature of bulk LSMO. Experimental data show the emergence of magnetic anisotropy with cooling, which becomes significantly stronger in the superconducting phase. The onset temperature of diamagnetism is observed at 86 K in the YBCO sample for the out-of-plane magnetization and at 89 K in the in-plane data. Interestingly, the diamagnetism sets in at about 86 K for both magnetization directions in the LSMO/YBCO film despite the presence of the ferromagnetic LSMO layer underneath. Ba 4d and Y 3d core-level spectra show different surface and bulk electronic structures. Surface contribution is reduced significantly in the LSMO/YBCO sample, suggesting enhanced bulk-like behavior due to an enhancement of electron density near the surface arising from charge transfer across the interface. These results reveal an outstanding platform for on-demand tuning of properties without affecting the superconductivity of the system for the exploration of fundamental science and applications in advanced technology.

Size-Dependence and High Temperature Stability of Radial Vortex Magnetic Textures Imprinted by Superconductor Stray Fields

Swirling spin textures, including topologically nontrivial states, such as skyrmions, chiral domain walls, and magnetic vortices, have garnered significant attention within the scientific community due to their appeal from both fundamental and applied points of view. However, their creation, controlled manipulation, and stability are typically constrained to certain systems with specific crystallographic symmetries, bulk or interface interactions, and/or a precise stacking sequence of materials. Recently, a new approach has shown potential for the imprint of magnetic radial vortices in soft ferromagnetic compounds making use of the stray field of YBa2Cu3O7-δ superconducting microstructures in ferromagnet/superconductor (FM/SC) hybrids at temperatures below the superconducting transition temperature (TC). Here, we explore the lower size limit for the imprint of magnetic radial vortices in square and disc shaped structures as well as the persistence of these spin textures above TC, with magnetic domains retaining partial memory. Structures with circular geometry and with FM patterned to smaller radius than the superconductor island facilitate the imprinting of magnetic radial vortices and improve their stability above TC, in contrast to square structures where the presence of magnetic domains increases the dipolar energy. Micromagnetic modeling coupled with a SC field model reveals that the stabilization mechanism above TC is mediated by microstructural defects. Superconducting control of swirling spin textures, and their stabilization above the superconducting transition temperature by means of defect engineering holds promising prospects for shaping superconducting spintronics based on magnetic textures.

Chiral Induced Spin Selectivity

Since the initial landmark study on the chiral induced spin selectivity (CISS) effect in 1999, considerable experimental and theoretical efforts have been made to understand the physical underpinnings and mechanistic features of this interesting phenomenon. As first formulated, the CISS effect refers to the innate ability of chiral materials to act as spin filters for electron transport; however, more recent experiments demonstrate that displacement currents arising from charge polarization of chiral molecules lead to spin polarization without the need for net charge flow. With its identification of a fundamental connection between chiral symmetry and electron spin in molecules and materials, CISS promises profound and ubiquitous implications for existing technologies and new approaches to answering age old questions, such as the homochiral nature of life. This review begins with a discussion of the different methods for measuring CISS and then provides a comprehensive overview of molecules and materials known to exhibit CISS-based phenomena before proceeding to identify structure-property relations and to delineate the leading theoretical models for the CISS effect. Next, it identifies some implications of CISS in physics, chemistry, and biology. The discussion ends with a critical assessment of the CISS field and some comments on its future outlook.

Finite-momentum Cooper pairing in proximitized altermagnets

Finite-momentum Cooper pairing is an unconventional form of superconductivity that is widely believed to require finite magnetization. Altermagnetism is an emerging magnetic phase with highly anisotropic spin-splitting of specific symmetries, but zero net magnetization. Here, we study Cooper pairing in metallic altermagnets connected to conventional s-wave superconductors. Remarkably, we find that the Cooper pairs induced in the altermagnets acquire a finite center-of-mass momentum, despite the zero net magnetization in the system. This anomalous Cooper-pair momentum strongly depends on the propagation direction and exhibits unusual symmetric patterns. Furthermore, it yields several unique features: (i) highly orientation-dependent oscillations in the order parameter, (ii) controllable 0-π transitions in the Josephson supercurrent, (iii) large-oblique-angle Cooper-pair transfer trajectories in junctions parallel with the direction where spin splitting vanishes, and (iv) distinct Fraunhofer patterns in junctions oriented along different directions. Finally, we discuss the implementation of our predictions in candidate materials such as RuO2 and KRu4O8.

Enhancement and switch effect of equal-spin Andreev reflection in ferromagnet/insulator/Ising superconductor junctions

We study the property of equal-spin Andreev reflection (ESAR) in the ferromagnet/insulator/Ising superconductor junction where Ising spin-orbit coupling is taken into account in the insulator. It is found that the ESAR exhibits a regular oscillation with the insulating barrier, the amplitude and period of which can be effectively controlled by the chemical potentials. Compared to that in the ferromagnet/Ising superconductor junction, the ESAR is greatly increased due to the resonant mode, suggesting an enhanced spin-triplet pairing. As an application, the proposed junction may work as a switch to turn on and off the ESAR. Furthermore, the insulating barrier does not change the magnetoanisotropic period of ESAR because of the invariant symmetry of the system, however, the magnetoanisotropy is strengthened.

Local control of superconductivity in a NbSe2/CrSBr van der Waals heterostructure

Two-dimensional magnets and superconductors are emerging as tunable building-blocks for quantum computing and superconducting spintronic devices, and have been used to fabricate all two-dimensional versions of traditional devices, such as Josephson junctions. However, novel devices enabled by unique features of two-dimensional materials have not yet been demonstrated. Here, we present NbSe2/CrSBr van der Waals superconducting spin valves that exhibit infinite magnetoresistance and nonreciprocal charge transport. These responses arise from a unique metamagnetic transition in CrSBr, which controls the presence of localized stray fields suitably oriented to suppress the NbSe2 superconductivity in nanoscale regions and to break time reversal symmetry. Moreover, by integrating different CrSBr crystals in a lateral heterostructure, we demonstrate a superconductive spin valve characterized by multiple stable resistance states. Our results show how the unique physical properties of layered materials enable the realization of high-performance quantum devices based on novel working principles.

Spin-orbit driven superconducting proximity effects in Pt/Nb thin films

Manipulating the spin state of thin layers of superconducting material is a promising route to generate dissipationless spin currents in spintronic devices. Approaches typically focus on using thin ferromagnetic elements to perturb the spin state of the superconducting condensate to create spin-triplet correlations. We have investigated simple structures that generate spin-triplet correlations without using ferromagnetic elements. Scanning tunneling spectroscopy and muon-spin rotation are used to probe the local electronic and magnetic properties of our hybrid structures, demonstrating a paramagnetic contribution to the magnetization that partially cancels the Meissner screening. This spin-orbit generated magnetization is shown to derive from the spin of the equal-spin pairs rather than from their orbital motion and is an important development in the field of superconducting spintronics.

Anisotropic proximity-induced superconductivity and edge supercurrent in Kagome metal, K1-xV3Sb5

Materials with Kagome nets are of particular importance for their potential combination of strong correlation, exotic magnetism, and electronic topology. KV₃Sb₅ was discovered to be a layered topological metal with a Kagome net of vanadium. Here, we fabricated Josephson Junctions of K_1-xV₃Sb₅ and induced superconductivity over long junction lengths. Through magnetoresistance and current versus phase measurements, we observed a magnetic field sweeping direction-dependent magnetoresistance and an anisotropic interference pattern with a Fraunhofer pattern for in-plane magnetic field but a suppression of critical current for out-of-plane magnetic field. These results indicate an anisotropic internal magnetic field in K_1-xV₃Sb₅ that influences the superconducting coupling in the junction, possibly giving rise to spin-triplet superconductivity. In addition, the observation of long-lived fast oscillations shows evidence of spatially localized conducting channels arising from edge states. These observations pave the way for studying unconventional superconductivity and Josephson device based on Kagome metals with electron correlation and topology.

Chiral antiferromagnetic Josephson junctions as spin-triplet supercurrent spin valves and d.c. SQUIDs

Spin-triplet supercurrent spin valves are of practical importance for the realization of superconducting spintronic logic circuits. In ferromagnetic Josephson junctions, the magnetic-field-controlled non-collinearity between the spin-mixer and spin-rotator magnetizations switches the spin-polarized triplet supercurrents on and off. Here we report an antiferromagnetic equivalent of such spin-triplet supercurrent spin valves in chiral antiferromagnetic Josephson junctions as well as a direct-current superconducting quantum interference device. We employ the topological chiral antiferromagnet Mn3Ge, in which the Berry curvature of the band structure produces fictitious magnetic fields, and the non-collinear atomic-scale spin arrangement accommodates triplet Cooper pairing over long distances (>150 nm). We theoretically verify the observed supercurrent spin-valve behaviours under a small magnetic field of <2 mT for current-biased junctions and the direct-current superconducting quantum interference device functionality. Our calculations reproduce the observed hysteretic field interference of the Josephson critical current and link these to the magnetic-field-modulated antiferromagnetic texture that alters the Berry curvature. Our work employs band topology to control the pairing amplitude of spin-triplet Cooper pairs in a single chiral antiferromagnet.

Observation of Magnetic State Dependent Thermoelectricity in Superconducting Spin Valves

Superconductor-ferromagnet tunnel junctions demonstrate giant thermoelectric effects that are being exploited to engineer ultrasensitive terahertz radiation detectors. Here, we experimentally observe the recently predicted complete magnetic control over thermoelectric effects in a superconducting spin valve, including the dependence of its sign on the magnetic state of the spin valve. The description of the experimental results is improved by the introduction of an interfacial domain wall in the spin filter layer interfacing the superconductor. Surprisingly, the application of high in-plane magnetic fields induces a double sign inversion of the thermoelectric effect, which exhibits large values even at applied fields twice the superconducting critical field.

Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene

The coexistence of gate-tunable superconducting, magnetic and topological orders in magic-angle twisted bilayer graphene provides opportunities for the creation of hybrid Josephson junctions. Here we report the fabrication of gate-defined symmetry-broken Josephson junctions in magic-angle twisted bilayer graphene, where the weak link is gate-tuned close to the correlated insulator state with a moiré filling factor of υ = -2. We observe a phase-shifted and asymmetric Fraunhofer pattern with a pronounced magnetic hysteresis. Our theoretical calculations of the junction weak link-with valley polarization and orbital magnetization-explain most of these unconventional features. The effects persist up to the critical temperature of 3.5 K, with magnetic hysteresis observed below 800 mK. We show how the combination of magnetization and its current-induced magnetization switching allows us to realise a programmable zero-field superconducting diode. Our results represent a major advance towards the creation of future superconducting quantum electronic devices.

Long-range skin Josephson supercurrent across a van der Waals ferromagnet

The emerging field of superconducting spintronics promises new quantum device architectures without energy dissipation. When entering a ferromagnet, a supercurrent commonly behaves as a spin singlet that decays rapidly; in contrast, a spin-triplet supercurrent can transport over much longer distances, and is therefore more desirable, but so far has been observed much less frequently. Here, by using the van der Waals ferromagnet Fe3GeTe2 (F) and spin-singlet superconductor NbSe2 (S), we construct lateral Josephson junctions of S/F/S with accurate interface control to realize long-range skin supercurrent. The observed supercurrent across the ferromagnet can extend over 300 nm, and exhibits distinct quantum interference patterns in an external magnetic field. Strikingly, the supercurrent displays pronounced skin characteristics, with its density peaked at the surfaces or edges of the ferromagnet. Our central findings shed new light on the convergence of superconductivity and spintronics based on two-dimensional materials.

High-pressure magnetic properties and electrical transport behaviors of half-metallic ferromagnet CrO2

The magnetic properties and electrical transport behaviors of half-metallic ferromagnet chromium dioxide (CrO₂) powders under high pressure have been investigated by in situ electrical resistivity, magneto-resistivity, and Hall-effect measurements. Our results reveal that the Hall coefficient, carrier concentration, and mobility all present discontinuous changes from 11.7 GPa to 14.9 GPa which can be attributed to the second-order structural transition from the rutile-type to CaCl₂-type. However, the resistivity decreases monotonically from ambient pressure to 16.5 GPa. This is due to, first, the decreased carrier concentration and the increased carrier mobility canceling the effects of each other on the resistivity; second, according to the calculation results, the bandgap of CrO₂ decreased gradually with the pressure, and the bandgaps of the rutile-type phase and the CaCl₂-type phase are extremely similar. CrO₂ exhibits a linear and negative magnetoresistance under the applied magnetic field (0∼ ± 15 kOe). As the pressure increases, the magnetoresistance remains negative, but it becomes nonlinear and less symmetric, suggesting that pressure has an appreciable impact on the double-exchange mechanism leading to ferromagnetism in CrO₂.

Experimental and theoretical study of field-dependent spin splitting at ferromagnetic insulator-superconductor interfaces

We present a combined experimental and theoretical work that investigates the magnetic proximity effect at a ferromagnetic insulator-superconductor (FI-S) interface. The calculations are based on the boundary condition for diffusive quasiclassical Green's functions, which accounts for arbitrarily strong spin-dependent effects and spin mixing angles. The resulting phase diagram shows a transition from a first-order to a second-order phase transition for large spin mixing angles. The experimentally found differential conductance of an EuS-Al heterostructure is compared with the theoretical calculation. With the assumption of a uniform spin mixing angle that depends on the externally applied field, we find good agreement between theory and experiment. The theory depends only on very few parameters, mostly specified by the experimental setup. We determine the effective spin of the interface moments as J ≈ 0.74ℏ.

Magnetoelectric effects in Josephson junctions

The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.

Electron beam evaporation of superconductor-ferromagnet heterostructures

We report on the electronic and magnetic properties of superconductor-ferromagnet heterostructures fabricated by electron beam evaporation on to unheated thermally oxidised Si substrates. Polycrystalline Nb thin films (5 to 50 nm thick) were shown to possess reliably high superconducting critical temperatures (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{c}$$\end{document}Tc), which correlate well with the residual resistivity ratio (RRR) of the film. These properties improved during ex-situ annealing, resulting in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta }T_{c}$$\end{document}ΔTc and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta }$$\end{document}ΔRRR increases of up 2.2 K (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document}∼ 40% of the pre-annealed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{c}$$\end{document}Tc) and 0.8 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document}∼ 60% of the pre-annealed RRR) respectively. Nb/Pt/Co/Pt heterostructures showed substantial perpendicular anisotropy in the ultrathin limit (≤ 2.5 nm), even in the extreme limit of Pt(0.8 nm)/Co(1 nm)/Pt(0.6 nm). These results point to the use of electron beam evaporation as route to line-of-sight deposited, low-thickness, high quality Nb-based superspintronic multilayers.

Transverse Magnetoresistance Induced by the Nonuniformity of Superconductor

The transverse magnetoresistance (R_xy) caused by inhomogeneous superconductivity is symmetric about the magnetic field around the critical magnetic field region. This has caused many disturbances during the study of vortex dynamics by Hall signals. Here, we found that the peak of R_xy measured in our samples was induced by the nonuniformity of the superconductors. The peak values of R_xy decrease with increasing applied current and temperature, which can be described by the theory of superconductivity inhomogeneity. Based on this, we have proposed and verified a method for separating the transverse voltage caused by the inhomogeneity of superconductivity. Additionally, quantity ΔB(0) can also be used to characterize the uniformity of superconductivity. This clears up the obstacles for studying vortex motion dynamics and reveals a way to study the influence of the domain wall on superconductivity.

Superconducting Triplet Rim Currents in a Spin-Textured Ferromagnetic Disk

Since the discovery of the long-range superconducting proximity effect, the interaction between spin-triplet Cooper pairs and magnetic structures such as domain walls and vortices has been the subject of intense theoretical discussions, while the relevant experiments remain scarce. We have developed nanostructured Josephson junctions with highly controllable spin texture, based on a disk-shaped Nb/Co bilayer. Here, the vortex magnetization of Co and the Cooper pairs of Nb conspire to induce long-range triplet (LRT) superconductivity in the ferromagnet. Surprisingly, the LRT correlations emerge in highly localized (sub-80 nm) channels at the rim of the ferromagnet, despite its trivial band structure. We show that these robust rim currents arise from the magnetization texture acting as an effective spin-orbit coupling, which results in spin accumulation at the bilayer-vacuum boundary. Lastly, we demonstrate that by altering the spin texture of a single ferromagnet, both 0 and π channels can be realized in the same device.

Extremely long-range, high-temperature Josephson coupling across a half-metallic ferromagnet

The Josephson effect results from the coupling of two superconductors across a spacer such as an insulator, a normal metal or a ferromagnet to yield a phase coherent quantum state. However, in junctions with ferromagnetic spacers, very long-range Josephson effects have remained elusive. Here we demonstrate extremely long-range (micrometric) high-temperature (tens of kelvins) Josephson coupling across the half-metallic manganite La_0.7Sr_0.3MnO₃ combined with the superconducting cuprate YBa₂Cu₃O₇. These planar junctions, in addition to large critical currents, display the hallmarks of Josephson physics, such as critical current oscillations driven by magnetic flux quantization and quantum phase locking effects under microwave excitation (Shapiro steps). The latter display an anomalous doubling of the Josephson frequency predicted by several theories. In addition to its fundamental interest, the marriage between high-temperature, dissipationless quantum coherent transport and full spin polarization brings opportunities for the practical realization of superconducting spintronics, and opens new perspectives for quantum computing.

Observation of Josephson-like Tunneling Junction Characteristics and Positive Magnetoresistance in Oxygen Deficient Nickelate Films of Nd0.8Sr0.2NiO3-δ

Nickelate films have recently attracted broad attention due to the observation of superconductivity in the infinite layer phase of Nd0.8Sr0.2NiO2 (obtained by reducing Sr doped NdNiO3 films) and their similarity to the cuprates high temperature superconductors. Here, we report on the observation of a new type of transport in oxygen poor Nd0.8Sr0.2NiO3-δ films. At high temperatures, variable range hopping is observed while at low temperatures a novel tunneling behavior is found where a Josephson-like tunneling junction characteristic with serial resistance is revealed. We attribute this phenomenon to coupling between superconductive (S) surfaces of the grains in our Oxygen poor films via the insulating (I) grain boundaries, which yields SIS junctions in series with the normal (N) resistance of the grains themselves. The similarity of the observed conductance spectra to the tunneling junction characteristic with Josephson-like current is striking, and seems to support the existence of superconductivity in our samples.

Magnon Spin Current Induced by Triplet Cooper Pair Supercurrents

At the interface between a ferromagnetic insulator and a superconductor there is a coupling between the spins of the two materials. We show that when a supercurrent carried by triplet Cooper pairs flows through the superconductor, the coupling induces a magnon spin current in the adjacent ferromagnetic insulator. The effect is dominated by Cooper pairs polarized in the same direction as the ferromagnetic insulator, so that charge and spin supercurrents produce similar results. Our findings demonstrate a way of converting Cooper pair supercurrents to magnon spin currents.

Long-range supercurrents through a chiral non-collinear antiferromagnet in lateral Josephson junctions

The proximity-coupling of a chiral non-collinear antiferromagnet (AFM)^1-5 with a singlet superconductor allows spin-unpolarized singlet Cooper pairs to be converted into spin-polarized triplet pairs^6-8, thereby enabling non-dissipative, long-range spin correlations^9-14. The mechanism of this conversion derives from fictitious magnetic fields that are created by a non-zero Berry phase¹⁵ in AFMs with non-collinear atomic-scale spin arrangements^1-5. Here we report long-ranged lateral Josephson supercurrents through an epitaxial thin film of the triangular chiral AFM Mn₃Ge (refs. ^3-5). The Josephson supercurrents in this chiral AFM decay by approximately one to two orders of magnitude slower than would be expected for singlet pair correlations^9-14 and their response to an external magnetic field reflects a clear spatial quantum interference. Given the long-range supercurrents present in both single- and mixed-phase Mn₃Ge, but absent in a collinear AFM IrMn¹⁶, our results pave a way for the topological generation of spin-polarized triplet pairs^6-8 via Berry phase engineering¹⁵ of the chiral AFMs.

Superconductivity assisted change of the perpendicular magnetic anisotropy in V/MgO/Fe junctions

Controlling the perpendicular magnetic anisotropy (PMA) in thin films has received considerable attention in recent years due to its technological importance. PMA based devices usually involve heavy-metal (oxide)/ferromagnetic-metal bilayers, where, thanks to interfacial spin-orbit coupling (SOC), the in-plane (IP) stability of the magnetisation is broken. Here we show that in V/MgO/Fe(001) epitaxial junctions with competing in-plane and out-of-plane (OOP) magnetic anisotropies, the SOC mediated interaction between a ferromagnet (FM) and a superconductor (SC) enhances the effective PMA below the superconducting transition. This produces a partial magnetisation reorientation without any applied field for all but the largest junctions, where the IP anisotropy is more robust; for the smallest junctions there is a reduction of the field required to induce a complete OOP transition (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\text {OOP}$$\end{document}HOOP) due to the stronger competition between the IP and OOP anisotropies. Our results suggest that the degree of effective PMA could be controlled by the junction lateral size in the presence of superconductivity and an applied electric field. We also discuss how the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\text {OOP}$$\end{document}HOOP field could be affected by the interaction between magnetic stray fields and superconducting vortices. Our experimental findings, supported by numerical modelling of the ferromagnet-superconductor interaction, open pathways to active control of magnetic anisotropy in the emerging dissipation-free superconducting spin electronics.

Unconventional domain wall magnetoresistance of patterned Ni/Nb bilayer structures below superconducting transition temperature of Nb

Scattering of spin-up and spin-down electrons while passing through a ferromagnetic domain wall (DW) leads to an additional resistance for transport current, usually observed prominently in constricted magnetic structures. In this report we use the resistance of the DW as a probe to find an indirect signatures of the theoretically predicted spin-singlet supercurrent to spin-triplet supercurrent conversion effect of ferromagnetic DWs. Here we examine the DW induced resistance in Ni stripe in a bilayer Ni/Nb geometry in the normal state and in the superconducting state of Nb. By making a 3μm wide gap in the top Nb layer we routed the transport current through the Ni layer in the normal state and in the superconducting state of Nb. In the normal state of Nb, in-field transport measurements showed a clear domain wall magneto-resistance (DWMR) peak of amplitude ∼5.9 mΩ near the coercive field, where the DW density is expected to be maximum. Interestingly, however, below the superconducting transition temperature of Nb, the DWMR peak of the Ni layer showed a sharp drop in the field range where the number of DWs become maximum. This observation may be a possible signature of magnetic DW induced spin-triplet correlations in the Ni layer due to the direct injection of spin-singlet Cooper pairs from Nb into the magnetic DWs.

Nanoscale Domain Wall Engineered Spin-Triplet Josephson Junctions and SQUID

Spin-singlet Cooper pairs convert to spin-triplet Cooper pairs on passing through a magnetically noncollinear structure at a superconductor(S)/ferromagnet(F) interface. In this context, the generation of triplet supercurrents through intrinsic ferromagnetic domain walls, which are naturally occurring noncollinear magnetic features, was proposed theoretically in the past decade. However, an experimental demonstration has been lacking in the literature, particularly because of the difficulty in accessing a single domain wall, which is typically buried between two domains in a ferromagnetic material. By patterning a ferromagnetic nanoconstriction, we have been able to realize a nanoscale S/F/S planar junction, where a single domain wall (pinned at the nanoconstriction) acts as a Josephson barrier. In this geometry, we are able to show the predicted long-range triplet supercurrent across a ferromagnetic barrier exceeding 70 nm. Using this technique, we have demonstrated a ferromagnetic planar nano-SQUID device consisting of two Nb/Ni/Nb spin-triplet Josephson junctions.

Temperature-Dependent Spin Transport and Current-Induced Torques in Superconductor-Ferromagnet Heterostructures

We investigate the injection of quasiparticle spin currents into a superconductor via spin pumping from an adjacent ferromagnetic metal layer. To this end, we use NbN-Ni_{80}Fe_{20}(Py) heterostructures with a Pt spin sink layer and excite ferromagnetic resonance in the Permalloy layer by placing the samples onto a coplanar waveguide. A phase sensitive detection of the microwave transmission signal is used to quantitatively extract the inductive coupling strength between the sample and the coplanar waveguide, interpreted in terms of inverse current-induced torques, in our heterostructures as a function of temperature. Below the superconducting transition temperature T_{c}, we observe a suppression of the dampinglike torque generated in the Pt layer by the inverse spin Hall effect, which can be understood by the changes in spin current transport in the superconducting NbN layer. Moreover, below T_{c} we find a large fieldlike current-induced torque.

Spin-orbit coupling suppression and singlet-state blocking of spin-triplet Cooper pairs

An inhomogeneous magnetic exchange field at a superconductor/ferromagnet interface converts spin-singlet Cooper pairs to a spin-polarized triplet state. Although the decay envelope of triplet pairs within ferromagnetic materials is well studied, little is known about their decay in nonmagnetic metals and superconductors and, in particular, in the presence of spin-orbit coupling (SOC). Here, we investigate devices in which singlet and triplet supercurrents propagate into the s-wave superconductor Nb. In the normal state of Nb, triplet supercurrents decay over a distance of 5 nm, which is an order of magnitude smaller than the decay of spin-singlet pairs due to the SOC. In the superconducting state of Nb, triplet supercurrents are not able to couple with the singlet wave function and are thus blocked by the absence of available equilibrium states in the singlet gap. The results offer insight into the dynamics between s-wave singlet and s-wave triplet states.

Spin current as a probe of quantum materials

Spin current historically referred to the flow of electrons carrying spin information, in particular since the discovery of giant magnetoresistance in the 1980s. Recently, it has been found that spin current can also be mediated by spin-triplet supercurrent, superconducting quasiparticles, spinons, magnons, spin superfluidity and so on. Here, we review key progress concerning the developing research direction utilizing spin current as a probe of quantum materials. We focus on spin-triplet superconductivity and spin dynamics in the ferromagnet/superconductor heterostructures, quantum spin liquids, magnetic phase transitions, magnon-polarons, magnon-polaritons, magnon Bose-Einstein condensates and spin superfluidity. The unique characteristics of spin current as a probe will be fruitful for future investigation of spin-dependent properties and the identification of new quantum materials.

Anomalous anisotropic behaviour of spin-triplet proximity effect in Au/SrRuO3/Sr2RuO4 junctions

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 the 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 ferromagnet SrRuO₃ epitaxially deposited on a spin-triplet superconductor Sr₂RuO₄, without any electronic spin-flip scattering. Here, we present systematic magnetic field dependence of the proximity effect in Au/SrRuO₃/Sr₂RuO₄ junctions. It is found that induced triplet correlations exhibit strongly anisotropic field response. Such behaviour is attributed to the rotation of the d-vector of Sr₂RuO₄. This anisotropic behaviour is in contrast with the vortex dynamic. Our results will stimulate study of interaction between ferromagnetism and unconventional superconductivity.

Heteroepitaxy of Co-Based Heusler Compound/Muscovite for Flexible Spintronics

Materials with high spin-polarization play an important role in the development of spintronics. Co-based Heusler compounds are a promising candidate for practical applications because of their high Curie temperature and tunable half-metallicity. However, it is a challenge to integrate Heusler compounds into thin film heterostructures because of the lack of control on crystallinity and chemical disorder, critical factors of novel behaviors. Here, muscovite is introduced as a growth substrate to fabricate epitaxial Co₂MnGa films with mechanical flexibility. The feature of heteroepitaxy is evidenced by the results of X-ray diffraction and transmission electron microscopy. Moreover, high chemical ordering with superior properties is delivered according to the observation of large Hall conductivity (680 Ω^-1 cm^-1) and highly saturated magnetic moment (∼3.93 μ_B/f.u.), matching well with bulk crystals. Furthermore, the excellence of magnetic and electrical properties is retained under the various mechanical bending conditions. Such a result suggests that the development of Co₂MnGa/muscovite heteroepitaxy provides not only a pathway to the thin film heterostructure based on high-quality Heusler compounds but also a new aspect of spintronic applications on flexible substrates.

Controlling spin supercurrents via nonequilibrium spin injection

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 the equilibrium spin current. This is interesting for several reasons: as a fundamental physical effect; due to possible applications as a way to control spin supercurrents; and timeliness in light of recent experiments on spin injection in proximitized superconductors.

The Route to Supercurrent Transparent Ferromagnetic Barriers in Superconducting Matrix

A ferromagnetic barrier thinner than the coherence length in high-temperature superconductors is realized in the multilayers of YBa₂Cu₃O_7-δ and La_0.67Ca_0.33MnO₃. We used epitaxial growth of YBCO on ⟨110⟩ SrTiO₃ substrates by pulsed laser deposition to prepare thin superconducting films with copper oxide planes oriented at an angle to the substrate surface. Subsequent deposition of LCMO and finally a second YBCO layer produces a superconductor/ferromagnet/superconductor trilayer containing an ultrathin ferromagnetic barrier with sophisticated geometry at which the long axis of coherence length ovoid of YBCO is pointing across the LCMO ferromagnetic layer. A detailed characterization of this structure is achieved using high-resolution electron microscopy.

Evidence for Spin-Triplet Electron Pairing in the Proximity-Induced Superconducting State of an Fe-Doped InAs Semiconductor

We provide evidence for spin-triplet electron pairing in proximity-induced superconductivity in a ferromagnetic semiconductor (In,Fe)As. As discovered in half-metallic materials, an extraordinarily long proximity range is observed. More surprising is a very strong concentration of supercurrent to the edges of the superconducting region, which is deduced from the extremely persistent oscillation of the critical current vs magnetic field. The maxima of the critical current appear not at the zero magnetic flux but at around the maximum magnetic disorder, reflecting the connectivity between the spin-triplet and singlet pairings. These spin-triplet natures in proximity superconductivity also reveal ferromagnetic properties of (In,Fe)As.

Tuning of Magnetic Activity in Spin-Filter Josephson Junctions Towards Spin-Triplet Transport

The study of superconductor-ferromagnet interfaces has generated great interest in the last decades, leading to the observation of spin-aligned triplet supercurrents and 0-π transitions in Josephson junctions where two superconductors are separated by an itinerant ferromagnet. Recently, spin-filter Josephson junctions with ferromagnetic barriers have shown unique transport properties, when compared to standard metallic ferromagnetic junctions, due to the intrinsically nondissipative nature of the tunneling process. Here we present the first extensive characterization of spin polarized Josephson junctions down to 0.3 K, and the first evidence of an incomplete 0-π transition in highly spin polarized tunnel ferromagnetic junctions. Experimental data are consistent with a progressive enhancement of the magnetic activity with the increase of the barrier thickness, as neatly captured by the simplest theoretical approach including a nonuniform exchange field. For very long junctions, unconventional magnetic activity of the barrier points to the presence of spin-triplet correlations.

Creation of equal-spin triplet superconductivity at the Al/EuS interface

In conventional superconductors, electrons of opposite spins are bound into Cooper pairs. However, when the superconductor is in contact with a non-uniformly ordered ferromagnet, an exotic type of superconductivity can appear at the interface, with electrons bound into three possible spin-triplet states. Triplet pairs with equal spin play a vital role in low-dissipation spintronics. Despite the observation of supercurrents through ferromagnets, spectroscopic evidence for the existence of equal-spin triplet pairs is still missing. Here we show a theoretical model that reveals a characteristic gap structure in the quasiparticle density of states which provides a unique signature for the presence of equal-spin triplet pairs. By scanning tunnelling spectroscopy we measure the local density of states to reveal the spin configuration of triplet pairs. We demonstrate that the Al/EuS interface causes strong and tunable spin-mixing by virtue of its spin-dependent transmission.

Tunable Electronic and Magnetic Properties of Graphene-Embedded Transition Metal-N4 Complexes: Insight From First-Principles Calculations

Motivated by the development of transition-metal-nitrogen-carbon (TM-N-C) materials for catalysts and molecular electronics, we investigated the electronic and magnetic properties of TMN₄ -graphene materials with different central atoms (TM=Ti, V, Cr, Mn, Fe, Co, Ni and Cu) and different concentrations. The first-principles results show that a widely tunable magnetic moment in the range from 0 to 4 μ_B can be obtained in this kind of material by varying the central TM atom, and a regular transition of the electronic property from metallic to half-metallic and to semiconducting characteristics is observed in MnN₄ -graphene upon changing the concentration. We find that the peculiar relationship between the electronic characteristics of graphene and its lattice parameters plays a decisive role in determining the electronic and magnetic properties. Our findings are useful for the design of TM-N-C materials for catalysis, spintronics, and molectronics.

Magnetic Exchange Fields and Domain Wall Superconductivity at an All-Oxide Superconductor-Ferromagnet Insulator Interface

At a superconductor-ferromagnet (S/F) interface, the F layer can introduce a magnetic exchange field within the S layer, which acts to locally spin split the superconducting density of states. The effect of magnetic exchange fields on superconductivity has been thoroughly explored at S-ferromagnet insulator (S/FI) interfaces for isotropic s-wave S and a thickness that is smaller than the superconducting coherence length. Here we report a magnetic exchange field effect at an all-oxide S/FI interface involving the anisotropic d-wave high temperature superconductor praseodymium cerium copper oxide (PCCO) and the FI praseodymium calcium manganese oxide (PCMO). The magnetic exchange field in PCCO, detected via magnetotransport measurements through the superconducting transition, is localized to the PCCO/PCMO interface with an average magnitude that depends on the presence or absence of magnetic domain walls in PCMO. The results are promising for the development of all-oxide superconducting spintronic devices involving unconventional pairing and high temperature superconductors.

Non-equilibrium charge and spin transport in superconducting-ferromagnetic-superconducting point contacts

The conventional Josephson effect may be modified by introducing spin-active scattering in the interface layer of the junction. Here, we discuss a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin that precesses with the Larmor frequency due to an external magnetic field. This magnetically active interface results in a time-dependent boundary condition with different tunnelling amplitudes for spin-up and -down quasi-particles and where the precession produces spin-flip scattering processes. As a result, the Andreev states develop sidebands and a non-equilibrium population that depend on the details of the spin precession. The Andreev states carry a steady-state Josephson charge current and a time-dependent spin current, whose current-phase relations could be used to characterize the precessing spin. The spin current is supported by spin-triplet correlations induced by the spin precession and creates a feedback effect on the classical spin in the form of a torque that shifts the precession frequency. By applying a bias voltage, the Josephson frequency adds another complexity to the situation and may create resonances together with the Larmor frequency. These Shapiro resonances manifest as torques and, under suitable conditions, are able to reverse the direction of the classical spin in sub-nanosecond time. Another characteristic feature is the subharmonic gap structure in the DC charge current displaying an even-odd effect attributable to precession-assisted multiple Andreev reflections.This article is part of the theme issue 'Andreev bound states'.

What can Andreev bound states tell us about superconductors?

Zero-energy Andreev bound states, which manifest themselves in the tunnelling spectra as zero-bias conductance peaks (ZBCPs), are abundant at interfaces between superconductors and other materials and on the nodal surface of high-temperature superconductors. In this review, we focus on the information such excitations can provide on the properties of superconductor systems. First, a general introduction to the physics of Andreev bound states in superconductor/normal metal interfaces is given with a particular emphasis on why they appear at zero energy in d-wave superconductors. Then, specific spectroscopic tunnelling studies of thin films, bilayers and junctions are described, focusing on the corresponding ZBCP features. Scanning tunnelling spectroscopy (STS) studies show that the ZBCPs on the c-axis YBa₂Cu₃O_7-δ (YBCO) films are correlated with the surface morphology and appear only in proximity to (110) facets. STS on c-axis La_1.88Sr_0.12CuO₄ (LSCO) films exhibiting the 1/8 anomaly shows spatially modulated peaks near zero bias associated with the anti-phase ordering of the d-wave order parameter predicted at this doping level. ZBCPs were also found in micrometre-size edge junctions of YBCO/SrRuO₃/YBCO, where SrRuO₃ is ferromagnetic. Here, the results are consistent with a crossed Andreev reflection effect (CARE) at the narrow domain walls of the SrRuO₃ ZBCPs measured in STS studies of manganite/cuprate bilayers could not be attributed to CARE because the manganite's domain wall is much larger than the coherence length in YBCO, and instead are attributed to proximity-induced triplet-pairing superconductivity with non-conventional symmetry. And finally, ZBCPs found in junctions of non-intentionally doped topological insulator films of Bi₂Se₃ and the s-wave superconductor NbN are attributed to proximity-induced p_x+ ip_y triplet order parameter in the topological material.This article is part of the theme issue 'Andreev bound states'.

Spin-triplet supercurrents in Josephson junctions containing strong ferromagnetic materials

The proximity effect between a superconducting material and a non-superconducting normal metal can extend over distances of the order of micrometres at sufficiently low temperatures. If the normal metal is replaced by a ferromagnetic material, the spatial extent of the proximity effect drops precipitously due to the exchange splitting between the majority and minority spin bands in the ferromagnet. In 2001, several theorists predicted that spin-triplet pair correlations could be induced in proximity systems involving multiple ferromagnetic materials (or multiple domains in one material) with non-collinear magnetizations. Such spin-triplet pair correlations should extend deep into the ferromagnet, producing a long-range proximity effect. In this paper, we review our experimental work in this area, which has focused primarily on Josephson junctions containing strong ferromagnetic materials. We show that Josephson junctions containing particular combinations of strong ferromagnetic materials can carry spin-triplet supercurrent over distances of at least several tens of nanometres, whereas spin-singlet supercurrent in similar samples decays over a length scale of about 1 nm. We also mention important work by other groups; however, this article is not intended to be a review of the whole field.This article is part of the theme issue 'Andreev bound states'.

Structural, magnetic and electronic properties of CrO2 at multimegabar pressures

As the only half-metallic ferromagnetic material in 3d transition metal dioxides, CrO2 has attracted great scientific interest from materials science to physical chemistry. Here, an investigation into the structural, magnetic and electronic properties of CrO2 under high pressure has been conducted by first-principles calculations based on density functional theory. Static calculations have predicted that CrO2 undergoes structural transitions with the sequence of rutile-type → CaCl2-type → pyrite-type → Pnma → (Fe2P-type→) I4/mmm at high pressures. In addition, a transition from the ferromagnetic state to the non-magnetic state with the magnetic collapse of Cr is observed in CrO2 at the pyrite-Pnma transition. This transition also delocalizes the 3d electrons of Cr and leads to a metallic character of CrO2. The equation of state, elasticity and band gap for each energetically favorable phase of CrO2 are determined. Our results not only bridge the gap about the high-pressure behavior of CrO2 in previous studies but also extend our understanding of its properties up to multimegabar conditions. According to previous data and present results, we further discuss and summarize the high-pressure behavior of various AO2 compounds. This can contribute to investigating properties of other AO2 compounds or exploring novel materials at high pressures.

Phase control in a spin-triplet SQUID

It is now well established that a Josephson junction made from conventional spin-singlet superconductors containing ferromagnetic layers can carry spin-triplet supercurrent under certain conditions. The first experimental signature of that fact is the propagation of such supercurrent over long distances through strong ferromagnetic materials. Surprisingly, one of the most salient predictions of the theory has yet to be verified experimentally-namely, that a Josephson junction containing three magnetic layers with coplanar magnetizations should exhibit a ground-state phase shift of either zero or π depending on the relative orientations of those magnetizations. We demonstrate this property using Josephson junctions containing three different types of magnetic layers, chosen so that the magnetization of one layer can be switched by 180° without disturbing the other two. Phase-sensitive detection is accomplished using a superconducting quantum interference device, or SQUID. Such a phase-controllable junction could be used as the memory element in a fully superconducting computer.

Superconductivity switch from spin-singlet to -triplet pairing in a topological superconducting junction

The interedge coupling is the cardinal characteristic of the narrow quantum spin Hall (QSH) insulator, and thus could bring about exotic transport phenomena. Herein, we present a theoretical investigation of the spin-resolved Andreev reflection (AR) in a QSH insulator strip touching on two neighbouring ferromagnetic insulators and one s-wave superconductor. It is demonstrated that, due to the interplay of the interedge coupling and ferromagnetic configuration, there could be not only usual local ARs leading to the spin-singlet pairing with the incident electron and Andreev-reflected hole from different spin subbands, but also novel local ARs giving rise to the spin-triplet pairing from the same spin subband. However, only the latter exists in the absence of the interedge coupling, and therefore the two pairings in turn testify the helical spin texture of the edge states. By proper tuning of the band structures of the ferromagnetic layers, under the resonance bias voltage, the usual and novel local ARs of [Formula: see text] can be all exhibited, resulting in fully spin-polarized pure spin-singlet superconductivity and pure spin-triplet superconductivity, respectively, which suggests a superconductivity switch from spin-singlet to -triplet pairing by electrical control. The results can be experimentally confirmed by the tunneling conductance and the noise power.

Current phase relation from graphs and diagrams and application to thick ferromagnetic Josephson junctions

In this work we present a method of representing terms in the current-phase-relation of a ballistic Josephson junction by combinations of diagrams, used in previous work to represent an equivalent of the matching condition determinant of the junction. This is accomplished by the expansion of the logarithm of this determinant in Taylor series and keeping track of surviving terms, i.e. terms that do not annihilate each other. The types of the surviving terms are represented by connected graphs, whose points represent diagrammatic terms of the determinant expansion. Then the theory is applied to obtain approximations of the current-phase relation of relatively thick ballistic ferromagnetic Josephson junctions with non-collinear magnetizations. This demonstrates the versatility of the method in developing approximations schemes and providing physical insight into the nature of contributions to the supercurrent from the available particle excitations in the junction. We also discuss the strong second harmonic contribution to the supercurrent in junctions with three mutually orthogonal magnetization vectors and a weak intermediate ferromagnet.

Equal-Spin Andreev Reflection on Junctions of Spin-Resolved Quantum Hall Bulk State and Spin-Singlet Superconductor

The recent development of superconducting spintronics has revealed the spin-triplet superconducting proximity effect from a spin-singlet superconductor into a spin-polarized normal metal. In addition recently superconducting junctions using semiconductors are in demand for highly controlled experiments to engineer topological superconductivity. Here we report experimental observation of Andreev reflection in junctions of spin-resolved quantum Hall (QH) states in an InAs quantum well and the spin-singlet superconductor NbTi. The measured conductance indicates a sub-gap feature and two peaks on the outer side of the sub-gap feature in the QH plateau-transition regime increases. The observed structures can be explained by considering transport with Andreev reflection from two channels, one originating from equal-spin Andreev reflection intermediated by spin-flip processes and second arising from normal Andreev reflection. This result indicates the possibility to induce the superconducting proximity gap in the the QH bulk state, and the possibility for the development of superconducting spintronics in semiconductor devices.

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 T_c. 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 T_c 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.