Single Vortex State Research Articles

Comparison of natural convection in liquid gallium under horizontal and vertical magnetic fields

The dynamics of two-dimensional natural convection in liquid metal under the influence of magnetic fields within a confined square enclosure are numerically investigated using a high-accuracy method. The study focuses on the flow transition process influenced by both horizontal and vertical magnetic fields, examining the impacts of temperature difference, magnetic field strength, and orientation on flow characteristics and heat transfer. The range of Rayleigh numbers (Ra) explored is from 104 to 106, while Hartmann numbers (Ha) vary from 0 to 100. Liquid gallium is used as the working fluid with a Prandtl number (Pr) of 0.025. Our investigation reveals rich variations in flow patterns, categorized into unsteady periodic, steady “two-in-one” vortex, and steady single vortex states. As Rayleigh numbers increase, a complex series of flow transitions is observed, leading to enhanced flow dynamics. The transition from a steady state to periodic motion is accompanied by a notable increase in heat transfer efficiency. However, increasing the strength of the magnetic field suppresses the flow. A sufficiently strong suppression transitions the flow from periodic motion back to a steady state, resulting in a gradual decrease in heat transfer efficiency. For the parameters considered, the suppression efficiency of horizontal magnetic fields is stronger than that of vertical ones, especially when Ra>6×105 and Ha=100, with a 14% greater suppression efficiency. A scaling law for heat transfer is also identified: Nu:Ra/Ha2γ, where 14≤γ≤12, independent of the magnetic field orientation.

Coupling nanoscopic tomography and micromagnetic modelling to assess the stability of geomagnetic recorders

The recording of planetary magnetic fields is often attributed to uniformly-magnetised nanoscopic iron oxides, called single-domain. Yet, the main magnetic constituents of rocks are more complex, non-uniformly magnetised grains in single or multi-vortex states. We know little about their behaviour due to limitations in defining their precise shape and internal magnetic structure. Here we combine non-destructive Ptychographic X-ray Computed Nano-tomography with micromagnetic modelling to explore the magnetic stability of remanence-bearing minerals. Applied to a microscopic rock sample, we identified hundreds of nanoscopic grains of magnetite/maghemite with diverse morphologies. Energy barrier calculations were performed for these irregularly shaped grains. For some grains, these morphological irregularities near the transition from single-domain to the single-vortex state allow for multiple domain states, some unstable and unable to record the field for significant periods. Additionally, some other grains exhibit temperature-dependent occupancy probabilities, potentially hampering experiments to recover the intensity of past magnetic fields.

Electro-osmotic flow instability of viscoelastic fluids in a nanochannel

The study of the complex rheological properties of viscoelastic fluids in nanochannels will facilitate the application of nanofluidics in biomedical and other fields. However, the flow of viscoelastic fluids in nanochannels has significant instabilities, and numerical simulation failures are prone to occur at high Weissenberg numbers (Wi). In this study, the simplified Phan-Thien-Tanner viscoelastic fluid model is solved using the log-conformation tensor approach, and the effects of rheological parameters of the viscoelastic fluid, such as the Weissenberg number (Wi), extensibility parameter (ε), and viscosity ratio (β), on the flow characteristics and flow instability within the nanochannel are investigated. The results indicate that the variation of rheological parameters of viscoelastic fluids has a significant effect on the flow state and flow instability of fluids in nanochannels. When the rheological parameters are in a specific range, the flow velocity and outlet current in the nanochannel exhibit relatively regular periodic fluctuations. As the flow transitions from an up-and-down moving single-vortex state to a symmetric double-vortex state, the average velocity of the central axis in the nanochannel is increased by about 15%. Furthermore, when Wi increases from 150 to 400, the length and height of the vortex increase by 50% and 100%, respectively.

Artificial Neuron Based on the Bloch-Point Domain Wall in Ferromagnetic Nanowires.

Nanomagnetism and spintronics are currently active areas of research, with one of the main goals being the creation of low-energy-consuming magnetic memories based on nanomagnet switching. These types of devices could also be implemented in neuromorphic computing by crafting artificial neurons (ANs) that emulate the characteristics of biological neurons through the implementation of neuron models such as the widely used leaky integrate-and-fire (LIF) with a refractory period. In this study, we have carried out numerical simulations of a 120 nm diameter, 250 nm length ferromagnetic nanowire (NW) with the aim of exploring the design of an artificial neuron based on the creation and destruction of a Bloch-point domain wall. To replicate signal integration, we applied pulsed trains of spin currents to the opposite faces of the ferromagnetic NW. These pulsed currents (previously studied only in the continuous form) are responsible for inducing transitions between the stable single vortex (SV) state and the metastable Bloch point domain wall (BP-DW) state. To ensure the system exhibits leak and refractory properties, the NW was placed in a homogeneous magnetic field of the order of mT in the axial direction. The suggested configuration fulfills the requirements and characteristics of a biological neuron, potentially leading to the future creation of artificial neural networks (ANNs) based on reversible changes in the topology of magnetic NWs.

The Impact of Grain‐Size Distributions of Iron‐Oxides on Paleomagnetic Measurements

AbstractMagnetic signals in igneous rocks arise from assemblages of iron‐oxide bearing minerals that differ in for example, size, shape, and chemistry. Paleomagnetic measurements on bulk samples measure millions of such grains simultaneously, producing a statistical ensemble of the magnetic moments of the individual grains. Scanning magnetometry techniques such as the Quantum Diamond Microscope (QDM) measure magnetic signals on micrometer scales, allowing the identification of magnetic moments of individual grains in a sample using for example, Micromagnetic Tomography (MMT). Here we produce a grain‐size distribution of iron‐oxides in a typical Hawaiian basalt from the superparamagnetic threshold (∼40 nm) to grains with a diameter of 10 µm. This grain‐size distribution is obtained by combining FIB‐SEM and MicroCT data from sister specimens, and normalizing them to the mineral surface area of non‐magnetic minerals. Then we use this grain‐size distribution to determine the contributions of individual magnetic carriers to bulk magnetic measurements and surface magnetometry. We found that measurements on bulk samples are sensitive to relatively small grain sizes in the realm of single domain or vortex states (<200 nm), while signals in surface magnetometry arise mainly from larger grains with diameters >1 µm. This implies that bulk measurements cannot be compared straightforwardly to signals from surface magnetometry from the same sample. Moreover, our observations explain why MMT results are insensitive to the presence of many small grains in a sample that intuitively should hamper their outcome.

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All superconductors in a magnetic field are characterized by three critical magnetic fields: lower critical Hc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{c1}$$\\end{document}, upper critical Hc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{c2}$$\\end{document} and thermodynamic critical field Hc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{c}$$\\end{document}. Only two sets of inequalities Hc2>Hc>Hc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{c2}>H_c>H_{c1}$$\\end{document} or Hc1>Hc>Hc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{c1}>H_c>H_{c2}$$\\end{document} are possible in a single-component superconductor. Here, we report our study of the critical fields in multicomponent superconductors with two superconducting components in the framework of the Ginzburg-Landau functional. We derive the relationship between the phases of the components of the superconducting complex order parameter from the charge conservation law in explicit form and insert it into the Ginzburg-Landau functional. Using the modified Ginzburg-Landau equation, we acquire the single vortex state including the analytical expression for asymptotics. Also, we obtain the analytical form for the state in the upper critical field. We find that in some cases an unusual sequence of critical fields Hc1,Hc2>Hc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{c1},H_{c2}>H_c$$\\end{document} can be realized in multicomponent superconductors.

Angular first-order reversal curve analysis of FeNi/Cu multilayered nanowire arrays with different diameters

The main goal of the emerging field of spintronics is the shrinkage of materials and devices while improving their magnetic performance for a variety of applications, especially three-dimensional information storage. This stipulates the understanding of fundamental magnetic mechanisms such as magnetization reversal and switching events in multilayer systems with tunable size. Here, a porous anodic alumina membrane-assisted electrochemical deposition method is employed to fabricate FeNi/Cu multilayered nanowire arrays (MNWAs) with diameters in the range of D = 35–80 nm. Angular magnetic properties of these MNWAs are investigated via hysteresis loop and first-order reversal curve (FORC) measurements for angle fields of 0° ≤ θ ≤ 90°. While the former indicates the existence of different contributions of vortex domain wall propagation for smaller (D ≤50 nm) and larger (D >50 nm) diameters, the latter reveals the occurrence of single vortex states, depending on θ and D. Moreover, at θ = 0°, a transition from single domain to multidomain-like behavior appears to occur with increasing D from 35 to 80 nm based on FORC diagrams, significantly influencing magnetization reversibility of magnetic FeNi segments with relatively high aspect ratios (>5). The variation of magnetostatic interactions with respect to θ is discussed and compared at each diameter as an effective factor in determining angular magnetic properties. Also, the axial variation behavior of coercivity as a function of D is correlated with changes in the reversible percentage, shedding light on the expectations from the vortex domain wall propagation.

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.

Electronic properties of -Mn-type non-centrosymmetric superconductor Re5.5Ta under hydrostatic pressure

We have studied the effect of hydrostatic pressure on the superconducting and normal state properties of the non-centrosymmetric superconductor Re5.5Ta using magnetotransport, magnetization, and band structure studies. The superconducting transition temperature () reveals a modest decrease of ∼0.52 K as the external pressure is raised to 8 GPa. We found the Maki parameter, both at ambient and high pressures, suggesting the significant role of the Pauli pair breaking effect. Furthermore, the lower critical field was found to decrease with a rate of −1.74 mT GPa−1 as pressure increases to 1.05 GPa. Analysis of the thermally activated flux flow region of using the Arrhenius equation reveals the coexistence of single and collective vortex states. Further analysis of the critical current density indicates that the surface and volume pinning centers coexist and remain unaffected with varying pressure. Band structure calculations were performed using density functional theory and reveal a large bulk modulus, ∼ 289 GPa with ∼ 3.7, suggesting poor compressibility. In addition, we found that the density of states at the Fermi level barely reduces, even at pressures of up to 20 GPa. This is consistent with the experimental observation of robust superconductivity under compression.

Tilted Poincaré sphere geodesics.

We provide the first, to the best of our knowledge, experimental demonstration of a geometric phase generated in association with closed Poincaré sphere trajectories comprising geodesic arcs that do not start, end, or necessarily even include, the north and south poles that represent pure Laguerre-Gaussian modes. Arbitrarily tilted (elliptical) single vortex states are prepared with a spatial light modulator, and Poincaré sphere circuits are driven by beam transit through a series of π-converters and Dove prisms.

Unidirectional emission and reconfigurability of channeled spin waves from a vortex core in a teardrop-shaped nanopatch

We propose the design of a teardrop-shaped magnetic patch as a unidirectional magnetically driven spin wave emitter capable of operating in a wide range of frequencies. We explore its potential through micromagnetic studies in line with vibrational sample magnetometry measurements and ferromagnetic resonance experiments. The proposed system is based on the excitation of a vortex core, acting as a source of spin waves, and a single Bloch domain wall, as a channel for the confinement and propagation of the mode in a sufficiently thick magnetic patch in the single magnetic vortex (SMV) state. The novelty consists in the reconfigurability and simplicity of the system, that is operational without the need of external saturating fields, retaining a single Bloch domain wall and a movable single vortex core. This allows significant suppression of the wave emission by means of an external bias field, which in turn allows a controllable valvelike effect. Following our proposed strategy for cultivating a single vortex core in the shape, and after a thorough micromagnetic study of the most prominent magnetization dynamics in the patch, we show that the SMV state can be obtained in a thick enough (80 nm) teardrop-shaped patch. Micromagnetic results show the potential of this simple structure as a tunable and unidirectional spin wave emitter. Experimental results also suggest that the required magnetic configuration has been experimentally obtained in the structure, in good agreement with micromagnetic simulations.

Molecular dynamics simulations of void-mediated polarization vortex domain switching in compressed BaTiO3 nanofilm

Molecular dynamics simulations based on the anisotropic shell model with the first-principles parameters are performed to investigate the void-mediated polarization vortex domain switching in compressed BaTiO3 nanofilms. When a unit-cell-size void is located at the nanofilm center, the polarization configuration is in a single-vortex state instead of a multi-vortex state. For different void length fractions along the [100] lattice orientation, a cylindrical vortex is formed around the void while a few small vortexes nucleate closely above and/or below the void. With increasing void area fraction in the [100] plane, the vortex around the void gradually switches from clockwise to counterclockwise. Both the void shape and orientation have important effects on the vortex domain switching. A void near the model center tends to induce a clockwise vortex around it, a void in the lower left region of model to motivate a counterclockwise vortex, but a void in other locations to induce a closure domain with different switching degrees. In addition, it is found that the degree of closure domain switching could be kept if a void changes its location only in a small area. These observations should be instructive for the design and application of ferroelectric devices.

Unveiling the Origin of Multidomain Structures in Compositionally Modulated Cylindrical Magnetic Nanowires.

CoNi/Ni multisegmented cylindrical nanowires were synthesized via an electrochemical route. The wires are 140 nm in diameter, with 1000 nm long Ni segments and CoNi segments between 600 and 1400 nm in length. The magnetic configuration was imaged by XMCD-PEEM in the demagnetized state and at remanence after magnetizing axially and perpendicularly. Ni segments, with cubic crystal symmetry, show an axial magnetic configuration with a small curling component at the surface. In turn, CoNi segments, with hexagonal crystal symmetry and a strong magnetocrystalline anisotropy perpendicular to the nanowires, show a single vortex state in the shorter segments and multivortex or multitransverse magnetic configurations in medium and long segments, respectively. A detailed study by micromagnetic simulations reveals that the magnetic configuration is determined mainly by the coupling between soft Ni and harder CoNi segments. For short CoNi segments, Ni segments are magnetostatically coupled and the chirality of the single vortex formed in CoNi remains the same as that of the curling in neighboring Ni segments. For longer CoNi segments, the remanent state is either the multivortex or multitransverse state depending on whether the previously applied field was parallel or perpendicular to the magnetocrystalline axis. The results point out the relevance of the cylindrical geometry to promote the occurrence of complex magneto-chiral effects and provide key information for the design of cylindrical magnetic nanowires for multiple applications.

Creation and Manipulation of Quantized Vortices in Bose–Einstein Condensates Using Reinforcement Learning

We apply the technique of reinforcement learning to the control of nonlinear matter waves. In this method, an agent controls the position, strength, and shape of an external Gaussian potential to create and manipulate quantized vortices in a Bose–Einstein condensate (BEC) trapped in a harmonic potential. The density and velocity distributions of the BEC at each moment obtained by the Gross–Pitaevskii evolution are directly input into a convolutional neural network to determine the next action of the agent. We demonstrate that a stationary single-vortex state can be produced in a two-dimensional system, and a stationary vortex-ring state can be produced in a three-dimensional system.

Interplay of Fermi velocities and healing lengths in two-band superconductors

By numerically solving the Bogoliubov-de Gennes equations for the single vortex state in a two-band superconductor, we demonstrate that the disparity between the healing lengths of two contributing condensates is strongly affected by the band Fermi velocities, even in the presence of the magnetic field and far beyond the regime of nearly zero Josephson-like coupling between bands. Changing the ratio of the band Fermi velocities alters the temperature dependence of the condensate lengths and significantly shifts parameters of the ``length-scales locking" regime at which the two characteristic lengths approach one another.

Ground state properties of trapped boson system with finite-range Gaussian repulsion: exact diagonalization study

We use exact diagonalization to study an interacting system of N spinless bosons with finite-range Gaussian repulsion, confined in a quasi-two-dimensional harmonic trap with and without an introduced rotation. The diagonalization of the Hamiltonian matrix using Davidson algorithm in subspaces of quantized total angular momentum Lz is carried out to obtain the N-body lowest eigenenergy and eigenstate. To bring out the effect of quantum (Bose) statistics and consequent phase stiffness (rigidity) of the variationally obtained many-body wavefunction on various physical quantities, our study spans from few-body (N = 2) to many-body (N = 16) systems. Further, to examine the finite-range effect of the repulsive Gaussian potential on many-body ground state properties of the Bose-condensate, we obtain the lowest eigenstate, the critical angular velocity of single vortex state and the quantum correlation (measured) in terms of von Neumann entanglement entropy and degree of condensation. It is found that for small values of the range (measured by the parameter σ) of Gaussian potential, the ground state energy increases for few-boson (2 ⩽ N ⩽ 8) systems but decreases for many-boson (N > 8) systems. On the other hand for relatively large values of the range of Gaussian potential, the ground state energy exhibits a monotonic decrease, regardless of the number of bosons N. For a given N, there is found an optimal value of the range of Gaussian potential for which the first vortex (with Lz = N) nucleates at a lower value of the rotational angular velocity Ωc1 compared to the zero-range (δ-function) potential. Further, we observe that the inter-particle interaction and the introduced rotation are competing effects with latter being dominant over the former. With increase in the range of Gaussian potential, the value of von Neumann entropy decreases and the degree of condensation increases implying an enhanced quantum correlation and phase rigidity.

Acoustic superradiance from a Bose–Einstein condensate vortex with a self-consistent background density profile

The propagation of acoustic perturbations in the velocity potential of a Bose–Einstein condensate (BEC) behave like minimally coupled massless scalar fields in a curved (1 + 1) dimensional Lorentzian space-time, where their propagation is governed by the Klein–Gordon wave equation. For linearized perturbations, this geometric picture can still apply in the presence of a single vortex state of the BEC. Thus far, the amplified scattering of axisymmetric perturbations from a vortex, as a manifestation of the acoustic superradiance, has been investigated by assuming a constant background density of the condensate. This paper addresses the validity of this approximation within the same theoretical workframe, by employing a self-consistent density profile that is obtained by solving the Gross–Pitaevskii equation for an unbound BEC and an approximation to the numerical solution is used throughout the paper. The resulting radial density profile around the vortex implies a radially varying speed of sound, which modifies the entire propagation dynamics as well as the loci of the event horizon and the ergosphere. We investigate the superradiance in temporal domain and, through an independent asymptotic formulation, in the spectral domain. The main conclusions are that the self-consistent density profile remedies the overshoot of the superradiance dynamics temporally and that the spectral profile of the superradiance differs significantly in the vortex-scaled low frequency regime between the constant density and self-consistent density formulations.

Evolution of magnetic vortex formation in micron-sized disks

Automotive magnetic field sensing applications require a robust sensing concept. One way to meet the corresponding sensor requirements, such as a negligible hysteresis and a large linear working range, is to employ the vortex state. Consequently, the nucleation field Hn of the vortex state becomes a highly important sensor parameter. In this study, we examine different factors that affect Hn. Tunneling magnetoresistance spin-valve sensors with disk-shaped CoFeB free layers, which energetically favor the nucleation of the vortex state, are electrically characterized and compared with micromagnetic simulations. Phase transitions into intermediate magnetic states, such as various buckling states, the S-state, or the double vortex state, are extracted from hysteresis loops. The resulting phase diagrams show that the formation of the S-state only occurs below a thickness of approximately 25 nm, whereas the double vortex state nucleates frequently only above approximately 35 nm. Both the S- and double vortex states lower the nucleation field of the single vortex state compared to higher order buckling states. Understanding both the origin and the influence of the intermediate phases opens the way to designing a robust and reliable vortex sensor concept.

Analog black holes and energy extraction by super-radiance from Bose Einstein condensates (BEC) with constant density

This paper investigates the acoustic superradiance of the density and phase fluctuations from the single vortex state of a Bose-Einstein condensate, by employing full time-domain and asymptotic frequency domain numerical calculations. The draining bathtub model of an incompressible barotropic fluid is adopted to describe the vortex. The propagation of the axisymmetric density and phase fluctuations in the condensate are governed by the massless scalar Klein-Gordon wave equation, which establishes the rotating black-hole analogy. Hence, the amplified scattering of these fluctuations from the vortex comprise the superradiance effect. A particular coordinate transformation is applied to reveal the event horizon and the ergosphere termwise in the metric and the respective asymptotic spectral solutions. A comparative analysis of the time domain and asymptotic frequency domain results are given for a range of rotational speed of the vortex and the frequency of the impinging fluctuations. The agreement at low rotational speeds of the vortex is shown to be very good, which starts to deteriorate at higher rotational speeds due to increasing constraint violations of the time-domain calculations. We further demonstrate an asymptotic upper bound for the superradiance as a function of vortex rotational speed, provided that the vortex remains stable.

Simple theoretical proposal of the dependence of the deGennes extrapolation parameter with the surface temperature of a superconducting sample

The Time-dependent Ginzburg–Landau model (TDGLM) is a robust tool widely used to analyze the magnetization of the single-vortex state of a mesoscopic superconducting sample in presence of a magnetic field. The algorithm implemented in this work is applied to a square geometry surrounded by different kinds of materials simulated by deGennes extrapolation length . The inside of the sample remains at constant temperature , while its boundary remains at temperature . This temperature variation in the sample can be generated by a continuous laser wave injected into all the internal points, except for a thin surface layer in the boundary of the material. We found that the b value at , which mimics the magnetization curve for a corresponding , presents a linear dependence with the temperature. Therefore, although within the domain of validity TDGLM the parameter is to be considered temperature-independent in the vicinity of the bulk critical temperature and that depends on the density of states near the surface, we propose a simple dependence of using a TDGLM.