Vortex State Research Articles

Probing Confined Vortices with a Superconducting Nanobridge

We realize a superconducting nanodevice in which vortex traps in the form of an aluminum square are integrated with a Dayem nanobridge. We perform field cooling of the traps arriving to different vortex configurations, dependent on the applied magnetic field, to demonstrate that the switching current of the bridge is highly sensitive to the presence and location of vortices in the trap. Our measurements exhibit unprecedented precision and ability to detect the first and successive vortex entries into all fabricated traps, from few hundred nm to $2\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ in size. The experimental results are corroborated by Ginzburg-Landau simulations, which reveal the subtle yet crucial changes in the density of the superconducting condensate in the vicinity of the bridge with every additional vortex entry and relocation inside the trap. An ease of integration and simplicity make our design a convenient platform for studying dynamics of vortices in strongly confining geometries, involving a promise to manipulate vortex states electronically with simultaneous in situ control and monitoring.

Theory of Caroli–de Gennes–Matricon analogs in full-shell hybrid nanowires

Full-shell nanowires are hybrid nanostructures consisting of a semiconducting core encapsulated in an epitaxial superconducting shell. When subject to an external magnetic flux, they exhibit the Little-Parks (LP) phenomenon of flux-modulated superconductivity, an effect connected to the physics of Abrikosov vortex lines in type-II superconductors. We show theoretically that full-shell nanowires can host subgap states that are a variant of the Caroli-de Gennes-Matricon (CdGM) states in vortices. These CdGM analogs are shell-induced Van Hove singularities in core subbands. We elucidate their structure, parameter dependence and behavior in tunneling spectroscopy through a series of models of growing complexity. Using microscopic numerical simulations, we show that CdGM analogs exhibit a characteristic skewness towards higher flux values inside non-zero LP lobes resulting from the interplay of three ingredients. First, the orbital coupling to the field shifts the energy of the CdGM analogs proportionally to the flux and to their generalized angular momentum. Second, CdGM analogs coalesce into degeneracy points at flux values for which their corresponding radial wavefunctions are threaded by an integer multiple of the flux quantum. And third, the average radii of all CdGM-analog wavefunctions inside the core are approximately equal and are controlled by the electrostatic band bending at the core/shell interface. As the average radius moves away from the interface, the degeneracy points shift towards larger fluxes from the center of the LP lobes, causing the skewness. This analysis provides a transparent interpretation of the nanowire spectrum that allows to extract microscopic information by measuring the number and skewness of CdGM analogs. Moreover, it allows to derive an efficient Hamiltonian of the full-shell nanowire in terms of a modified hollow-core model at the average radius.

Globally correlated states and control of vortex lattices in active roller fluids

Active fluids demonstrate complex collective behavior and self-organization often resulting in the emergence of localized vortices. We report on a combined experimental and computational study of the spontaneous formation of globally correlated vortex lattices formed in active roller fluids. The vortices are comprised of active ferromagnetic rollers placed on a patterned substrate promoting localization of self-organized vortices in a lattice with square symmetry. Each individual vortex spontaneously selects its chiral state (clockwise or counterclockwise). Nevertheless, confined to a square lattice, an ensemble of interacting active vortices is capable of developing correlations between chiral states of neighboring vortices. We show that such ensembles of active vortices can spontaneously evolve towards a globally correlated state with the antiferromagnetic ordering of their vorticities. We explore the correlations between chiral states of neighboring vortex pairs in response to changes in the geometry of the confining lattice. The results are supported by numerical simulations based on phenomenological coarse grained particle dynamics coupled to shallow water Navier-Stokes hydrodynamics. We show that these ordered vortex lattices formed by magnetic rollers have the ability to self-heal the antiferromagnetic order and stabilize individual vortical states in the activity regimes beyond optimal conditions for the collective vortex states. The results provide insights into the collective behavior of active magnetic roller fluids in the presence of geometrical confinement.

Palaeosecular variation in Northern Patagonia recorded by 0–5 Ma Caviahue–Copahue lava flows

SUMMARY Palaeosecular variation (PSV) determinations and studies of the geometry of the Earth’s main magnetic field provide important information about the field evolution, and to constrain numerical geodynamo models. Palaeomagnetic directional data from lava flows over the last few million years is of particular interest because the regional and global tectonic effects are minimal. However, the distribution of this type of palaeomagnetic data is uneven where the Southern Hemisphere is the destitute side. Therefore, the better knowledge of the geomagnetic field behaviour depends on the increased availability of high-quality data, especially in the Southern Hemisphere. A PSV and the time-averaged field (TAF) study was then performed in 0–5 Ma lava flows from the Caviahue–Copahue Volcanic Complex located in Northern Patagonia, Argentina (37°0′S, 71°10′W). The magnetic mineralogy of lava flows was investigated through thermomagnetic susceptibility curves, isothermal remanent magnetization (IRM) acquisition curves, hysteresis loops and first-order reversal curves (FORCs). Samples are essentially comprised of titanomagnetite with different Ti contents and magnetic domain structures typical of vortex state particles. A total of 50 volcanic sites were sampled, which provided 42 reliable palaeomagnetic site-mean directions after alternating field and thermal demagnetization. From these 42 sites, 36 are of normal and 6 are of reversed polarity. The mean direction from normal (reversed) sites is D = 356.2°, I = −50.1°, α95 = 4.0° and N = 36 (D = 176.5°, I = 59.5°, α95 = 14.1° and N = 6). Using only site-level data with the precision parameter k ≥ 100, we obtain 26 palaeomagnetic sites for PSV and TAF investigations in the study region. The filtered data set has a mean direction (D = 354.4°, I = −53.2° and α95 = 5.1°) close to the expected direction for a geocentric axial dipole (GAD) field (IGAD = −57.3°). The palaeopole (Plat = 84.4°, Plon = 229.1° and A95 = 5.7°) coincides with the Earth’s spin axis within the 95 per cent confidence interval. Virtual geomagnetic pole scatter ($S_{B} = {15.8^{18.9}_{11.8}}^{\circ }$) and the inclination anomaly ($\Delta I = 4.1_{-1.0}^{{9.2}^{\circ }}$) are both consistent at the 95 per cent confidence level with recent PSV and TAF models, respectively. Our results support the presence of small non-dipole field contributions (<3 per cent) superimposed on the GAD term, as reported by South American studies at mid southern latitudes.

Frequency Tunability of Spin‐Torque Vortex Oscillator in Permalloy Nanodisks with Modified Material Properties

The manipulation of the vortex state in magnetic nanostructures has received a lot of interest in recent decades, with potential applications in nonvolatile magnetic random‐access memory and logic networks. For wireless communication advancements, nano‐sized, and low‐phase‐noise, adjustable transmitter‐receiver networks are critical. Herein, it is shown that by using micromagnetic simulations when the saturation magnetization is reduced in a particular region of a magnetic nanodisk, the frequency tunability in such disks can be achieved. The gyrotropic mode of the vortex core is excited with spin‐polarized current and an in‐plane static magnetic field and found that an isolated magnetic vortex shows different resonance frequencies at different saturation magnetization regions. The dynamics of the mutual synchronization between two such dipolarly coupled magnetic vortices are numerically investigated, and the essential distances at which synchronization occurs are also identified. These incredibly small vortex‐based oscillator devices have linewidths of the order of 40–60 MHz, making them prospective candidates for signal‐processing applications and a strong new tool for basic research on vortex dynamics in magnetic nanostructures.

Time-reversal symmetry breaking in the superconducting low carrier density quasiskutterudite Lu3Os4Ge13

The complex structure of the Remeika phases, the intriguing quantum states they display, and their low carrier concentrations are strong motivations to study the nature of their superconducting phases. In this Letter, the microscopic properties of the superconducting phase of single-crystalline ${\mathrm{Lu}}_{3}{\mathrm{Os}}_{4}{\mathrm{Ge}}_{13}$ are investigated by muon-spin relaxation and rotation ($\ensuremath{\mu}\mathrm{SR}$) measurements. The zero-field $\ensuremath{\mu}\mathrm{SR}$ data reveal the presence of spontaneous static or quasistatic magnetic fields in the superconducting state, breaking time-reversal symmetry; the associated internal magnetic-field scale is found to be exceptionally large ($\ensuremath{\simeq}$ 0.11 mT). Furthermore, transverse-field $\ensuremath{\mu}\mathrm{SR}$ measurements in the vortex state of ${\mathrm{Lu}}_{3}{\mathrm{Os}}_{4}{\mathrm{Ge}}_{13}$ imply a complex gap function with significantly different strengths on different parts of the Fermi surface. Although our measurements do not completely determine the order parameter, they strongly indicate that electron-electron interactions are essential to stabilizing pairing in the system, thus, demonstrating its unconventional nature.

Nanobridge SQUIDs as Multilevel Memory Elements

With the development of alternative computing schemes working at cryogenic temperatures, superconducting memory elements have gained interest. In this context, superconducting quantum interference devices (SQUIDs) are promising candidates, as they may trap different discrete amounts of magnetic flux. We demonstrate that a field-assisted writing scheme allows such a device to operate as a multilevel memory by the readout of eight distinct vorticity states at zero magnetic field. We present an alternative mechanism based on single phase slips, which allows the vorticity state to be switched while preserving superconductivity. This mechanism provides a possibly deterministic channel for flux control in SQUID-based memories, under the condition that the field-dependent energy of different vorticity states are nearby.

Forced vortex merging and splitting events in ferrofluidic Couette flow

Time-dependent boundary conditions are ubiquitous in numerous natural and industrial flows. However, to date, the influence of such temporal modulations has been given minor attention. This research addresses ferrofluidic Couette flow in between co-rotating cylinders in a spatially homogeneous magnetic field subject to time-periodic modulation. Using a modified Niklas approximation, we study the effect of amplitude and frequency modulation onto the transition scenarios between different toroidal flow structures, non-propagating vortex (nV) states, via vortex merging and splitting. Thereby, the system response appears to be quite sensitive/dependent on the driving frequency ΩH, which can cause a notable “delay” in the system response. Further, as a result of the inertia of the ferrofluid, resisting the fast-changing accelerating Kelvin force, new, temporal nV states appear within an alternating field. These states are unstable under static fields. Finally, we show that within the same nV state, while keeping similar flow dynamics, large discrepancies in angular momentum and torque can be observed.

Closed vortex state in three-dimensional mesoscopic superconducting films under an applied transport current

By using the full 3D generalized time-dependent Ginzbug-Landau equation, we study a long superconducting film of finite width and thickness under an applied transport current. We show that, for sufficiently large thickness, the vortices and the antivortices become curved before they annihilate each other. As they approach the center of the sample, their ends combine, producing a single closed vortex. We also determine the critical values of the thickness for which the closed vortex sets in for different values of the Ginzburg-Ladau parameter. Finally, we propose a model of how to detect a closed vortex experimentally.

Chirality coupling in topological magnetic textures with multiple magnetochiral parameters

Chiral effects originate from the lack of inversion symmetry within the lattice unit cell or sample’s shape. Being mapped onto magnetic ordering, chirality enables topologically non-trivial textures with a given handedness. Here, we demonstrate the existence of a static 3D texture characterized by two magnetochiral parameters being magnetic helicity of the vortex and geometrical chirality of the core string itself in geometrically curved asymmetric permalloy cap with a size of 80 nm and a vortex ground state. We experimentally validate the nonlocal chiral symmetry breaking effect in this object, which leads to the geometric deformation of the vortex string into a helix with curvature 3 μm−1 and torsion 11 μm−1. The geometric chirality of the vortex string is determined by the magnetic helicity of the vortex texture, constituting coupling of two chiral parameters within the same texture. Beyond the vortex state, we anticipate that complex curvilinear objects hosting 3D magnetic textures like curved skyrmion tubes and hopfions can be characterized by multiple coupled magnetochiral parameters, that influence their statics and field- or current-driven dynamics for spin-orbitronics and magnonics.

Sparse Modeling Approach for Quasiclassical Theory of Superconductivity

We propose the sparse modeling approach for quasiclassical theory of superconductivity, which reduces the computational cost of solving the gap equations. The recently proposed sparse modeling approach is a consequence of the Green’s function having less information than its spectral function and hence is compressible without loss of relevant information. Using the intermediate representation of the Green’s function in the sparse modeling approach, the gap equation can be solved with only 10–100 sampled Matsubara Green’s functions, whereas the conventional quasiclassical theory requires 100–1000. The efficiency of the proposed method is demonstrated in bulk and vortex states, through self-consistently solve of the Eilenberger and gap equations. Consequently, the sparse modeling approach is concluded to be appropriate for all theoretical methods based on the Matsubara formalism in the quasiclassical theory of superconductivity.

Viscoelastic instabilities of Taylor-Couette flows with different rotation regimes.

The critical modes of the instabilities of viscoelastic Taylor-Couette flow are investigated using both experiments and linear stability analysis when only one cylinder rotates and the other is fixed. A viscoelastic Rayleigh circulation criterion highlights that the elasticity of the polymer solution can induce a flow instability even if the Newtonian counterpart is stable. When the inner cylinder solely rotates, experimental results show three critical modes: stationary axisymmetric vortices or Taylor vortices for small elasticity, standing waves, also called ribbons for intermediate values of elasticity, and disordered vortices (DV) for large elasticity values. When the outer cylinder rotates and the inner cylinder is fixed and for large values of elasticity, the critical modes appear in the form of DV. There is a good agreement between experimental and theoretical results provided that the elasticity of the polymer solution is accurately determined. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Dragging a defect in a droplet Bose-Einstein condensate

In the present work we consider models of quantum droplets within a weakly interacting mass-balanced binary Bose-Bose mixture in the presence of a defect in the form of a laser beam moving through the respective condensates including the Lee-Huang-Yang correction. Our analysis features separately an exploration of the existence, stability, bifurcations, and dynamics in one-, two-, and three-dimensional settings. In the absence of an explicit solution of the problem, we provide an analysis of the speed of sound and observe how the states traveling with the defect may feature a saddle-center bifurcation as the speed or the strength of the defect is modified. Relevant bifurcation diagrams are constructed systematically and the unstable states, as well as the dynamics past the existence of stable states, are monitored. The connection of the resulting states with dark solitonic patterns in one dimension, vortical states in two dimensions, and vortex rings in three dimensions is accordingly elucidated.

Rotation of a Ferromanganese Nodule in the Penrhyn Basin, South Pacific, Tracked by the Earth's Magnetic Field

AbstractFerromanganese nodules are cm‐sized, authigenic, abyssal manganese‐iron‐hydroxide concretions. They grow very slowly at rates of a few mm per million years. Although their ages are older than millions of years, they are often found half buried on the modern sediment surface. The mechanisms for the nodules' persistence at the surface without complete burial could be linked to their occasional motion or agitation. Here, we report evidence for the rotation of a nodule from the Penrhyn Basin, South Pacific detected by paleomagnetism. The paleomagnetic inclinations of specimens from the nodules' surface are consistent with the recent geomagnetic fields. The paleomagnetic directions from the surface to the core show successive changes and form a great circle with a pole at (azimuth = 53.9°, dip = 32.1°). This suggests that the nodule rotated along its pole while successively recording magnetizations. As the nodule was found on a gentle slope at the foot of an abyssal hill, it may have moved downslope due to bottom current underwashing. Rock magnetic analyses of the nodule suggest the presence of magnetite in single domain and vortex states. Low temperature magnetometry revealed that magnetite grains were heavily oxidized to maghemite, especially close to the core of the nodule. The rotation may have exposed the rising part of the nodule to oxidative pore water. Oxygenated Antarctic Bottom Water might have caused remagnetization due to low temperature oxidation of magnetite. The rotation would also facilitate the omnidirectional growth of the nodules' mixed layer of diagenetic buserite and hydrogenetic vernadite.

Fragmentation and correlations in a rotating Bose–Einstein condensate undergoing breakup

The theoretical investigation of rotating Bose–Einstein condensates has mainly focused on the emergence of quantum vortex states and the condensed properties of such systems. In the present work, we concentrate on other facets by examining the impact of rotation on the ground state of weakly interacting bosons confined in anharmonic potentials computed both at the mean-field level and particularly at the many-body level of theory. For the many-body computations, we employ the well-established many-body method known as the multiconfigurational time-dependent Hartree method for bosons. We present how various degrees of fragmentation can be generated following the breakup of the ground state densities in anharmonic traps without ramping up a potential barrier for strong rotations. The breakup of the densities is found to be associated with the acquisition of angular momentum in the condensate due to the rotation. In addition to fragmentation, the presence of many-body correlations is examined by computing the variances of the many-particle position and momentum operators. For strong rotations, the many-body variances become smaller than their mean-field counterparts, and one even finds a scenario with opposite anisotropies of the mean-field and many-body variances. Further, it is observed that for higher discrete symmetric systems of order k, namely three-fold and four-fold symmetry, breakup to k sub-clouds and emergence of k-fold fragmentation take place. All in all, we provide a thorough many-body investigation of how and which correlations build up when a trapped Bose–Einstein condensate breaks up under rotation.

Modification of three-magnon splitting in a flexed magnetic vortex

We present an experimental and numerical study of three-magnon splitting in a micrometer-sized magnetic disk with a vortex state strongly deformed by static in-plane magnetic fields. Excited with large enough power at frequency fRF, the primary radial magnon modes of a cylindrical magnetic vortex can decay into secondary azimuthal modes via spontaneous three-magnon splitting. This nonlinear process exhibits selection rules leading to well-defined and distinct frequencies fRF/2±Δf of the secondary modes. Here, we demonstrate that three-magnon splitting in vortices can be significantly modified by deforming the magnetic vortex with in-plane magnetic fields, leading to a much richer three-magnon response. We find that, with increasing field, an additional class of secondary modes is excited, which are localized to highly flexed regions adjacent to the displaced vortex core. While these modes satisfy the same selection rules of three-magnon splitting, they exhibit much lower three-magnon threshold power compared to regular secondary modes of a centered vortex. The applied static magnetic fields are small (≃10 mT), providing an effective parameter to control the nonlinear spectral response of confined vortices. Our work expands the understanding of nonlinear magnon dynamics in vortices and advertises these for potential neuromorphic applications based on magnons.

How spanwise travelling transversal surface waves change the near-wall flow

The alteration of the near-wall flow field of a turbulent boundary layer flow subjected to spanwise travelling transversal surface waves at a friction Reynolds number $Re_\tau \approx 1525$ is investigated. The results of a spatial noise-assisted multivariate empirical mode decomposition reveal that this flow control method periodically induces near-wall large-scale bursts while simultaneously lowering the energetic content of small-scale features. The increasing occurrence of intense large-scale ejections in the near-wall region is of particular importance for reducing the wall-shear stress since these ejections balance large-scale sweeps originating from the outer layer. Thus, they corrupt the outer-layer impact on the near-wall dynamics and, consequently, the overall fluctuation intensity at the wall is attenuated. This disturbed top-down momentum exchange is highlighted by an inner–outer interaction analysis, which further reveals an increased bottom-up communication provoked by the large-scale ejections. Moreover, it is shown that the periodic secondary flow field induced by the actuation interferes with the quasi-streamwise vortices in the near-wall region. The velocity gradients of the secondary flow field deform the vortices’ cross-section into an elliptic shape, which yields an unstable vortex state resulting in vortex disintegration. In combination with the effect of the large-scale ejections, the reduced number of quasi-streamwise vortices compared with the undisturbed boundary layer flow results in a decreased wall-normal momentum exchange and the widening and weakening of near-wall streaks. This yields a reduced fluctuation intensity in the near-wall region that lowers the overall wall-shear stress level.

Vortex state in a two-condensate superconducting film considering a topological coupling

In this work, we studied the magnetization and the Cooper pairs density in a conventional superconducting thin square film in the presence of an external magnetic field H. Our investigation was carried out to solve the [Formula: see text]-wave-two-band Ginzburg–Landau equations (TB-TDGL) considering a topological-type coupling between the bands. We vary the size of the sample [Formula: see text], the weighty of the coupling [Formula: see text] and the effective Ginzburg–Landau parameter [Formula: see text], as a magnetic field function. We found an interesting vortex configuration and the respective generation of vortex clusters due to the coupling used between condensates. A high (weak) dependence of the first (second) critical field on the weight of the coupling is found. We revealed interesting magnetization curves, their dependence with the size of the sample, the relationship with the coherence length and penetration length and finally with the weight of the coupling between the bands ([Formula: see text]).

Intense nonlinear laser field longitudinal vector potential breaks motion symmetry of stimulated electron and produces highly collimated radiation

The effects of longitudinal fields on electron dynamics, power, and radiation spectrum in tightly-focused circularly polarized laser pulses are investigated in detail. When the longitudinal field vector potential is not considered at the intense relativistic laser field, the longitudinal acceleration of the electron subjected to the ponderomotive force is oscillatory, and the electron will be pushed out of the laser field. The peak radiation power, along with peak angle, varies exponentially with the laser peak amplitude. The longitudinal field leads to the appearance of spatial radiation vortex states when the laser peak is strong, increasing the collimation of the power and spectrum of spatial radiation as well as the focus.

Multilevel Spiral Axicon for High-Order Bessel-Gauss Beams Generation.

This paper presents an efficient method to generate high-order Bessel-Gauss beams carrying orbital angular momentum (OAM) by using a thin and compact optical element such as a multilevel spiral axicon. This approach represents an excellent alternative for diffraction-free OAM beam generation instead of complex methods based on a doublet formed by a physical spiral phase plate and zero-order axicon, phase holograms loaded on spatial light modulators (SLMs), or the interferometric method. Here, we present the fabrication process for axicons with 16 and 32 levels, characterized by high mode conversion efficiency and good transmission for visible light (λ = 633 nm wavelength). The Bessel vortex states generated with the proposed diffractive optical elements (DOEs) can be exploited as a very useful resource for optical and quantum communication in free-space channels or in optical fibers.