Enhanced spin pumping into superconductors provides evidence for superconducting pure spin currents

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.

Ultrafast all-optical toggle writing of magnetic bits without relying on heat

Ultrafast excitation of matter can violate Curie's principle that the symmetry of the cause must be found in the symmetry of the effect. For instance, heating alone cannot result in a deterministic reversal of magnetization. However, if the heating is ultrafast, it facilitates toggle switching of magnetization between stable bit-states without any magnetic field. Here we show that the regime of ultrafast toggle switching can be also realized via a mechanism without relying on heat. Ultrafast laser excitation of iron-garnet with linearly polarized light modifies magnetic anisotropy and thus causes toggling magnetization between two stable bit states. This new regime of 'cold' toggle switching can be observed in ferrimagnets without a compensation point and over an exceptionally broad temperature range. The control of magnetic anisotropy required for the toggle switching exhibits reduced dissipation compared to laser-induced-heating mechanism, however the dissipation and the switching-time are shown to be competing parameters.

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.

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.

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.

Electrical detection of spin pumping in van der Waals ferromagnetic Cr2Ge2Te6 with low magnetic damping

The discovery of magnetic order in atomically-thin van der Waals materials has strengthened the alliance between spintronics and two-dimensional materials. An important use of magnetic two-dimensional materials in spintronic devices, which has not yet been demonstrated, would be for coherent spin injection via the spin-pumping effect. Here, we report spin pumping from Cr₂Ge₂Te₆ into Pt or W and detection of the spin current by inverse spin Hall effect. The magnetization dynamics of the hybrid Cr₂Ge₂Te₆/Pt system are measured, and a magnetic damping constant of ~ 4-10 × 10^-4 is obtained for thick Cr₂Ge₂Te₆ flakes, a record low for ferromagnetic van der Waals materials. Moreover, a high interface spin transmission efficiency (a spin mixing conductance of 2.4 × 10¹⁹/m²) is directly extracted, which is instrumental in delivering spin-related quantities such as spin angular momentum and spin-orbit torque across an interface of the van der Waals system. The low magnetic damping that promotes efficient spin current generation together with high interfacial spin transmission efficiency suggests promising applications for integrating Cr₂Ge₂Te₆ into low-temperature two-dimensional spintronic devices as the source of coherent spin or magnon current.

Emergent Multifunctional Magnetic Proximity in van der Waals Layered Heterostructures

Proximity effect, which is the coupling between distinct order parameters across interfaces of heterostructures, has attracted immense interest owing to the customizable multifunctionalities of diverse 3D materials. This facilitates various physical phenomena, such as spin order, charge transfer, spin torque, spin density wave, spin current, skyrmions, and Majorana fermions. These exotic physics play important roles for future spintronic applications. Nevertheless, several fundamental challenges remain for effective applications: unavoidable disorder and lattice mismatch limits in the growth process, short characteristic length of proximity, magnetic fluctuation in ultrathin films, and relatively weak spin-orbit coupling (SOC). Meanwhile, the extensive library of atomically thin, 2D van der Waals (vdW) layered materials, with unique characteristics such as strong SOC, magnetic anisotropy, and ultraclean surfaces, offers many opportunities to tailor versatile and more effective functionalities through proximity effects. Here, this paper focuses on magnetic proximity, i.e., proximitized magnetism and reviews the engineering of magnetism-related functionalities in 2D vdW layered heterostructures for next-generation electronic and spintronic devices. The essential factors of magnetism and interfacial engineering induced by magnetic layers are studied. The current limitations and future challenges associated with magnetic proximity-related physics phenomena in 2D heterostructures are further discussed.

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.

Dynamics of Two Ferromagnetic Insulators Coupled by Superconducting Spin Current

A conventional superconductor sandwiched between two ferromagnets can maintain coherent equilibrium spin current. This spin supercurrent results from the rotation of odd-frequency spin correlations induced in the superconductor by the magnetic proximity effect. In the absence of intrinsic magnetization, the superconductor cannot maintain multiple rotations of the triplet component but instead provides a Josephson type weak link for the spin supercurrent. We determine the analog of the current-phase relation in various circumstances and show how it can be accessed in experiments on dynamic magnetization. In particular, concentrating on the magnetic hysteresis and the ferromagnetic resonance response, we show how the spin supercurrent affects the nonequilibrium dynamics of magnetization which depends on a competition between spin supercurrent mediated static exchange contribution and a dynamic spin pumping contribution. Depending on the outcome of this competition, a mode crossing in the system can either be an avoided crossing or mode locking.

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.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Giant oscillatory Gilbert damping in superconductor/ferromagnet/superconductor junctions

Interfaces between materials with differently ordered phases present unique opportunities for exotic physical properties, especially the interplay between ferromagnetism and superconductivity in the ferromagnet/superconductor heterostructures. The investigation of zero- and π-junctions has been of particular interest for both fundamental physical science and emerging technologies. Here, we report the experimental observation of giant oscillatory Gilbert damping in the superconducting niobium/nickel-iron/niobium junctions with respect to the nickel-iron thickness. This observation suggests an unconventional spin pumping and relaxation via zero-energy Andreev bound states that exist not only in the niobium/nickel-iron/niobium π-junctions but also in the niobium/nickel-iron/niobium zero-junctions. Our findings could be important for further exploring the exotic physical properties of ferromagnet/superconductor heterostructures and potential applications of ferromagnet π-junctions in quantum computing, such as half-quantum flux qubits.

Evidence for anisotropic spin-triplet Andreev reflection at the 2D van der Waals ferromagnet/superconductor interface

Fundamental symmetry breaking and relativistic spin-orbit coupling give rise to fascinating phenomena in quantum materials. Of particular interest are the interfaces between ferromagnets and common s-wave superconductors, where the emergent spin-orbit fields support elusive spin-triplet superconductivity, crucial for superconducting spintronics and topologically-protected Majorana bound states. Here, we report the observation of large magnetoresistances at the interface between a quasi-two-dimensional van der Waals ferromagnet Fe0.29TaS2 and a conventional s-wave superconductor NbN, which provides the possible experimental evidence for the spin-triplet Andreev reflection and induced spin-triplet superconductivity at ferromagnet/superconductor interface arising from Rashba spin-orbit coupling. The temperature, voltage, and interfacial barrier dependences of the magnetoresistance further support the induced spin-triplet superconductivity and spin-triplet Andreev reflection. This discovery, together with the impressive advances in two-dimensional van der Waals ferromagnets, opens an important opportunity to design and probe superconducting interfaces with exotic properties.

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.

Pt and CoB trilayer Josephson [Formula: see text] junctions with perpendicular magnetic anisotropy

We report on the electrical transport properties of Nb based Josephson junctions with Pt/Co[Formula: see text]B[Formula: see text]/Pt ferromagnetic barriers. The barriers exhibit perpendicular magnetic anisotropy, which has the main advantage for potential applications over magnetisation in-plane systems of not affecting the Fraunhofer response of the junction. In addition, we report that there is no magnetic dead layer at the Pt/Co[Formula: see text]B[Formula: see text] interfaces, allowing us to study barriers with ultra-thin Co[Formula: see text]B[Formula: see text]. In the junctions, we observe that the magnitude of the critical current oscillates with increasing thickness of the Co[Formula: see text]B[Formula: see text] strong ferromagnetic alloy layer. The oscillations are attributed to the ground state phase difference across the junctions being modified from zero to [Formula: see text]. The multiple oscillations in the thickness range [Formula: see text] nm suggests that we have access to the first zero-[Formula: see text] and [Formula: see text]-zero phase transitions. Our results fuel the development of low-temperature memory devices based on ferromagnetic 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.

Writing 3D Nanomagnets Using Focused Electron Beams

Focused electron beam induced deposition (FEBID) is a direct-write nanofabrication technique able to pattern three-dimensional magnetic nanostructures at resolutions comparable to the characteristic magnetic length scales. FEBID is thus a powerful tool for 3D nanomagnetism which enables unique fundamental studies involving complex 3D geometries, as well as nano-prototyping and specialized applications compatible with low throughputs. In this focused review, we discuss recent developments of this technique for applications in 3D nanomagnetism, namely the substantial progress on FEBID computational methods, and new routes followed to tune the magnetic properties of ferromagnetic FEBID materials. We also review a selection of recent works involving FEBID 3D nanostructures in areas such as scanning probe microscopy sensing, magnetic frustration phenomena, curvilinear magnetism, magnonics and fluxonics, offering a wide perspective of the important role FEBID is likely to have in the coming years in the study of new phenomena involving 3D magnetic nanostructures.

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.

Variable spin-charge conversion across metal-insulator transition

The charge-to-spin conversion efficiency is a crucial parameter in determining the performance of many useful spintronic materials. Usually, this conversion efficiency is predetermined by the intrinsic nature of solid-state materials, which cannot be easily modified without invoking chemical or structural changes in the underlying system. Here we report on successful modulation of charge-spin conversion efficiency via the metal-insulator transition in a quintessential strongly correlated electron compound vanadium dioxide (VO₂). By employing ferromagnetic resonance driven spin pumping and the inverse spin Hall effect measurement, we find a dramatic change in the spin pumping signal (decrease by > 80%) and charge-spin conversion efficiency (increase by five times) upon insulator to metal transition. The abrupt change in the structural and electrical properties of this material therefore provides useful insights on the spin related physics in a strongly correlated material undergoing a phase transition.

The interconversion of spin and charge is fundamental to the operation of spintronic devices. Here the authors demonstrate spin-to-charge conversion in the correlated material vanadium dioxide, and show that the efficiency changes dramatically across the metal-insulator transition.

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.

Fraunhofer patterns in magnetic Josephson junctions with non-uniform magnetic susceptibility

The development of superconducting memory and logic based on magnetic Josephson junctions relies on an understanding of junction properties and, in particular, the dependence of critical current on external magnetic flux (i.e. Fraunhofer patterns). With the rapid development of Josephson junctions with various forms of inhomogeneous barrier magnetism, Fraunhofer patterns are increasingly complex. In this paper we model Fraunhofer patterns for magnetic Josephson junctions in which the barrier magnetic susceptibility is position- and external-magnetic-field dependent. The model predicts anomalous Fraunhofer patterns in which local minima in the Josephson critical current can be nonzero and non-periodic with external magnetic flux due to an interference effect between magnetised and demagnetised regions.

Nonlocal Spin Transport Mediated by a Vortex Liquid in Superconductors

Departing from the conventional view on superconducting vortices as a parasitic source of dissipation for charge transport, we propose to use mobile vortices as topologically stable information carriers. To this end, we start by constructing a phenomenological theory for the interconversion between spin and vorticity, a topological charge carried by vortices, at the interface between a magnetic insulator and a superconductor, by invoking the interfacial spin Hall effect therein. We then show that a vortex liquid in superconductors can serve as a spin-transport channel between two magnetic insulators by encoding spin information in the vorticity. The vortex-mediated nonlocal signal between the two magnetic insulators is shown to decay algebraically as a function of their separation, contrasting with the exponential decay of the quasiparticle-mediated spin transport. We envision that hydrodynamics of topological excitations, such as vortices in superconductors and domain walls in magnets, may serve as a universal framework to discuss long-range transport properties of ordered materials.