Gyrotropic Motion 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.

Magnetic field effects and transverse ratchets in charge lattices coupled to asymmetric substrates

We examine a charge lattice coupled to a one-dimensional asymmetric potential in the presence of an applied magnetic field, which induces gyrotropic effects in the charge motion. This system could be realized for Wigner crystals in nanostructured samples, dusty plasmas, or other classical charge-ordered states where gyrotropic motion and damping can arise. For zero magnetic field, an applied external ac drive can produce a ratchet effect in which the particles move along the easy flow direction of the substrate asymmetry. The zero field ratchet effect can only occur when the ac drive is aligned with the substrate asymmetry direction; however, when a magnetic field is added, the gyrotropic forces generate a Hall effect that leads to a variety of new behaviors, including a transverse ratchet motion that occurs when the ac drive is perpendicular to the substrate asymmetry direction. We show that this system exhibits commensuration effects as well as reversals in the ratchet effect and the Hall angle of the motion. The magnetic field also produces a nonmonotonic ratchet efficiency when the particles become localized at high fields.

Resonant excitation of vortex gyrotropic mode via surface acoustic waves

Finding new energy-efficient methods for exciting magnetization dynamics is one of the key challenges in magnonics. In this work, we present an approach to excite the gyrotropic dynamics of magnetic vortices through the phenomenon of inverse magnetostriction, also known as the Villari effect. We develop an analytical model based on the Thiele formalism that describes the gyrotropic motion of the vortex core including the energy contributions due to inverse magnetostriction. Based on this model, we predict excitations of the vortex core resonances by surface acoustic waves whose frequency is resonant with the frequency of the vortex core. We verify the model's prediction using micromagnetic simulations and show the dependence of the vortex core's oscillation radius on the surface acoustic wave amplitude and the static bias field. Our study contributes to the advancement of energy-efficient magnetic excitations by relying on voltage-induced driven dynamics, which is an alternative to conventional current-induced excitations.

Correlated gyrotropic motion of skyrmion clusters in ultrathin ferromagnetic nanodisks

We report the correlated gyrotropic motion of two-dimensional skyrmion clusters in ferromagnetic nanodisks. Based on the massless Thiele equation, we calculate the gyrotropic eigenmodes for the multi-skyrmion system. Micromagnetic simulations are performed to verify theoretical predictions with a good agreement. By applying an in-plane magnetic field pulse on four-skyrmion system, four gyrotropic modes have been excited. One of them has all skyrmions moving in-phase; two modes have the face-to-face skyrmions pair moving out-of-phase; the rest one has a pair of face-to-face skyrmions moving in-phase with side skyrmions rotating out-of-phase. Meanwhile, we identify a reversal of phase and rotation direction originating from the complex interaction between skyrmions for five-skyrmion system. By applying an out-of-plane magnetic field pulse, we observe the correlated breathing modes for four-skyrmion system with the face-to-face skyrmions breathing in-phase or out-of-phase, and all skyrmions breathing consistently in-phase. In particular, for the five-skyrmion system, a hybridization mode has been clarified with side skyrmions breathing and central skyrmion rotation. Our results provide useful insights for controlling the dynamic behavior of multiple skyrmions that are indispensable in the future skyrmion-based spintronic devices.

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 anisotropy-controlled vortex nano-oscillator for neuromorphic computing

Chiral magnetic vortex has shown great potential for high-density magnetic storage, modern telecommunication and computation devices, thanks to its topological stability and rich dynamic behaviours. Particularly, the synchronization of magnetic vortex nano-oscillators leads to the emergence of fascinating collective phenomena used for microwave generator and neuromorphic computing. In this work, by means of micromagnetic simulations, we create stable chiral magnetic vortices by exploiting the chiral coupling principle and study the gyrotropic motion of the vortex core under spin-transfer torques. The gyrotropic oscillation frequency can be tuned by injecting spin-polarised current as well as the change of the magnetic anisotropy in the vortex area, resulting from the modification of the vortex confine potential and the size of the vortex core. Two vortex nano-oscillators can be synchronized wherein the synchronization state can be modulated by the spin-polarised current and the magnetic anisotropy. Moreover, we demonstrate that the magnetic anisotropy can modify the synchronization patterns when integrating six vortices into an oscillator network, making it potentially serve as an oscillator-based neural network. Our work provides a new route to constructing a flexible oscillator network for neuromorphic computing hardware.

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.

Thermal motion of skyrmion arrays in granular films

Magnetic skyrmions are topologically distinct swirls of magnetic moments which display particlelike behavior, including the ability to undergo thermally driven diffusion. In this paper we study the thermally activated motion of arrays of skyrmions using temperature dependent micromagnetic simulations where the skyrmions form spontaneously. In particular, we study the interaction of skyrmions with grain boundaries, which are a typical feature of sputtered ultrathin films used in experimental devices. We find the interactions lead to two distinct regimes. For longer lag times the grains lead to a reduction in the diffusion coefficient, which is strongest for grain sizes similar to the skyrmion diameter. At shorter lag times the presence of grains enhances the effective diffusion coefficient due to the gyrotropic motion of the skyrmions induced by their interactions with grain boundaries. For grain sizes significantly larger than the skyrmion diameter clustering of the skyrmions occurs in grains with lower magnetic anisotropy.

Gyrotropic Modes of Ferromagnetic Resonance in System of Two Exchange-Coupled Magnetic Vortices

We report the results of micromagnetic simulations of low-frequency resonances associated with gyrotropic motion of exchange-coupled magnetic vortices in a system of two overlapping ferromagnetic disks. The dependences of the resonance frequencies on the method of excitation, the mutual direction of the vortex cores and on the external magnetizing magnetic field are analyzed. The modeling demonstrates that the most effective influence on the change in the resonance frequency is realized when the system is magnetized in the sample plane in the direction perpendicular to the line connecting the disks centers, opposite to the direction of magnetization in the area of disks overlapping. It is shown that for the state with opposite core polarity there are two resonant modes in which the cores and consequently the in-plane dipole moments induced in vortex shells are rotated in the opposite directions. On the contrary, in the resonant mode of the state with the same core polarity, the cores are rotated in the same directions and induced dipole moments are rotated in phase. The possibilities of using the overlapping disks system for the synchronization of vortex nano-oscillators are discussed.

Features in the Resonance Behavior of Magnetization in Arrays of Triangular and Square Nanodots

Collective modes of the gyrotropic motion of a magnetic vortex core in ordered arrays of triangular and square ferromagnetic film nanodots have been theoretically investigated. The dispersion relations have been derived. The dipole–dipole interaction of the magnetic moments of the magnetic vortex cores of elements has been taken into account in the approximation of a small shift from the equilibrium position. It is shown that the effective rigidity of the magnetic subsystem of triangular elements is noticeably higher than that of the subsystem of square elements of the same linear sizes. The potential application of the polygonal film nanodisks as nanoscalpels for noninvasive tumor cell surgery is discussed

Observation of Defect-Assisted Magnetic Vortex Core Reversal at Ultralow Critical Velocity

The stability of structures with nontrivial topology is a subject of great interest, both from fundamental and technological perspectives. The topology of a magnetic vortex, for example, results in high stability of the vortex core polarity, which is attractive for applications. This high stability, however, greatly impedes the required deterministic polarity switching, which is typically only achieved with large magnetic fields or strong dynamic driving. Here, we show that the interaction between the vortex core and manufactured nanoscale defects in the magnetic material lowers the required driving strength for core polarity reversal by more than an order of magnitude. We excite vortex dynamics in thin permalloy disks, and map the two-dimensional (2D) vortex core trajectory using 3D time-resolved Kerr microscopy. In pristine samples, we observe normal gyrotropic motion of the vortex core. After laser-induced generation of defects, however, we observe repeated vortex core reversal at much-reduced driving strength. Micromagnetic simulations reveal how local reduction of exchange coupling and saturation magnetization can create vortex core reversal sites for deterministic vortex core switching.

Strain manipulation of vortex core in bi-component magnetic nanodisks

Magnetic vortex as one of the quintessentially non-uniform magnetic structure that can be found to commonly exist in micrometer or submicrometer sized ferromagnetic thin films. Here, we present that the vortex core can be efficiently expelled from the central region and excited into gyrotropic motion by using a voltage induced strain in bi-component magnetic nanodisks. In particular, the polarity can be deterministic switched by proper modulation the amplitude and frequency of applied voltage. The related results of micromagnetic simulations indicated that the magnetic vortex polarity is reversed through the nucleation-annihilation process of topological vortex-antivortex pairs or rotation-fusion edge soliton pairs. This voltage-controlled low-power vortex polarity switching scheme has the ability to accurately address individual magnets in dense arrays and also is compatible with integrated circuit techniques, which provides an additional route for the design of vortex-based on-chip devices.

Flicker and random telegraph noise between gyrotropic and dynamic C-state of a vortex based spin torque nano oscillator

Vortex based spin torque nano oscillators (STVOs) can present more complex dynamics than the spin torque induced gyrotropic (G) motion of the vortex core. The respective dynamic modes and the transition between them can be controlled by experimental parameters such as the applied dc current. An interesting behavior is the stochastic transition from the G-to a dynamic C-state occurring for large current densities. Moreover, the C-state oscillations exhibit a constant active magnetic volume. We present noise measurements in the different dynamic states that allow accessing specific properties of the stochastic transition, such as the characteristic state transition frequency. Furthermore, we confirm, as theoretically predicted, an increase of flicker noise with Idc2 when the oscillation volume remains constant with the current. These results bring insight into the potential optimization of noise properties sought for many potential rf applications with spin torque oscillators. Furthermore, the investigated stochastic characteristics open up new potentialities, for instance in the emerging field of neuromorphic computing schemes.

Beyond the gyrotropic motion: Dynamic C-state in vortex spin torque oscillators

In the present study, we investigate a dynamical mode beyond the gyrotropic (G) motion of a magnetic vortex core in a confined magnetic disk of a nano-pillar spin torque nano-oscillator (STNO). It is characterized by the in-plane circular precession associated with a C-shaped magnetization distribution. We show a transition between G- and C-state modes, which is found to be stochastic in a current-controllable range. Supporting our experimental findings with micromagnetic simulations, we believe that the results provide further opportunities for the dynamic and stochastic control of STNOs, which could be interesting to be implemented, for example, in neuromorphic networks.

Magnetic Resonance Force Spectroscopy of Magnetic Vortex Oscillations

Forced oscillations of magnetization of NiFe circular disk in the presence of external longitudinal magnetic field are studied with the aid of micromagnetic simulation and experiments using magnetic resonance force spectroscopy. Main attention is paid to low-frequency resonance related to gyrotropic motion of the core of magnetic vortex. The resonance frequency of the gyromode is significantly shifted when the external magnetic field is applied in the sample plane. Effect of nonuniform magnetic field of the probe on the oscillations of magnetization is discussed.

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.

Impurity-dependent gyrotropic motion, deflection and pinning of current-driven ultrasmall skyrmions in PdFe/Ir(111) surface

Resting on multi-scale modelling simulations, we explore dynamical aspects characterizing magnetic skyrmions driven by spin-transfer-torque towards repulsive and pinning 3d and 4d single atomic defects embedded in a Pd layer deposited on the Fe/Ir(111) surface. The latter is known to host sub-10 nm skyrmions which are of great interest in information technology. The Landau–Lifshitz–Gilbert equation is parametrized with magnetic exchange interactions extracted from the ab-initio all-electron full potential Korringa–Kohn–Rostoker Green function method, where spin–orbit coupling is added self-consistently. Depending on the nature of the defect and the magnitude of the applied magnetic field, the skyrmion deforms by either shrinking or increasing in size, experiencing thereby elliptical distortions. After applying a magnetic field of 10 T, ultrasmall skyrmions are driven along a straight line towards the various defects which permits a simple analysis of the impact of the impurities. Independently from the nature of the skyrmion-defect complex interaction, being repulsive or pinning, a gyrotropic motion is observed. A repulsive force leads to a skyrmion trajectory similar to the one induced by an attractive one. We unveil that the circular motion is clockwise around pinning impurities but counter clockwise around the repulsive ones, which can be used to identify the interaction nature of the defects by observing the skyrmions trajectories. Moreover, and as expected, the skyrmion always escapes the repulsive defects in contrast to the pinning defects, which require a minimal depinning current to observe impurity avoidance. This unveils the richness of the motion regimes of skyrmions. We discuss the results of the simulations in terms of the Thiele equation, which provides a reasonable qualitative description of the observed phenomena. Finally, we show an example of a double track made of pinning impurities, where the engineering of their mutual distance allows to control the skyrmion motion with enhanced velocity.

Synchronization in linear chains of non-identical vortex-based spin-torque oscillators

Arrays of interacting oscillators having different individual frequencies can exhibit transitions to synchronization depending on array and individual oscillator parameters. In particular, vortex-based spin-torque nanopillar oscillators have gyrotropic frequencies depending inversely on the free layer disk radius. Here the effect of random distribution of radii on synchronization for chains of oscillators is investigated, since in actual systems of spin torque oscillator’s radii will be non-identical owing to fabrication control limitations. The vortex dynamics of linear chains interacting through the dipolar interaction are modeled by the Thiele equations with the free layer radii given by a random distribution about a mean. It is shown that there are two critical current densities for each chain: first, the onset of synchronized gyrotropic motion of the largest radius free layer oscillator, and second, the loss of synchronization as the individual oscillator amplitudes increase. The second critical current density is strongly dependent on the free layer radii of the particular chain. However, the synchronized frequency only weakly depends on the mean radius of each chain, and it is shown to be practically independent of the radii distribution.

Strong Skyrmion Oscillations Driven by Spatially Dependent Spin Current

Nanoscale spintronic oscillators have attracted research interest in recent years because of their potential application in neuromorphic computing. Sustainable magnetization precession or gyrotropic motion of a skyrmion triggered by spin-polarized current or spin current gives rise to spintronic oscillation. However, the amplitude of skyrmion oscillation is exceedingly small. In this work, we report a skyrmion oscillation with a much larger amplitude based on periodical deformation of the skyrmion in a region with geometric confinement. This periodical deformation is induced by spatial-dependent spin current and is relevant to the skyrmion Hall effect. The amplitude and period of the oscillation can be well manipulated by modifying the damping coefficient, the slope of spin-current density, and the dimension of medium. The characteristic frequency of skyrmion oscillation determined by fast Fourier transformation is split under an external magnetic field that breaks the symmetry for the oscillation in the left and right parts of the skyrmion. This work paves the way to develop nanoscale skyrmion oscillators with tunable frequency and amplitude for neuromorphic computing.

Correlated gyrotropic modes of multi-skyrmion in elliptical ferromagnetic nanodisks

We reported a systematic study on the correlated gyrotropic motion of a chain of multiple skyrmions coexistent in an elliptical thin-film ferromagnetic nanodisk. A theoretic model with modified massless Thiele’s equations has been set up. The analytical solutions of the model have suggested several gyrotropic eigen modes for the two-skyrmion and three-skyrmion systems with their unique relative configurations among skyrmion cores. Using micromagnetic simulations, we have confirmed the existence of all these analytic modes and their characterized behaviors. In addition, by applying an in-plane exciting magnetic field in the simulations, we exhibited several spin wave modes at higher resonant frequencies with mixing feature of azimuthal and breathing modes.