Vortex Core Polarity Research Articles

Current-controlled periodic double-polarity reversals in a spin-torque vortex oscillator

Micromagnetic simulations are used to study a spin-torque vortex oscillator excited by an out-of-plane dc current. The vortex core gyration amplitude is confined between two orbits due to periodical vortex core polarity reversals. The upper limit corresponds to the orbit where the vortex core reaches its critical velocity triggering the first polarity reversal which is immediately followed by a second one. After this double polarity reversal, the vortex core is on a smaller orbit that defines the lower limit of the vortex core gyration amplitude. This double reversal process is a periodic phenomenon and its frequency, as well as the upper and lower limit of the vortex core gyration, is controlled by the input current density while the vortex chirality determines the apparition of this confinement regime. In this non-linear regime, the vortex core never reaches a stable orbit and thus, it can be of interest for neuromorphic application as a leaky integrate-and-fire neuron for example.

Effects of rf current and bias-field direction on the transition from linear to nonlinear gyrotropic dynamics in magnetic vortex structures

We present a frequency-domain study of the dynamic behavior of a magnetic vortex core within a single Permalloy disk by means of electrical detection and micromagnetic simulations. When exciting the vortex core dynamics in a nonlinear regime, the lineshape of the rectified dc signal reveals a resonance peak splitting which depends on the excitation amplitude. Using micromagnetic simulations, we show that at high excitation power the peak splitting originates from the nanosecond time scale quasiperiodic switching of the vortex core polarity. Using lock-in detection, the rectified voltage is integrated over a ms time scale, so that the net signal detected between the two resonant peaks for a given range of parameters cancels out. The results are in agreement with the reported effects of the in-plane static field magnitude on the gyration dynamics, and complement them by detailed analysis of the effects of the rf current amplitude and the azimuthal angle of the in-plane bias magnetic field. Systematic characterization shows that a transition from linear to nonlinear dynamical regime can be controlled by rf current as well as by varying the magnitude and the direction of the bias magnetic field.

Reliable control of magnetic vortex chirality in asymmetrically optimized magnetic nanodisk

Magnetic vortex has attracted attention in the field of information storage because their topological spin structures with chiral bistable states. If the vortex core polarity and vortex circulation sense can be controlled simultaneously in a nanodisk, which will be more beneficial to realize the multi-bit ultrahigh density storage. In this paper, a reliable control scheme for magnetic vortex chirality is proposed by optimizing the structure of Pac-Man-like nanodisk. The results show that the polarity and circulation of the vortex can be controlled simultaneously by changing the direction of the global magnetic field, and even the chiral states of the vortex can be determined by detecting the stray field distribution on the surface of the nanodisk. The optimized Pac-Man-like nanodisk provide an experimental method for the control and detection of magnetic vortex chirality, which will be beneficial to the realization of multi-bit magnetic storage or magnetic logic technology in the future.

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.

Micromagnetic simulation of vortex core polarity in bi-component magnetic nanodisks

The nucleation and management of the vortex state in magnetic nanostructures has received a lot of interest in recent decades, with potential applications in logic networks and non-volatile magnetic random-access memory. Because of their potential use in magnetic memory, magnetic vortex structures are of considerable technical importance. Investigation of bi-component magnetic nanodisks as prospective storage systems, in both single and coupled configurations, has been performed, where the information unit is represented by vortex core polarity. The work mainly engages in magnetic nanodisks of permalloy and iron having a diameter of 200 nm and a thickness of 40 nm. The potential of adjusting the polarity of the vortex core by the application of a magnetic field using micromagnetic simulations has been illustrated. Micromagnetic simulation studies show that bi-material structures are important not just for fundamental research but also for data storage.

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.

Stress-induced modification of gyration dynamics in stacked double-vortex structures studied by micromagnetic simulations

In this paper, using micromagnetic simulations, we investigate the stress-induced frequency tunability of double-vortex nano-oscillators comprising magnetostrictive and non-magnetostrictive ferromagnetic layers separated vertically by a non-magnetic spacer. We show that the relative orientations of the vortex core polarities p 1 and p 2 have a strong impact on the eigen-frequencies of the dynamic modes. When the two vortices with antiparallel polarities have different eigen-frequencies and the magnetostatic coupling between them is sufficiently strong, the stress-induced magnetoelastic anisotropy can lead to the single-frequency resonant gyration mode of the two vortex cores. Additionally, for the case of parallel polarities, we demonstrate that for sufficiently strong magnetostatic coupling, the magnetoelastic anisotropy leads to the coupled vortex gyration in the chaotic regime and to the lateral separation of the vortex core trajectories. These findings offer a path for achieving a fine control over gyration frequencies and trajectories in vortex-based oscillators via adjustable elastic stress, which can be easily generated and tuned electrically, mechanically or optically.

Strain-driven radial vortex core reversal in geometric confined multiferroic heterostructures

The magnetic radial vortex is a nanoscale magnetization configuration that is typically stabilized by the interfacial Dzyaloshinskii–Moriya interaction (i-DMI). The existing control methods for the radial vortex core polarity rely on the use of current flow or magnetic fields, which may cause long consumption times or limit device miniaturization. Here, we investigate a repeated reversal of a radial vortex that can be driven by strain from a piezoelectric substrate using micromagnetic simulations. A phase diagram for the representative regions against perpendicular anisotropy, i-DMI, and the applied strain was obtained. The derived phase diagram was used to associate the mechanism of the core reversal with edge magnetization rotation during core magnetization switching, which exhibits a relationship by transforming a quasi-Bloch wall into a Néel wall. The existence of the i-DMI effect causes the core polarity and radial chirality of the radial vortex to be reversed simultaneously without resulting in larger core movements. These results offer an alternative and efficient way to achieve core reversal, which is expected to stimulate the radial vortex application in magnetoresistive memory devices.

Magnetic vortex states in chromium(IV) oxide (CrO2)

As an exploration for probable magnetic vortex state in chromium(IV) oxide (CrO2), we performed micro-magnetic simulations on CrO2 nanodiscs. For our simulation studies, we considered CrO2 nanodiscs with 100 nm diameter and 20 nm thickness. After the ferromagnetic positive or negative saturation, when the applied magnetic field along the ±x-axis was reduced, vortex states with its magnetization winding in xy-plane nucleated in the CrO2 nanodisc at ∓12 mT, and annihilated at ∓41 mT. The magnetic vortex states were found to be stable even after reducing the applied magnetic field to 0 mT. Further, switching the magnetic vortex core polarity pointing up to down and vice versa using DC as well as AC magnetic fields has been simulated. The magnetization of the vortex core instantaneously flipped by an applied DC magnetic field of ±138 mT and within 2 ns by applied 6 GHz resonance AC magnetic field with 8 mT amplitude. Furthermore, we present a comparison about the formation, remanent state and switching of the magnetic vortex state in CrO2 nanodisc with that of the most widely studied permalloy nanodisc having same dimensions.

Selective control of vortex polarities by microwave field in two robustly synchronized spin-torque nano-oscillators

Manipulating operation states of coupled spin-torque nano-oscillators (STNOs), including their synchronization, is essential for applications such as complex oscillator networks. In this work, we experimentally demonstrate selective control of two coupled vortex STNOs through microwave-assisted switching of their vortex core polarities. First, the two oscillators are shown to synchronize due to the dipolar interaction in a broad frequency range tuned by an external biasing field. Coherent output is demonstrated along with strong linewidth reduction. Then, we show individual vortex polarity control of each oscillator, which leads to synchronization/desynchronization due to accompanied frequency shift. Our methods can be easily extended to multiple-element coupled oscillator networks.

Subnanosecond Radial Vortex Core Polarity Reversal Using Linearly Attenuated Perpendicular Magnetic Field

The dynamic properties of radial vortex core (RVC) polarity reversal in PtCo20Fe60B 20Ti multilayers induced by a linearly attenuated perpendicular magnetic field are investigated. Micromagnetic simulation indicates that the polarity of the RVC can be quickly reversed through a continuous distortion of circular chirality around the core. The reversal time can be reduced to below one nanosecond when the magnitudes of the magnetic field and the attenuation time are selected properly. A quantitative analysis of the core exchange-energy density, Zeeman energy density, and magnetostatic energy density explains the RVC polarity reversal. At the moment of RVC polarity switching, the exchange energy density is sharply reduced, accompanied by the emission of strong spin waves. This scheme provides a new method to achieve ultra-fast RVC polarity reversal, which lays a foundation for radial vortex-based magnetoresistive memory devices.

Reconfigurable magnetic domain wall pinning using vortex-generated magnetic fields

Although often important for domain wall device applications, reproducible fabrication of pinning sites at the nano-scale remains challenging. Here, we demonstrate that the stray magnetic field generated beneath magnetic vortex cores can be used to generate localized pinning sites for magnetic domain walls in an underlying, perpendicularly magnetized nanostrip. Moreover, we show that the pinning strength can be tuned by switching the vortex core polarity: switching the core polarity so that it is aligned with the magnetization of the expanding domain (rather than against it) can reduce the vortex-mediated wall depinning field by between 40% and 90%, depending on the system geometry. Significant reductions in the depinning field are also demonstrated in narrow strips by shifting the core away from the strips' centers.

Electrical measurement of magnetic-field-impeded polarity switching of a ferromagnetic vortex core

Vortex core polarity switching in NiFe disks has been evidenced using an all-electrical rectification scheme. Both simulation and experiments yield a consistent loss of the rectified signal when driving the core at high powers near its gyrotropic resonant frequency. The frequency range over which the loss occurs grows and shifts with increasing signal power, consistent with non-linear core dynamics and periodic switching of the core polarity induced by the core attaining its critical velocity. We demonstrate that core polarity switching can be impeded by displacing the core towards the disk's edge where an increased core stiffness reduces the maximum attainable core velocity.

Magnetic Radial Vortex Stabilization and Efficient Manipulation Driven by the Dzyaloshinskii-Moriya Interaction and Spin-Transfer Torque.

Solitons are very promising for the design of the next generation of ultralow power devices for storage and computation. The key ingredient to achieving this goal is the fundamental understanding of their stabilization and manipulation. Here, we show how the interfacial Dzyaloshinskii-Moriya Interaction (IDMI) is able to lift the energy degeneracy of a magnetic vortex state by stabilizing a topological soliton with radial chirality, hereafter called radial vortex. It has a noninteger Skyrmion number S (0.5<|S|<1) due to both the vortex core polarity and the magnetization tilting induced by the IDMI boundary conditions. Micromagnetic simulations predict that a magnetoresistive memory based on the radial vortex state in both free and polarizer layers can be efficiently switched by a threshold current density smaller than 10^{6} A/cm^{2}. The switching processes occur via the nucleation of topologically connected vortices and vortex-antivortex pairs, followed by spin-wave emissions due to vortex-antivortex annihilations.

Numerical analysis of inductive detection of magnetic vortex motion excited with circularly polarized field

In the present study, the rotation and switching of a vortex core in submicron-size square dots were numerically analyzed by micromagnetic simulation. This study clarified that the eigenfrequency of the vortex core is strongly dependent on the magnetostatic energy and that rapid switching can be realized by circularly polarized fields with practical amplitudes at the corresponding eigenfrequency. The inductive detection of vortex core rotation, which can distinguish vortex core polarity, was successfully demonstrated and the structural design of the detector was optimized.

Spin wave mediated unidirectional vortex core reversal by two orthogonal monopolar field pulses: The essential role of three-dimensional magnetization dynamics

Scanning transmission x-ray microscopy is employed to investigate experimentally the reversal of the magnetic vortex core polarity in cylindrical Ni81Fe19 nanodisks triggered by two orthogonal monopolar magnetic field pulses with peak amplitude B0, pulse length τ=60 ps, and delay time Δt in the range from −400 ps to +400 ps between the two pulses. The two pulses are oriented in-plane in the x- and y-directions. We have experimentally studied vortex core reversal as a function of B0 and Δt. The resulting phase diagram shows large regions of unidirectional vortex core switching where the switching threshold is modulated due to resonant amplification of azimuthal spin waves. The switching behavior changes dramatically depending on whether the first pulse is applied in the x- or the y-direction. This asymmetry can be reproduced by three-dimensional micromagnetic simulations but not by two-dimensional simulations. This behavior demonstrates that in contrast to the previous experiments on vortex core reversal, the three-dimensionality in the dynamics is essential here.

Indirect switching of vortex polarity through magnetic dynamic coupling

Magnetic vortex cores exhibit a gyrotropic motion and may reach a critical velocity, at which point they invert their z-component of the magnetization. We performed micromagnetic simulations to describe this vortex core polarity reversal in magnetic nanodisks with a perpendicular anisotropy. We found that the critical velocity decreases with the increase in perpendicular anisotropy, therefore departing from a universal criterion that relates this velocity only to the exchange stiffness of the material. This leads to a critical velocity inversely proportional to the vortex core radius. We have also shown that in a pair of interacting disks, it is possible to switch the core vortex polarity through a non-local excitation; exciting one disk by applying a rotating magnetic field, one is able to switch the polarity of a neighbor disk, with a larger perpendicular anisotropy.

Simulation of vortex cores switching in nanocolumnar conducting triplex structure

With the generalized Landau-Lifshitz equation the dynamics of the magnetization in the permalloy nanopillars of small diameter of 120 nm is studied. For the numerical calculation of the magnetic vortices bound dynamics a software package for micromagnetic simulations SpinPM was used. The nanopillars have two magnetic layers separated by a nonmagnetic layer. The study of two coupled magnetic vortices dynamics under the influence of an external magnetic field perpendicular to the plane of the sample and polarized electric current was conducted. The coupled magnetic vortices were taken with the same polarity and chirality. By using micromagnetic simulation the dependence of the magnetic field, switching the polarity of the vortex core in thin and thick layers, on the current strength was found. For the case of low currents, the vortex polarity switch in thin and thick layers was observed with a low exit of the vortex from the geometric center. For the case of high currents, the «dynamic» mechanism for the vortex core polarity switching was observed for a vortex in a thick layer for all values of the current polarization. For the vortex in a thin layer the "dynamic" mechanism of the vortex core polarity switching was observed only for the case of a large polarization. The minimum current value in the high current region (similarly to the case of nanocylinder with a diameter of 200 nm) significantly decreases with the increase of the current polarization value.

Nanoscale switch for vortex polarization mediated by Bloch core formation in magnetic hybrid systems.

Vortices are fundamental magnetic topological structures characterized by a curling magnetization around a highly stable nanometric core. The control of the polarization of this core and its gyration is key to the utilization of vortices in technological applications. So far polarization control has been achieved in single-material structures using magnetic fields, spin-polarized currents or spin waves. Here we demonstrate local control of the vortex core orientation in hybrid structures where the vortex in an in-plane Permalloy film coexists with out-of-plane maze domains in a Co/Pd multilayer. The vortex core reverses its polarization on crossing a maze domain boundary. This reversal is mediated by a pair of magnetic singularities, known as Bloch points, and leads to the transient formation of a three-dimensional magnetization structure: a Bloch core. The interaction between vortex and domain wall thus acts as a nanoscale switch for the vortex core polarization.

Band structure engineering of two-dimensional magnonic vortex crystals

Magnonic vortex crystals are studied via scanning transmission x-ray microscopy and ferromagnetic-resonance spectroscopy. We investigate a two-dimensional vortex crystal by imprinting waves with tunable wave vectors. The dispersion relation $\ensuremath{\omega}(k)$ is determined via ferromagnetic-resonance spectroscopy with a tunable frequency and wave vector for two vortex core polarization patterns that are adjusted by self-organized state formation prior to the measurement. We demonstrate that the band structure of the crystal is reprogrammed by tuning the vortex polarizations.