Dynamics Of Magnetic Vortices Research Articles

Spectrum of Gyrotropic Modes and Energy Transfer between Dipolar‐Coupled Magnetic Vortices in a Square Lattice via Triggered Vortex Gyration: A Promise for Spintronics Technology

AbstractThe atoms in a crystal lattice vibrate together and generate vibrational modes known as acoustic and optical phonon modes. Similarly, collective vortex gyration motion can be generated in artificial magnetic vortex lattices, created from periodically arranged nanodisks of specific dimensions and aspect ratios. This study uses micromagnetic simulations to characterize the spectra of gyrotropic modes in two‐dimensional magnetic vortex‐based, tailor‐made square lattice arrangements. The shifting of mode frequencies and mode splitting is witnessed depending on the vortex configurations in the lattice. The obtained gyrotropic modes are analogous to two‐dimensional square lattice structures exhibiting acoustic and optical phonon modes. The dynamics of magnetic vortices are also discussed in the transfer of magnetic energy at three points along the three high symmetry directions of the lattice when the central magnetic vortex is excited by a spin‐polarized current with an excitation frequency equal to the collective gyrotropic frequencies of the vortices. Similar to the higher contribution of acoustic phonon modes in the heat transmission process in a crystal lattice, acoustic‐like gyrotropic modes transfer more energy than optical‐like gyration modes in the vortex lattices. These magnetic metastructures hold promise for novel applications in magnetic waveguides and information processing devices, as well as for advancing spintronics.

Dynamics of magnetic vortices in the field of local inhomogeneity of a ferromagnet

The rotation of a magnetic vortex in a ferromagnet with a local smooth change in the exchange interaction is considered. The frequency of this precession is found for all distances of the vortex from defect center. The rotation velocity of the vortex nonmonotonically depends on the distance to the center, reaching a maximum at a distance of the order of the characteristic dimension of the defect. The decrease in velocity at large distances agrees with the data known in the literature. Accounting of attenuation leads to the vortex escape the defect or falling onto it along a logarithmic spiral.

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.

Piezostrain as a Local Handle to Control Gyrotropic Dynamics of Magnetic Vortices

Piezostrain as a Local Handle to Control Gyrotropic Dynamics of Magnetic Vortices

Influences of quenching treatment and cobalt-doping on the thermally activated flux-flow behavior in KCa2(FeCo )4As4F2

Owing to the unique double-FeAs-layered structure between neighboring insulating layers, the 12442-type Fe-based superconductors are expected to host rich vortex phenomena in the mixed state. Here, we report a systematic investigation on the influences of quenching treatment and cobalt-doping on the magnetic vortex dynamics of KCa2(FeCo x )4As4F2 (x = 0, 0.1) single crystals via electrical transport measurements. It is found that the slopes of the upper critical field near Tc , along both directions ( and ), are doubled by the cobalt-doping with x = 0.1. The activation energy is acquired by analyzing the Arrhenius plots, which shows a H −α dependence with a change in the exponent α at around 3 T, indicating the evolution of the dominant pinning mechanisms in different field regions. Importantly, the quenching treatment obviously enhances the magnitude of activation energy and critical current density J c, which can be suppressed by the introduction of cobalt-doping. Possible mechanisms for such evolutions of these important parameters are discussed. Our results emphasize the important role of quenching treatment in enhancing the activation energy and critical current density in 12442 system.

Influence of the thickness of a nonmagnetic layer on the coupled dynamics of magnetic vortices in a spin-transfer nanooscillator

A spin torque nano-oscillator in the form of a three-layer magnetic tunneling junction of small diameter (120 nm), where the magnetizations in both magnetic layers are in vortex state, is considered. The effect of the thickness of a nonmagnetic layer on the coupled dynamics of two magnetic vortices in a spin torque nano-oscillator has been studied. The thick permalloy magnetic layer has a thickness of 15 nm, the middle non-magnetic layer has a thickness in the first case of 12.5 and in the second 15 nm, and the thin permalloy magnetic layer has a thickness of 4 nm. Numerical calculation of the dynamics of magnetostatically coupled vortices was carried out using the software package SpinPM for micromagnetic modeling. The features of the vortex motion dynamic are studied for different thicknesses of the nonmagnetic interlayer. It is shown that in all cases of thickness of the nonmagnetic interlayer, three regimes of vortex dynamics are observed: the oscillations of magnetic vortices damped over time, the mode of stationary coupled oscillations of magnetic vortices, and regime, when vortices “leave” the edge of the disk. It is found that increasing in the thickness of the nonmagnetic layer leads to decreasing in the values of the first, second, and third critical currents.

Type-II Weyl Excitation in Vortex Arrays

Weyl-like magnon excitations in ordered magnets have attracted significant recent attention. Despite the tantalizing physics and application prospects, the experimental observation of Weyl magnons is still challenging owing to their extraordinarily high frequency that is not accessible to the microstrip antenna technique. Here we predict gigahertz Weyl excitations in the collective dynamics of dipolar-coupled magnetic vortices arranged in a three-dimensional stacked honeycomb lattice. It is found that inversion symmetry breaking leads to the emergence of the type-II Weyl semimetal (WSM) state with tilted dispersion. We derive the full phase diagram of the vortex arrays that support WSMs with both single and double pairs of Weyl nodes, and the topological insulator phase. We observe robust arc surface states in a dual-segment fashion due to the tilted nature of type-II WSMs. Our findings uncover the low-frequency WSM phase in magnetic-texture-based crystals that are indispensable for future Weyltronic applications.

Operation of Magnetic Vortex Transistor by Spin‐Polarized Current: A Micromagnetic Approach

To avoid electron leakage and energy consumption as in present‐day bipolar junction transistor, the magnetic analog of the bipolar junction transistor using magnetic vortices proves to be an excellent alternative. This alternative exploration is implemented using micromagnetic simulations, which use spin‐polarized current to study the dynamics of magnetic vortices in physically separated but magnetostatically coupled nanodisks. Here, a magnetic vortex transistor (MVT), when the nanodisks are arranged in a triangular layout, is designed. Significant gain is observed for the scalene triangle configuration for a three‐vortex system when the polarities of the vortices are +1, −1, +1 and for the equilateral triangular configuration when the polarities are −1, +1, +1, respectively. The mechanism of energy transfer in such magnetostatically coupled vortices has been explained in terms of the dynamics of antivortex solitons’ movement through the stray field. The variation of damping parameters has no significant effect on signal transfer and amplification. Through this extensive micromagnetic calculation, the possibility of tuning the MVT by varying the configuration, polarity combination, and changing the position of the input signal is demonstrated. This study offers a prospect for nonvolatile, all magnetic information‐carrying nanoscale devices and magnetic logic gates and switches.

Pinning and gyration dynamics of magnetic vortices revealed by correlative Lorentz and bright-field imaging

Topological magnetic textures are of great interest in various scientific and technological fields. To allow for precise control of nanoscale magnetism, it is of great importance to understand the role of intrinsic defects in the host material. Here we use conventional and time-resolved Lorentz microscopy to study the effect of grain size in polycrystalline permalloy films on the pinning and gyration orbits of vortex cores inside magnetic nanoislands. To assess static pinning, we use in-plane magnetic fields to shift the core across the island while recording its position. This enables us to produce highly accurate two-dimensional maps of pinning sites. Based on this technique, we can generate a quantitative map of the pinning potential for the core, which we identify as being governed by grain boundaries. Furthermore, we investigate the effects of pinning on the dynamic behavior of the vortex core using stroboscopic Lorentz microscopy, harnessing a new photoemission source that accelerates image acquisition by about two orders of magnitude. We find characteristic changes to the vortex gyration in the form of increased dissipation and enhanced bistability in samples with larger grains.

Joint Effect of a Magnetic Field and a Spin-Polarized Current on the Coupled Dynamics of Magnetic Vortices in a Spin-Transfer Nano-Oscillator

Joint Effect of a Magnetic Field and a Spin-Polarized Current on the Coupled Dynamics of Magnetic Vortices in a Spin-Transfer Nano-Oscillator

Magnetic vortices in media with spatially inhomogeneous exchange interaction

In the framework of the classical equations for the magnetization dynamics and the collective variables approximation, the dynamics of magnetic vortices in two-dimensional ferromagnets with the easy-plane anisotropy and spatially inhomogeneous exchange interaction is considered. In the case of a wide straight line of the interface between magnetic media with different but slightly different exchange interaction, the dependence of the magnetic vortex velocity on its distance to the structure defect and position inside the interface domain is obtained.

The Effect of the Spin-Polarized Current on the Dynamics and Structural Changes of Magnetic Vortices in a Large-Diameter Three-Layer Conducting Nanocylinder

The structure and magnetization dynamics are investigated in a vortex spin-transfer nanooscillator, which is a three-layer spin-valve magnetic nanocolumn with a large diameter of 400 nm, under flowing spin-polarized current through it. The dynamic variation in the structure of vortices and their trajectory of motion are studied, using micromagnetic modeling, as a function of the value of the spin-polarized current. It is demonstrated that different modes of motion of vortices may exist: decaying oscillations of vortices, stationary oscillations of vortices, and the mode of switching polarity of one of vortices. The time for which different dynamic modes are settled is determined. The dependence of the oscillation frequency on the value of spin-polarized current is determined for the case of stationary dynamics of coupled vortices. It is shown that, at large values of current, switching of vortex polarity is only possible in a thick layer with the dynamic switching mechanism accompanied by generation of a vortex–antivortex pair. The software package for micromagnetic simulation, SpinPM, is used for numerical calculations of the dynamics of magnetic vortices.

Совместное влияние магнитного поля и спин-поляризованного тока на связанную динамику магнитных вихрей в спин-трансферном наноосцилляторе

The joint effect of the spin polarized current and an external magnetic field on the dynamics of magnetization in vortex spin-transfer nano-oscillators with a diameter of 400 nm is investigated. For the numerical calculation of the coupled dynamics of magnetic vortices, the SpinPM software package for micromagnetic modeling was used. The dependence of the frequency of stationary coupled oscillations of vortices on the magnitude of the magnetic field, which determines the operating frequency range of a tunable vortex spin-transfer nano-oscillator.

Direct observation of temperature dependent vortex dynamics in a La0.7Sr0.3MnO3 micromagnet

This work explores the magnetization dynamics in an epitaxial nanomagnet. The authors link the observed vortex core switching dynamics to the critical velocity switching model using micromagnetic modeling.

Temperature-dependent anisotropic magnetoresistance and spin-torque-driven vortex dynamics in a single microdisk

Spin–orbit-torque-driven dynamics have recently gained interest in the field of magnetism due to the reduced requirement of current densities and an increase in efficiency, as well as the ease of implementation of different devices and materials. From a practical point of view, the low-frequency dynamics below 1 GHz is particularly interesting since dynamics associated with magnetic domains lie in this frequency range. While spin-torque excitation of high-frequency modes has been extensively studied, the intermediate low-frequency dynamics have received less attention, although spin torques could potentially be used for both manipulation of the spin texture and the excitation of dynamics. In this work, we demonstrate that it is possible to drive magnetic vortex dynamics in a single microdisk by spin-Hall torque at varying temperatures and relate the results to transport properties. We find that the gyrotropic mode of the core couples to the low-frequency microwave signal and produces a measurable voltage. The dynamic measurements are in agreement with magnetic transport measurements and are supported by micromagnetic simulations. Our results open the door for integrating magnetic vortex devices in spintronic applications.

Nondestructive ultrafast steering of a magnetic vortex by terahertz pulses

Electric control of magnetic vortex dynamics in a reproducible way on an ultrafast time scale is a key element in the quest for efficient spintronic devices with low-energy consumption. To be useful, the control scheme should ideally be swift, be scalable, be noninvasive, and result in reliable magnetic switching. Such requirements, particularly the reproducibility of altering the vortex chirality and/or polarity, are not yet met by magnetic vortex switching via external magnetic fields, spin-polarized currents, spin waves, or laser pulses. Here, we demonstrate a novel packaged-skyrmion-mediated vortex switching process driven by a simple sequence of picosecond electrical field pulses via magnetoelectric interactions. Both the vortex chirality and polarity show a well-defined reversal behavior. The unambiguous repeated switching between four different magnetic vortex states provides an energy-efficient, highly localized, and coherent control method for nonvolatile magnetic vortex-based information storage and handling.

Piezo-electrical control of gyration dynamics of magnetic vortices

In this work, we first statically image the electrically controlled magnetostatic configuration of magnetic vortex states and then we dynamically image the time-resolved vortex core gyration tuned by electric fields. We demonstrate the manipulation of the vortex core gyration orbit by engineering the magnetic anisotropies. We achieve this by electric fields in a synthetic heterostructure consisting of a piezoelement coupled with magnetostrictive microstructures, where the magnetic anisotropy can be controlled by strain. We directly show the strong impact of the tailored anisotropy on the static shape of the vortex state and the dynamic vortex core orbit. The results demonstrate the possibility of using electric field induced strain as a low-power approach to tune the dynamical response of magnetic vortices.

Speeding up the extended Kalman filter approach for denoising XMCD movies of fast magnetization dynamics

The Kalman filter is a well-established approach to get information on the time-dependent state of a system from noisy observations. In former times it has been used for systems with only a few degrees of freedom (typically about 10). The fast magnetization dynamics is often investigated by x-ray magnetic circular dichroism movies (XMCD movies) where the number of components of the state vector is very large (typically about 105). For such systems the Jacobian matrix which is required in the extended Kalman filter approach cannot be calculated numerically (as it is done in former papers) by use of the Landau-Lifschitz-Gilbert equation of motion in a finite time because of the many degrees of freedom of the state vector. In the present paper it is shown that the calculation of the Jacobian matrix can be much speeded up by using good analytical approximations, which are derived by a tensorial Green’s function method to solve the linearized Landau-Lifschitz-Gilbert equation of motion. This makes it possible to investigate the dynamics of magnetic vortices and spin waves in circular discs of Permalloy, which are initiated by time-dependent external magnetic fields.

Magnetic Radial Vortex Core and Coupled Edge-Soliton Pair Gyration Dynamics

We studied the gyration dynamics of a magnetic radial vortex core by injecting spin-polarized current into a nanodisk through a nanocontact. The simulation results indicate that the radial vortex core can rotate in an approximately circular orbit with a stable frequency. As the current density increases, the radius and frequency of rotation increase, while the rotation stabilization time decreases. Simultaneously, the intensity of the interfacial Dzyaloshinskii–Moriya interaction has a great influence on the frequency and the maximum drive current density of the gyration. The Oersted field generated by the current can reduce the stabilization time. The radial vortex core transforms into an edge soliton pair and rotates stably along the boundary of the disk for a certain range of current densities. This work provides deeper insight into the gyration dynamics of magnetic radial vortices and the potential for the development of nano-oscillators based on radial vortices.

Dynamics of Coupled Magnetic Vortices in Trilayer Conducting Nanocylinder

Solving numerically the generalized Landau–Lifshitz equation, we have carried out the micromagnetic investigation of the dynamics of two dipole-coupled magnetic vortices in a trilayer nanocolumn under the action of the external magnetic field directed perpendicular to the sample plane and spin-polarized electric field. The possible existence of different regimes of vortex motion, depending on the polarized current, is demonstrated. The current dependence of the oscillation frequency for the case of stationary dynamics of coupled vortices with the same frequency has been established. The possibility of controlling the frequency of the stationary vortex motion and tuning the control current amplitude by the external magnetic field is shown. Using the analytical method for simplified description of the dynamics of coupled vortices, the current and magnetic-field dependences of the frequency have been obtained, which are qualitatively consistent with the numerical data.