Azimuthal Spin Wave Research Articles

Static and dynamic magnetic characteristics in concentric permalloy nanorings

Magnetic nanodisks and nanorings have been focus of attention for quite some time due to their applicability in magnetic memory devices. In this paper, static and dynamic magnetic properties of Permalloy concentric thin ring nanostructures are reported as a function of the number of rings by using micromagnetic simulations. The maximum outer radius (R) and thickness (t) of the concentric rings are fixed at 100 nm and 20 nm respectively. The distance between any two neighbouring rings is always maintained equal to the width of each ring while the number of nanorings is increased starting from one to five. In-plane magnetic hysteresis loops show that in all cases, the remanence and coercivity values are found to be almost zero while vortex state is exhibited with opposite helicity in adjacent nanorings. When the number of nanorings reach five, the narrowest hysteresis loop is observed with almost no hysteresis at all. Dynamic susceptibility spectra was computed by relaxing the system from a out of plane saturated state followed by an in-plane excitation using a small field pulse. In most of the cases, the in plane magnetic field pulse excites azimuthal spin wave modes. The resonance frequency corresponding to these excitation modes depends on the remanent configuration and the number of peaks increase with increment in the number of rings. The ferromagnetic resonance mode that is common for all the samples considered, moves towards lower frequency with increase in number of concentric rings.

Spin wave modes of skyrmioniums in the presence of Dzyaloshinskii-Moriya interaction

A skyrmionium or 2π skyrmion is an exotic magnetic configuration that can be stabilized in ferromagnetic nanostructures, e.g., nanodisks. Differently from the standard (or π) skyrmion, it can move without suffering deflections due to the skyrmion Hall effect (SkHE), a property that is desirable for potential applications in spintronics. In this work, using micromagnetic simulations, it is investigated the influence of the Dzyaloshinskii-Moriya interaction on the azimuthal and radial spin wave spectra of the skyrmionium. First, the ground state of the ferromagnetic disk is obtained for several values of Dzyaloshinskii-Moriya exchange constant Dint and a fixed value of perpendicular anisotropy constant Kz. The spin wave modes of the skyrmionium were obtained using in-plane and out-of-plane magnetic pulses. The results show that the values of the frequencies of the spin wave modes depend on the values of Dint. Additionally, it is shown that it is possible to create a skyrmionium using in-plane rotating magnetic fields, by tuning parameters such as the intensity of the applied perpendicular magnetic fields, and their duration.

The internal dynamic modes of an antiskyrmion in ultrathin ferromagnetic nanodisks

We report a numerical study on the internal resonant modes of an antiskyrmion structure in thin-film ferromagnetic nanodisks by using micromagnetic simulations. As the samples are excited by an oscillating magnetic field along different directions, we are able to resolve several sets of resonant eigenmodes: gyrotropic mode and azimuthal and radial spin wave modes. At the in-plane field excitation, the gyrotropic mode at the low frequency behaves consistently with Thiele’s analytic theory, while a pair of twin azimuthal spin wave modes at higher frequencies demonstrate that their splitting is strongly relevant to the coexistent gyrotropic mode. At the out-of-plane field excitation, several breathing-like radial spin wave modes have been found. In addition, we carry out a brief comparison between these modes and their counterpart modes of an isolated skyrmion structure. We also quantitatively investigate the dependence of the eigenfrequencies of these modes on the different parameter sets of the sample size and internal interactions, which exhibit complex relationships between the internal dynamic modes of an antiskrymion and the geometry and material of the sample.

Spin dynamics of anisotropic azimuthal modes in heterogeneous magnetic nanodisks

It is well known that azimuthal spin wave modes of magnetic vortex state in permalloy nanodisks have circular symmetry. Intuitively, magnetic materials having magnetocrystalline anisotropy is not compatible with the circular symmetry of the azimuthal modes. In this article, however, we report cubic azimuthal modes in heterogeneous nanodisks consisting of a permalloy core and a Fe shell. The fourfold symmetry of azimuthal modes is due to the exchange, and magneto-static, interactions between the permalloy core and the Fe shell. In comparison to the results of circular azimuthal mode, the vortex switching occurs considerably faster under the excitation of cubic azimuthal mode. The gyration path of vortex core turns into square under the influence of induced cubic anisotropy in the permalloy region. We find out periodic oscillation of the vortex core size and the gyration speed as well. Our findings may offer a new route for spintronic applications using heterogeneous magnetic nanostructures.

Azimuthal spin-wave excitations in magnetic nanodots over the soliton background: Vortex, Bloch, and Néel-like skyrmions

We study azimuthal spin-wave (SW) excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex, Bloch-type skyrmion and N\'eel-type skyrmion states. Continuous mapping of the SW spectrum between these states is realized with gradual change of the out-of-plane magnetic anisotropy and Dzyaloshinskii-Moriya exchange interaction (DMI). Our study shows lifting of the SW frequencies degeneracy and change in systematics of the frequency levels. The change is induced by a geometrical Berry phase, that is present for the dot-edge localized SWs in a vortex state and vanishes in skyrmion states. Furthermore, channeling of the azimuthal SWs localized at the skyrmion edge is present and induces large frequency splitting. This is attributed to DMI induced nonreciprocity, while coupling of the breathing and gyrotropic modes is related to soliton motion. Finally, an efficient coupling of the dynamic magnetization in the skyrmion state to uniform magnetic field in nanodots with non-circular symmetry is shown.

Spin excitation spectrum in a magnetic nanodot with continuous transitions between the vortex, Bloch-type skyrmion, and Néel-type skyrmion states

We study spin-wave excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex and skyrmion states. Gradual change in the strength of the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction leads to continuous phase transitions between different stable magnetic configurations and allows for mapping of dynamic spin modes in and between the vortex, Bloch-type skyrmion and N\'eel-type skyrmion states. Our study elucidates the connections between gyrotropic modes, azimuthal spin waves and breathing modes in various stable magnetization states and helps to understand the rich spin excitation spectrum on the skyrmion background.

Vortex-dynamics-mediated low-field magnetization switching in an exchange-coupled system

A magnetic vortex has attracted significant attention since it is a topologically stable magnetic structure in a soft magnetic nanodisk. Many studies have been devoted to understanding the nature of magnetic vortex in isolated systems. Here we show a new aspect of a magnetic vortex the dynamics of which strongly affects the magnetic structures of environment. We exploit a nanodot of an exchange-coupled bilayer with a soft magnetic Ni81Fe19 (permalloy; Py) having a magnetic vortex and a perpendicularly magnetized L10-FePt exhibiting a large switching field (Hsw). The vortex dynamics with azimuthal spin waves makes the excess energy accumulate in the Py, which triggers the reversed-domain nucleation in the L10-FePt at a low magnetic field. Our results shed light on the non-local mechanism of a reversed-domain nucleation, and provide with a route for efficient Hsw reduction that is needed for ultralow-power spintronic devices.

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.

Size dependence of spin-wave modes in Ni80Fe20 nanodisks

We investigate the radial and azimuthal spin-wave (SW) resonance modes in permalloy (Py: Ni80Fe20) disks at zero external magnetic field, as function of disk diameter and thickness, using broadband ferromagnetic resonance spectroscopy. We observed, from both experimental and micromagnetic simulation results that the number of SW absorption peaks increases with disk diameter. Numerically calculated SW mode profiles revealed a characteristic minimum size, which does not scale proportionately with the increasing disk diameter. We show that higher order modes could thus be avoided with an appropriate choice of the disk diameter (smaller than the minimum mode size). Moreover, based on the mode profiles, the existence of azimuthal SW modes with even number of crests or troughs can be ruled out. These results could be useful in enhancing our fundamental understanding as well as engineering of new magnonic devices.

Imaging spin dynamics on the nanoscale using X-Ray microscopy

The dynamics of emergent magnetic quasiparticles, such as vortices, domain walls, and bubbles are studied by scanning transmission x-ray microscopy (STXM), combining magnetic (XMCD) contrast with about 25 nm lateral resolution as well as 70 ps time resolution. Essential progress in the understanding of magnetic vortex dynamics is achieved by vortex core reversal observed by sub-GHz excitation of the vortex gyromode, either by ac magnetic fields or spin transfer torque. The basic switching scheme for this vortex core reversal is the generation of a vortex-antivortex pair. Much faster vortex core reversal is obtained by exciting azimuthal spin wave modes with (multi-GHz) rotating magnetic fields or orthogonal monopolar field pulses in x and y direction, down to 45 ps in duration. In that way unidirectional vortex core reversal to the vortex core 'down' or 'up' state only can be achieved with switching times well below 100 ps. Coupled modes of interacting vortices mimic crystal properties. The individual vortex oscillators determine the properties of the ensemble, where the gyrotropic mode represents the fundamental excitation. By self-organized state formation we investigate distinct vortex core polarization configurations and understand these eigenmodes in an extended Thiele model. Analogies with photonic crystals are drawn. Oersted fields and spin-polarized currents are used to excite the dynamics of domain walls and magnetic bubbles. From the measured phase and amplitude of the displacement of domain walls we deduce the size of the non-adiabatic spin-transfer torque. For sensing applications, the displacement of domain walls is studied and a direct correlation between domain wall velocity and spin structure is found. Finally the synchronous displacement of multiple domain walls using perpendicular field pulses is demonstrated as a possible paradigm shift for magnetic memory and logic applications.

Azimuthal spin wave modes in an elliptical nanomagnet with single vortex configuration

In comparison with uniformly magnetized states, vortex structures demonstrate a rich frequency spectrum of spin-wave (SW) excitations. However, a detailed theoretical description of the magnetic modes is generally still a challenge due to the difficulty of analytic calculation, except for the well-defined symmetric circular states. In contrast, the method of micromagnetic simulations combined with Fourier analysis is shown to be very powerful for gaining insight into the nature of magnetic excitation modes. Vortex excitation modes have been reported to be directly influenced by the geometric symmetry of the elements and/or the nature of the initial perturbation of pulse field. In order to understand how the reduced symmetry affects the vortex SW modes, we perform the micromagnetic simulations on vortex modes excited in a submicron-sized thin ellipse. In order to excite the spin-wave modes, a short in-plane Gaussian field pulse is applied along the short axis direction. After the pulse, the off-centered vortex core moves following an elliptical trajectory around its equilibrium position. Simulations provide the time evolution of the local magnetizations (at each discretization point) and dynamics of the spatially averaged magnetization. To determine the mode frequencies, the spectrum is obtained from the average magnetization through Fourier transformation from time domain the frequency domain. By means of Fourier analysis, a variety of azimuthal SW modes can be observed in the excitation spectrum. The ellipse in single vortex state has a twofold rotational symmetry with a rotation of πup around the z-axis (out-of plane) and can be described by the C2 group. The observed azimuthal modes can be divided into two categories according to their symmetry. Two modes occur alternately with increasing azimuthal number, indicating that the magnetic excitation modes remain to keep the symmetry of the ellipse structure. Their frequencies are found to increase linearly with the azimuthal index number. An increase of the SW frequency with increasing number of nodal planes is rather well known, which results from the competition between exchange and dipolar energy terms. According to the temporal evolution of the ellipse's spatially averaged energy densities, our micromagnetic simulation shows that the average exchange energy is significantly higher than the magnetostatic energy, suggesting that the exchange interaction plays a more important role in the excitation modes. The exchange energy density is mainly focused on the core origin while the largest contribution of the magnetostatic energy is distributed near the long axis. Thus, we can conclude that the exchange interaction provides the principal contribution to the vortex energy in such small ellipses with a single vortex state, resulting in the increasing frequency versus the azimuthal number, that is observed.

Unidirectional sub-100-ps magnetic vortex core reversal

The magnetic vortex structure, an important ground state configuration in micron and sub-micron sized ferromagnetic thin film platelets, is characterized by a curling in-plane magnetization and, in the center, a minuscule region with out-of-plane magnetization, the vortex core, which points either up or down. It has already been demonstrated that the vortex core polarity can be reversed with external AC magnetic fields, frequency-tuned to the (sub-GHz) gyrotropic eigenmode or to (multi-GHz) azimuthal spin wave modes, where reversal times in the sub-ns regime can be realized. This fast vortex core switching may also be of technological interest as the vortex core polarity can be regarded as one data bit. Here we experimentally demonstrate that unidirectional vortex core reversal by excitation with sub-100 ps long orthogonal monopolar magnetic pulse sequences is possible in a wide range of pulse lengths and amplitudes. The application of such short digital pulses is the favourable excitation scheme for technological applications. Measured phase diagrams of this unidirectional, spin wave mediated vortex core reversal are in good qualitative agreement with phase diagrams obtained from micromagnetic simulations. The time dependence of the reversal process, observed by time-resolved scanning transmission X-ray microscopy indicates a switching time of 100 ps and fits well with our simulations. The origin of the asymmetric response to clockwise and counter clockwise excitation which is a prerequisite for reliable unidirectional switching is discussed, based on the gyromode - spin wave coupling.

Low-amplitude magnetic vortex core reversal by non-linear interaction between azimuthal spin waves and the vortex gyromode

We show, by experiments and micromagnetic simulations in vortex structures, that an active “dual frequency” excitation of both the sub-GHz vortex gyromode and multi-GHz spin waves considerably changes the frequency response of spin wave mediated vortex core reversal. Besides additional minima in the switching threshold, a significant broadband reduction of the switching amplitudes is observed, which can be explained by non-linear interaction between the vortex gyromode and the spin waves. We conclude that the well known frequency spectra of azimuthal spin waves in vortex structures are altered substantially, when the vortex gyromode is actively excited simultaneously.

Spin-wave interference in microscopic permalloy tubes

We present permalloy coated needles which act as spin-wave resonators. The permalloy coated needles were investigated using microwave absorption spectroscopy. Thereby, we found up to three resonant modes which correspond to constructively interfering azimuthal spin waves. The resonant modes are well reproduced in calculations based on an analytical model for the spin-wave dispersion employing periodic boundary conditions. The dependence of the resonance frequencies on the needles' radii and the external magnetic field is demonstrated experimentally.

Spin Wave Excitations and Winter’s Magnons in Vertically Coupled Vortex State Permalloy Dots

Circular soft magnetic dots are the main elements of many proposed novel spintronics devices, capable of fascinating spin-based electronics applications, from extremely sensitive magnetic field sensors, to current-tunable microwave vortex oscillators. Here, we investigate static and broadband dynamic magnetization responses of vertically coupled Permalloy (Py) magnetic dots in the vortex state in layered nanopillars (experiment and simulations), which were explored as a function of in-plane magnetic field and interlayer separation. Under reduction of magnetic field from saturation for the field range just above vortex-vortex ground state. We observe a metastable double vortex state for each of the dots. In this state, novel kinds of spin waves (Winter’s magnons along domain walls between vortex cores and half-edge antivortex) are excited. For dipolarly coupled circular Py(25 nm)/Cu(20 nm)/Py(25 nm) trilayer nanopilars of diameter 600 nm, a small in-plane field splits the eigenfrequencies of azimuthal spin wave modes inducing an abrupt transition between acoustic (in-phase) and optic (out-of-phase) kinds of the low-lying coupled spin wave modes. Qualitatively similar changes (although more gradual and at higher values of in-plane fields) occur in the exchange coupled Py(25 nm)/Cu(1 nm)/Py(25 nm) trilayer nanopillars. These findings are in qualitative agreement with micromagnetic dynamic simulations.

Broadband probing magnetization dynamics of the coupled vortex state permalloy layers in nanopillars

Broadband magnetization response of coupled vortex state magnetic dots in layered nanopillars was explored as a function of in-plane magnetic field and interlayer separation. For dipolarly coupled circular Py(25 nm)/Cu(20 nm)/Py(25 nm) nanopillars of 600 nm diameter, a small in-plane field splits the eigenfrequencies of azimuthal spin wave modes inducing an abrupt transition between in-phase and out-of-phase kinds of the low-lying coupled spin wave modes. The critical field for this splitting is determined by antiparallel chiralities of the vortices in the layers. Qualitatively similar (although more gradual) changes occur also in the exchange coupled Py(25 nm)/Cu(1 nm)/Py(25 nm) tri-layer nanopillars. These findings are in qualitative agreement with micromagnetic dynamic simulations.

Spin excitation frequencies in magnetostatically coupled arrays of vortex state circular Permalloy dots

Broadband ferromagnetic resonance in square arrays of Permalloy circular dots with different interdot separations was measured in the vortex ground state. The detected spin excitations show a complicated dependence of their frequencies on the interdot coupling strength. A considerable influence of the interdot separation on the gyrotropic vortex frequency and splitting of the azimuthal spin wave frequencies was detected. The gyrotropic frequency and the first azimuthal doublet frequency splitting depend nonmonotonously on the interdot spacing, whereas the dependence of the second doublet frequency splitting on this parameter is monotonous. The observed effects are explained by the influence of both the dipolar and quadrupolar contributions to the dynamic magnetostatic interactions.

Azimuthal Spin Wave Modes Excited in an Elliptical Nanomagnet With Vortex Pair States

The ferromagnetic thin-film elements can be prepared to form a ?diamond? remanent state that contains two vortices with opposite circulation and with the same or opposite core polarities. The vortex polarity could influence their normal modes through the magnetostatic interactions between two vortices. In this paper, micromagnetic simulations, combined with Fourier techniques, are employed to study the spin-wave (SW) modes excited in a submicron Permalloy ellipse with a vortex pair configuration. After the application of an inplane Gaussian field pulse, it is found that a series of azimuthal SW modes is excited and the high-order harmonics of SW modes are strongly dependent of the core polarities due to the dynamic magnetic interactions between the two vortices.

Precise probing spin wave mode frequencies in the vortex state of circular magnetic dots

We report on detailed broadband ferromagnetic resonance measurements of azimuthal and radial spin wave excitations in circular Permalloy dots in the vortex ground state. Dots with aspect ratio (β=height over radius) varied from 0.03 to 0.1 were explored. The frequency splitting of two lowest azimuthal modes was observed. The experimentally observed dependence of the frequency splitting on β was reasonably well described by dynamic splitting model accounting the spin waves and vortex gyrotropic mode interaction.

Spin dynamics of a magnetic antivortex: Micromagnetic simulations

We report on a study of the dynamics of a magnetic antivortex in a submicrometer, asteroid-shaped, permalloy ferromagnet using micromagnetic simulations. As with vortex states in disk and square geometries, a gyrotropic mode was found in which a shifted antivortex core orbits about the center of the asteroid. Pulsed magnetic fields were used to generate azimuthal or radial spin wave modes, depending on the field orientation. The degeneracy of low-frequency azimuthal mode frequencies is lifted by gyrotropic motion of the antivortex core, and restored by inserting a hole in the center of the particle to suppress this motion. We briefly compare the dynamics of the vortex state of the asteroid to the antivortex. The size dependence of the antivortex modes is reported.