Motion Of Vortex Core Research Articles

Magnetic vortex polarity reversal induced gyrotropic motion spectrum splitting in a ferromagnetic disk

We investigate the gyrotropic motion of the magnetic vortex core in a chain of a few micron-sized Permalloy disks by electrical resistance measurement with amplitude-modulated magnetic field. We observe a distinctive splitting of the resistance peak due to the resonant vortex-core motion under heightened radio frequency (RF) magnetic field excitation. Our micromagnetic simulation identifies the splitting of the resonant peak as an outcome of vortex polarity reversal under substantial RF amplitudes. This study enhances our understanding of nonlinear magnetic vortex dynamics amidst large RF amplitudes and proposes a potential pathway for spintronic neural computing thanks to their unique and controllable magnetization dynamics.

Mutual friction and diffusion of two-dimensional quantum vortices

We present a microscopic open quantum systems theory of thermally-damped vortex motion in oblate atomic superfluids that includes previously neglected energy-damping interactions between superfluid and thermal atoms. This mechanism couples strongly to vortex core motion and causes dissipation of vortex energy due to mutual friction, as well as Brownian motion of vortices due to thermal fluctuations. We derive an analytic expression for the dimensionless mutual friction coefficient that gives excellent quantitative agreement with experimentally measured values, without any fitted parameters. Our work closes an existing two orders of magnitude gap between dissipation theory and experiments, previously bridged by fitted parameters, and provides a microscopic origin for the mutual friction and diffusion of quantized vortices in two-dimensional atomic superfluids.

Influence of dual-axial swirler configuration on hydrodynamic stability in combustor

To improve hydrodynamic stability in a combustor, an unsteady flow analysis method is needed. Hence, the proper orthogonal decomposition (POD) method based on a large eddy simulation (LES) unsteady flow field and corresponding experimental verification were utilized to analyze and assess the influence of the precession vortex core (PVC) motion law on the pulsation downstream of different swirler configurations. The pulsation outcomes of the unsteady simulation match the experimental data quite well, with case 1 having the highest pulsation quantity. The POD analysis reveals that the majority of pulsation energy is concentrated in the first two modes. The results of the motion state, regularity of the time coefficient, and frequency characteristics also demonstrate that the combustor's PVC features are compatible with modes 1 and 2. There is an optimum value of swirl number, 0.72, for which the flow field's stability has the lowest degree of disturbance. Moreover, the airfoil vane's stability is beyond that of the straight vane. The mean flow field and the coherent flow field in the pulsation flow field of case 3 are the most beneficial factors concerning combustion stability, and the unstable aspects of the transition flow field and the turbulent flow field are the least in shape and energy ratio. The data procured from the experiment certify that there is no characteristic frequency of pulsation within 5000 Hz that exists in case 3.

Nutation Excitations in the Gyrotropic Vortex Dynamics in a Circular Magnetic Nanodot.

A significant activity is devoted to the investigation of the ultrafast spin dynamic processes, holding a great potential for science and applications. However, a challenge of the understanding of the mechanisms of underlying spin dynamics in nanomaterials at pico- and femtosecond timescales remains under discussion. In this article, we explore the gyrotropic vortex dynamics in a circular soft magnetic nanodot, highlighting the impacts given by nutations in the high-frequency part of the dot spin excitation spectrum. Using a modified Thiele equation of the vortex core motion with a nutation term, we analyze the dynamic response of the vortex to an oscillating magnetic field applied in the dot plane. It is found that nutations affect the trajectory of the vortex core. Namely, we show that the directions of the vortex core motion in the low-frequency gyrotropic mode and the high-frequency nutation mode are opposite. The resonant frequencies of gyrotropic and nutational vortex core motions reveal themselves on different scales: gigahertz for the gyrotropic motion and terahertz for the nutations. We argue that the nutations induce a dynamic vortex mass, present estimates of the nutational mass, and conduct comparison with the mass appearing due to moving vortex interactions with spin waves and Doering domain wall mass.

Magnetic Vortex Core String Gyrotropic Oscillations in Thick Cylindrical Dots

The nonuniform magnetic vortex gyrotropic oscillations along the cylindrical dot thickness were calculated. A generalized Thiele equation was used for describing the vortex core motion including magnetostatic and exchange forces. The magnetostatic interaction was accounted for in a local form. This allowed reducing the Thiele equation of motion to the Schrödinger differential equation and analytically determining the spin eigenmode spatial profiles and eigenfrequencies using the Liouville–Green method for the high-frequency modes. The mapping of the Schrödinger equation to the Mathieu equation was used for the low-frequency gyrotropic mode. The lowest-frequency gyrotropic mode transformed to the dot faces localized mode, increasing the dot thickness. The vortex gyrotropic modes are described for a wide range of the dot thicknesses according to the concept of the turning points in the magnetostatic potential. This approach allows treating the vortex localized modes (turning points) and nonlocalized modes within a unified picture.

Effects of Closing Times and Laws on Water Hammer in a Ball Valve Pipeline

Water hammers seriously endanger the stability and safety of pipeline transportation systems, and its protection mechanism has been a hotspot for research. In order to study the change of water hammer pressure caused by the ball valve under different closing laws, the computational fluid dynamics method was used to perform transient numerical simulation of the ball valve under different closing times and closing laws. The results show that the faster the valve closing speed in the early stage, the greater the water hammer pressure. The vortex core motion and pressure vibration were affected by the closing law. Extending the valve closing time can effectively reduce the maximum water hammer pressure. These findings could provide reference for water hammer protection during the closing process of the pipeline system with the ball valve.

Impact of magnetic resonance force microscope probe on gyrotropic mode of magnetic vortex oscillations

We study the influence of magnetic resonance force microscope (MRFM) probe on the low frequency magnetization oscillations in a single permalloy disk connected with gyrotropic motion of magnetic vortex core. It is shown that the resonant frequency of gyrotropic mode can be tuned over a wide range by changing the distance between the probe and the sample. The possibility of switching the vortex core polarity under the action of the field of MRFM probe with large magnetic moment is demonstrated. The experimental data are analyzed using micromagnetic simulations and simple analytical models.

Classification of flow-field patterns in burst-mode actuation of a dielectric-barrier-discharge plasma actuator

This study investigates the characteristics of flow-field patterns generated by burst-mode actuation of a dielectric-barrier-discharge plasma actuator in quiescent air. Particle-image velocimetry and background-oriented schlieren measurements conducted over a wide range of burst-signal parameters show that there are three types of flow-field patterns. Type 1 is the wall-surface jet seen in continuous mode actuation; type 2 features periodical independent vortices traveling along the wall surface; type 3 features such vortices moving away from the surface. The vortex sizes in types 2 and 3 are proportional to the energy consumed in generating one vortex. When the time-averaged jet velocity estimated by the power consumption is used as the characteristic velocity in the nondimensional scaling law, the time profiles of the vortex location in the type 3 flow-field pattern collapse into a single line, independently of the burst frequency and ratio. However, in the initial phase, the nondimensional vortex-core motion is better described using the jet velocity in continuous-mode actuation as the characteristic velocity. The transitions of the flow-field pattern from type 1 to type 3 result from interference between cyclically generated vortices and depend on the inter-vortex distances and the energy consumed in generating one vortex.

Transient numerical simulations of a cold-flow bidirectional vortex chamber

Bidirectional chambers are well-studied in terms of the flow structure and influence of their input parameters. However, most of the available studies are based on steady-state or time-averaged research methods and do not allow to obtain data on bidirectional flow dynamics over time. The present paper reports on detailed numerical studies based on detached eddy simulations (DESs) and unsteady Reynolds-averaged Navier–Stokes methods applied for two vortex chambers with different aspect ratios. A comparison of the numerical results with the available experimental data shows that the DES method gives the most accurate results on bidirectional flow structure, turbulent fluctuations, and precessing vortex core (PVC) motion. A notable feature of the studied bidirectional flow is the central recirculation zone (CRZ) formation, which is correctly predicted by the DES method only. The presence of a CRZ in a bidirectional flow has a significant effect on turbulent velocity fluctuations and PVC behavior. It is found that CRZ formation leads to a significant decrease in radial and circumferential velocity fluctuations whereas the axial velocity fluctuations are slightly increased. Additionally, the paper reports new findings on CRZ and PVC interaction in bidirectional flows. PVC motion is almost completely nullified by the presence of a CRZ. This can prove useful in many industrial applications of bidirectional chambers, e.g., vortex thrusters and gas turbine combustors. The bidirectional swirling flow transient properties studied in this paper could assist in determining the most efficient operational modes and geometric configuration of industrial chambers as well as enabling control of turbulent fluctuations, which would allow for reliable ignition and stable combustion.

Chirality-dependent asymmetric vortex core structures in a harmonic excitation mode

Chirality of the magnetic vortex plays an essential role in dynamic excitations of the magnetic vortex structure. In a harmonic excitation of the vortex gyrotropic motion, it has been known that the chirality determines its phase to the driving force. From our micromagnetic simulations, we find an additional role of chirality in the harmonic excitation of the vortex gyration. The shear deformation of the three-dimensional structure of the vortex core is determined by the chirality of the vortex. We confirm that this is due to the gyrotropic field. For the same vortex core motion with the same polarization but with opposite chirality, it turns out that the opposite gyrotropic field is formed at the spiral magnetization in the vicinity of the vortex core structure.

Analysis of effect of radial confluence flow on vortex core motion

The precessing vortex core (PVC) is evidently responsive to the escape of small particles. In this study, a computational fluid dynamics simulation was applied to the gas flow inside a cyclone separator to investigate the PVC phenomenon, particularly to observe the deviation of the vortex core away from the separator geometric center. The results reveal that the interaction between the gas and particles evidently contributes to the PVC unsteadiness. Consequently, a distinct deviation of the vortex core reappeared in the working cyclone with symmetric inlets, while it was too weak to be observed during the pure gas cyclone flow. However, an apex cone at the dust outlet evidently weakened the vortex core motion deviation and decelerated its rotation in the gas-particle flow within the working cyclone. Owing to the radial confluence flow from the outer to inner vortex over the separation space, the upward inner flow swung unsteadily. If >13% of mechanical energy within the downward gas flow was injected into the upward inner vortex with a radial confluence flow, the vortex core deviated from the separator geometric center, resulting in evident vortex core deviation.

Spin wave dynamics in elliptical dots

We investigate the ferromagnetic resonance modes of the magnetic vortex states on ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ ellipses using broadband ferromagnetic resonance measurements and micromagnetic simulations. Experiments show a rich structure of modes in the resonance absorption spectra, with absorption peak amplitudes dependent on the direction of the probing radio-frequency field. The evolution of the resonant modes is observed to be symmetric around zero field, due to the reversibility of the vortex core motion. The simulated absorption spectra reproduce the main features of the experimental results. A detailed analysis of the resonant modes at zero field shows that the observed absorption profiles result from the overlap of resonant modes which have an increasing complexity with the frequency. Besides, the simplest resonant modes are not those that exhibit the larger absorption amplitudes. Furthermore, the observed frequency splitting of some of the oscillation modes with the external field is correlated to the symmetry breaking during the vortex motion.

Spin current induced dynamics and polarity switching of coupled magnetic vertices in three-layer nanopillars

Abstract We study dynamics of two magnetostatically coupled magnetic vortices excited by spin-polarized electrical current in a nanopillar consisting of permalloy magnetic layers with different thickness separated by a nonmagnetic spacer. We demonstrate three dynamical regimes of the vortices bound motion: damped oscillations, stationary oscillations and a regime of the polarity switching of one of the vortices; the critical currents for each dynamical phase are identified. The structure and trajectory of the vortex core motion in each magnetic layer are studied for the case of the vortex polarity switching in a thick layer. We show that the vortex polarity switching process has a dynamic nature and is associated with a vortex-antivortex pair formation.

Vortex spin-torque oscillator usingCo2FexMn1−xSiHeusler alloys

We show spin-transfer-torque-driven vortex oscillations in current-perpendicular-to-plane giant magnetoresistance junctions using epitaxially grown ${\mathrm{Co}}_{2}{\mathrm{Fe}}_{x}{\mathrm{Mn}}_{1\ensuremath{-}x}\mathrm{Si}$ (CFMS) Heusler alloy thin films. The soft magnetic property and high spin polarization of CFMS enable us to realize vortex oscillation emitting large microwave power with a low threshold current. The output power is maximized for a certain Fe-Mn composition ratio associated with a reduction of the threshold current for the oscillation, which is in agreement with a general model for spin-torque oscillation. Through comparison with an analytical theory that describes the translational motion of a vortex core, we show that the vortex core motion excited in the present device is inhomogeneous along the thickness direction. In spite of the inhomogeneity, the gyration radius at the CFMS/spacer interface region was estimated to be $\ensuremath{\sim}75%$ of the actual ferromagnetic layer radius, which indicates that the CFMS-based all-metallic junction is useful for achieving large-amplitude vortex core motion. This comprehensive investigation would also be useful for designing high-performance all-metallic nano-oscillators based on magnetic vortex dynamics.

Dynamics of trapped interacting vortices in Bose–Einstein condensates: a role of breathing degree of freedom

With use of a variational principle, we investigate a role of breathing width degree of freedom in the effective theory of interacting vortices in a trapped single-component Bose–Einstein condensates in two dimensions, under strong repulsive cubic nonlinearity. For the trial function, we choose a product of two vortex functions, assuming a pair interaction, and employ the amplitude form of each vortex function in the Padé approximation, which accommodates a hallmark of the vortex core. We obtain the Lagrange equation for the interacting vortex-core coordinates coupled with the time-derivative of width and also its Hamilton formalism by having recourse to a non-standard Poisson bracket. By solving the Hamilton equation, we find rapid radial breathing oscillations superposed on the slower rotational motion of vortex cores, consistent with numerical solutions of the Gross–Pitaevskii equation. In higher-energy states of two vortex systems, the breathing width degree of freedom plays the role of a kicking in the kicked rotator, and generates chaos with a structure of sea-urchin needles. The by-products of the present variational approach include: (1) the charge-dependent logarithmic inter-vortex interaction multiplied with a pre-factor, which depends on the scalar product of a pair of core-position vectors; (2) the charge-independent short-range repulsive inter-vortex interaction and spring force.

Vortex Dynamics in Magnetic Nanodisks With a Ring of Magnetic Defects

Recently, nanoscale ferromagnetic disk-shaped elements have aroused intensive investigation for their potential applications in numerous magnetoelectronic devices [1-2]. In a magnetic nanodisk, the equilibrium between the exchange interaction and the magnetostatic energy leads to one special magnetization configuration, called magnetic vortex. Many theoretical and experimental researches have verified that the gyrotropic mode of the vortex core motion can be induced by the external field or spin polarized current [2], and then some works focused on investigating the precession frequency. It is well known that the oscillation frequency is one most important parameter for spin-transfer nano-oscillators (STNOs) based on vortex precession [3]. Nowadays, great efforts have been devoted to study the effect of pointlike magnetic defects in the eigenfrequency of vortex core [2], however, the effect of ring-shaped magnetic defects in the precession frequency has not yet been detailed studied. In this paper, we inserted a ring of magnetic defects into magnetic nano-disk, and studied the dynamics of magnetic vortex by micromagnetic simulation (Fig. 1).

Correction: Corrigendum: Resonantly excited precession motion of three-dimensional vortex core in magnetic nanospheres

We found resonantly excited precession motions of a three-dimensional vortex core in soft magnetic nanospheres and controllable precession frequency with the sphere diameter 2R, as studied by micromagnetic numerical and analytical calculations. The precession angular frequency for an applied static field HDC is given as ωMV = γeffHDC, where γeff = γ〈mΓ〉 is the effective gyromagnetic ratio in collective vortex dynamics, with the gyromagnetic ratio γ and the average magnetization component 〈mΓ〉 of the ground-state vortex in the core direction. Fitting to the micromagnetic simulation data for 〈mΓ〉 yields a simple explicit form of 〈mΓ〉 ≈ (73.6 ± 3.4)(lex/2R)2.20±0.14, where lex is the exchange length of a given material. This dynamic behavior might serve as a foundation for potential bio-applications of size-specific resonant excitation of magnetic vortex-state nanoparticles, for example, magnetic particle resonance imaging.

Resonantly excited precession motion of three-dimensional vortex core in magnetic nanospheres [corrected

We found resonantly excited precession motions of a three-dimensional vortex core in soft magnetic nanospheres and controllable precession frequency with the sphere diameter 2R, as studied by micromagnetic numerical and analytical calculations. The precession angular frequency for an applied static field HDC is given as ωMV = γeffHDC, where γeff = γ〈mΓ〉 is the effective gyromagnetic ratio in collective vortex dynamics, with the gyromagnetic ratio γ and the average magnetization component 〈mΓ〉 of the ground-state vortex in the core direction. Fitting to the micromagnetic simulation data for 〈mΓ〉 yields a simple explicit form of 〈mΓ〉 ≈ (73.6 ± 3.4)(lex/2R)2.20±0.14, where lex is the exchange length of a given material. This dynamic behavior might serve as a foundation for potential bio-applications of size-specific resonant excitation of magnetic vortex-state nanoparticles, for example, magnetic particle resonance imaging.

Dynamics and efficiency of magnetic vortex circulation reversal

Author(s): Urbanek, M; Uhliř, V; Lambert, CH; Kan, JJ; Eibagi, N; Vaňatka, M; Flajsman, L; Kalousek, R; Im, MY; Fischer, P; Sikola, T; Fullerton, EE | Abstract: Dynamic switching of the vortex circulation in magnetic nanodisks by fast-rising magnetic field pulse requires annihilation of the vortex core at the disk and reforming a new vortex with the opposite sense of circulation. Here we study the influence of pulse parameters on the dynamics and efficiency of the vortex core annihilation in permalloy (Ni80Fe20) nanodisks. We use magnetic transmission soft x-ray microscopy to experimentally determine a pulse rise time-pulse amplitude phase diagram for vortex circulation switching and investigate the time-resolved evolution of magnetization in different regions of the phase diagram. The experimental phase diagram is compared with an analytical model based on Thiele's equation describing high-amplitude vortex core motion in a parabolic potential. We find that the analytical model is in good agreement with experimental data for a wide range of disk geometries. From the analytical model and in accordance with our experimental finding we determine the geometrical condition for dynamic vortex core annihilation and pulse parameters needed for the most efficient and fastest circulation switching. The comparison of our experimental results with micromagnetic simulations shows that the micromagnetic simulations of ideal disks with diameters larger than ∼250 nm overestimate nonlinearities in susceptibility and eigenfrequency. This overestimation leads to the core polarity switching near the disk boundary, which then in disagreement with experimental findings prevents the core annihilation and circulation switching. We modify the micromagnetic simulations by introducing the boundary region of reduced magnetization to simulate the experimentally determined susceptibility and in these modified micromagnetic simulations we are able to reproduce the experimentally observed dynamic vortex core annihilation and circulation switching.

Topologically confined vortex oscillations in hybrid [Co/Pd]8-Permalloy structures

We report on a reciprocal magnetic interaction mechanism in micrometer-sized hybrid Co/Pd-Permalloy square elements. Time-resolved scanning transmission X-ray microscopy using X-ray magnetic circular dichroism contrast together with micromagnetic simulations demonstrate that there exists a mutual imprint of vortices in the Permalloy and in the stripe domains of the Co/Pd. This results in a hybrid magnetic domain structure leading to a domain confined gyroscopic vortex precession. These observations open the exciting possibility for topological control of vortex core motion.