United States

The topological number of micromagnetic textures (&lt;i&gt;Q&lt;/i&gt;) is a useful quantity for information encoding and transport [1,2], and determines the dynamics of magnetic objects such as skyrmions, merons and domain walls. Recent developments allow us to tune the strength of the interfacial Dzyaloshinskii-Moriya interaction, thereby inducing the formation of different states and generating a rich energy landscape for a given physical device, leading to new and potentially useful applications [3].&lt;br/&gt;This energy landscape determines the thermal stability of a given state which is strongly dependent on the barrier that separates neighboring minima [4-6]. In this work we use the String Method for the Study of Rare Events to determine transition states and thermal barriers of a circular nanodisk at different magnitudes of the Dzialoshinskii-Moriya constant (&lt;i&gt;D&lt;/i&gt;).&lt;br/&gt;Low values of &lt;i&gt;D&lt;/i&gt; are associated with high energies of domain wall formation; in this regime mostly uniform magnetizations with isolated skyrmions correspond to the lowest energy states. The transition between these states occurs by the motion of entire skyrmions across the material&#39;s edge. At intermediate values of &lt;i&gt;D&lt;/i&gt;, domain walls require less energy, skyrmions have large radii and leave the nanodisk via an intermediate minima in which a meron is expelled from the film (Figures 1 and 2). Very large &lt;i&gt;D&lt;/i&gt; values cause complex textures to form but transtions are still mediated by meron motion across the device&#39;s edge.&lt;br/&gt;This work emphasizes the importance of considering meron-mediated-transitions to appropriately create the initial path used in methods that use chain-of-states to estimate transition barriers.

![](https://assets.underline.io/uploads/markdown_image/1/image/1eaa5816c8a78055e4675a6f428397e1.jpg)

String Method results showing energy and skyrmion number along the transition path. The images above correspond to points indicated in the images. The disk diameter is 80nm and its thickness is 0.4nm.

![](https://assets.underline.io/uploads/markdown_image/1/image/43f1086b40436f45582a732b611bd679.jpg)

Skyrmion Number vs Energy for the same transition path of Fig.1. The skyrmion numbers of energy minima differ by roughly 1/2, highlighting the importance of meron motion across the edges as a mechanism for switching between energy minima. The values are not half-integer due to magnetization tilting at the sample&#39;s edge.

2022 Joint MMM-INTERMAG

Thermally Activated Transitions in Confined Terromagnets with Perpendicular Magnetic Anisotropy as Function of the Interfacial Dzialoshinskii-Moriya Interaction Strength.

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The topological number of micromagnetic textures (Q) is a useful quantity for information encoding and transport [1,2], and determines the dynamics of magnetic objects such as skyrmions, merons and domain walls. Recent developments allow us to tune the strength of the interfacial Dzyaloshinskii-Moriya interaction, thereby inducing the formation of different states and generating a rich energy landscape for a given physical device, leading to new and potentially useful applications [3]. This energy landscape determines the thermal stability of a given state which is strongly dependent on the barrier that separates neighboring minima [4-6]. In this work we use the String Method for the Study of Rare Events to determine transition states and thermal barriers of a circular nanodisk at different magnitudes of the Dzialoshinskii-Moriya constant (D). Low values of D are associated with high energies of domain wall formation; in this regime mostly uniform magnetizations with isolated skyrmions correspond to the lowest energy states. The transition between these states occurs by the motion of entire skyrmions across the material's edge. At intermediate values of D, domain walls require less energy, skyrmions have large radii and leave the nanodisk via an intermediate minima in which a meron is expelled from the film (Figures 1 and 2). Very large D values cause complex textures to form but transtions are still mediated by meron motion across the device's edge. This work emphasizes the importance of considering meron-mediated-transitions to appropriately create the initial path used in methods that use chain-of-states to estimate transition barriers.

![](https://assets.underline.io/uploads/markdown_image/1/image/1eaa5816c8a78055e4675a6f428397e1.jpg)

String Method results showing energy and skyrmion number along the transition path. The images above correspond to points indicated in the images. The disk diameter is 80nm and its thickness is 0.4nm.

![](https://assets.underline.io/uploads/markdown_image/1/image/43f1086b40436f45582a732b611bd679.jpg)

Skyrmion Number vs Energy for the same transition path of Fig.1. The skyrmion numbers of energy minima differ by roughly 1/2, highlighting the importance of meron motion across the edges as a mechanism for switching between energy minima. The values are not half-integer due to magnetization tilting at the sample's edge.

technical paper

The recent reports on magnetodynamic properties of soft magnetic thin films attain the lowest damping factor [1-3]. The damping is required for spin-wave propagation and spin manipulation investigation where the reduced spin-wave dissipation leads to a larger decay length. The low damping thin films are important for microwave applications [4], spin transfer switching devices, and other application in magnon spintronics. In order to achieve the lowest damping, the FeGaB has chosen with Al2O3 in this study. Ta(10nm)/FeGaB(15nm)/Al2O3(3nm)/Ta(3nm) thin film were deposited on Si/SiO2(190nm) substrate by sputtering and was annealed at 300oC for 3 hours in the Ar gas. The static magnetization results inform that saturation and remanent magnetization has increased for annealed thin film shown in Fig.1 (a). After annealing, the dipolar field influence has reduced, the magnetic moment fluctuation has not observed. Fig. 1 (b) shows the annealed films have monotonously increased. The dynamics properties are studied with temperature variation with 100 K to 300 K and exciting frequency from 2 to 20 GHz. Fig.2 (a) illustrates the absorption spectrum of both films at 100K, the spectrum has shifted to lower fields for annealed films. The unannealed thin film have existed the small hump at higher magnetic films before resonance peak, which may be impurities and surface defects of the thin film. But, the hump has disappeared for annealed films in Fig. 2 (b). The absorption spectrum provides linewidth and resonance fields (Hr) for excitation frequency. The linewidth –frequency plot provides damping factor and inhomogeneous linewidth [5]. The damping factor of both films are decreasing with decreasing temperature as Fig.2 (c). Fig.2 (d) shows the annealed film has larger effective magnetization value than that of unannealed thin film.

![](https://assets.underline.io/uploads/markdown_image/1/image/456a20cfd7f6097c2f6a3fe240b5f535.jpg)

Fig.1 (a) Normalized M-H loop for unannealed and annealed thin films at 300K. Insets shows M-H loop at different temperatures; (b) Coercive fields (Hc) versus temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/f9b3d8de83b131c23c6946adfb17f683.jpg)

Fig.2 (a) Absorption spectrum of both thin films at 100K, (b) absorption of annealed thin film at 20GHz with different temperatures, (c) damping factor (α) versus temperature, (d) effective magnetization versus temperature.

Temperature dependence static and dynamic properties of soft magnetic thin film FeGaB/Al2O3 for microwave applications

Magnetization dynamics in laterally confined nanodots have potential applications in spin-torque nano oscillators,1 magnetic logic and sensors2. The ground state of nanodot shows vortex at remanence and it exhibits rich spin dynamics spectra3. With the application of magnetic field, the vortex and saturated magnetization states are observed at low and high field regions respectively4. In our present work, we have studied the magnetization dynamics in high aspect ratio single and trilayer nanodots. Circular Permalloy (Py) nanodots (diameter = 120nm) are fabricated over a large area using deep ultraviolet lithography technique. The structures consist of single layer nanodots with thicknesses (L) 20 and 50 nm and a trilayer with two Py layers separated by a non-magnetic layer: Py(20)/Pd(10)/Py(50). Numbers within the brackets are in nm. The dynamic properties are characterized using the ferromagnetic resonance (FMR) technique. The simulated hysteresis loops are shown in Fig. 1(a). The FMR absorptions show rich spectra as a function of magnetic field and thickness. For instance, we discuss the experimental results at an excitation frequency of 10 GHz as shown in Fig. 1(b). We observed two modes for L = 20 nm nanodots at resonance fields 130 and 220 mT and a single mode appears at 210 mT for L = 50 nm nanodots. We performed micromagnetic simulations to understand the experimental results. The simulated mode profiles reveal that the high intense mode corresponds to the center mode (CM) and the low intense mode corresponds to the edge mode (EM) arising due to the inhomogeneous effective field. The CM is found to be sensitive to the thickness of the nanodot. On the other hand, in the FMR spectra of Py(20)/Pd(2)/Py(50), two resonant modes appear at 200 mT and 250 mT. These two center modes arise due to the in-phase and out-of-phase precession of spins in magneto-dynamically coupled layers. These results can be useful for nanoscale magnonic applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/2e01f4ef86e02401510bbe909771a373.jpg)

Fig 1: (a) Simulated hysteresis loops for single and trilayer nanodot arrays. The remanent states are shown in the inset. (b) Experimental FMR spectra of single and trilayer nanodot arrays.

Magnetization Dynamics of Single and Trilayer Permalloy Nanodots

Tailoring and control of electromagnetic properties of synthetic magnetic structures is advantageous for high frequency applications, such as shielding materials in magnetic recording, where characterisation in the gigahertz frequency range is necessary to determine parameters for simulations and aid component design. In such applications it is desirable to have a high saturation magnetisation, low coercivity, high permeability and close to zero magnetostriction. Meeting almost all these requirements, NiFe is the material of choice for many high frequency applications. We present a systematic study of the ferromagnetic resonance (FMR) and spin wave properties of NixFe100-x alloy thin superlattice films of the form n[NixFe100-x/NiyFe100-y], where n is the number of bilayers. Films were fabricated by planar magnetron sputtering and the effects of deposition conditions were investigated. Magnetic and material properties were measured using FMR [1], vibrating sample magnetometer and x-ray diffraction, with the aim to determine any relation between microstructure and the static and dynamic magnetic properties. Layer compositions within the bilayers have been chosen with particular interest in fcc/bcc layer combinations such as Ni80Fe20/Ni20Fe80, which may have benefits for some static properties such as high magnetisation and low magnetostriction [2]. Studies on single layers have shown dramatic changes in FMR response across the fcc-bcc boundary near x = 40, figure 1. However, for bilayer films it was found that increasing the thickness of the bcc Ni20Fe80 layer in the structure increased the resonant frequency but did not significantly reduce the FMR signal, figure 2.

![](https://assets.underline.io/uploads/markdown_image/1/image/2d9c99cff6d1c85880be60efcc3b4eb1.jpg)

Fig. 1: FMR spectra of 100nm NixFe100-x single layer thin films with x varying from 10 to 60. Note that all measurements were performed at an applied field H=253Oe. XRD is inset.

![](https://assets.underline.io/uploads/markdown_image/1/image/80e55db23ea15b0120ab8fa67c4beb0e.jpg)

Fig. 2: FMR spectra of Ni80Fe20(60-t nm)/Ni20Fe80(t nm) thin films with t varying from 50 to 10. Note that all measurements were performed at an applied field of 253Oe. XRD is inset.

Ferromagnetic Resonance of Tuneable Low Magnetostrictive NixFe100-x Superlattice Structures for High Frequency Application

I Introduction Accurate iron loss prediction is of great significance to the optimal design of electrical equipment[1]. At present, the application of silicon steel lamination in complex excitation greatly increases the difficulty of accurately predicting iron loss, especially eddy current loss. To solve the above problems, various eddy current loss prediction methods have been proposed[2]-[3], but these methods lack the physical background. A physical-based improved parametric magneto-dynamics (IPMD) model is proposed. For the sake of calculating the eddy current loss more accurately, the Tellinen (TLN) hysteresis model is used in the implementation of the IPMD model. II Improved Parametric Magneto-Dynamic Model To solve the problem of inaccurate calculation caused by nonuniform magnetic field distribution of silicon steel lamination at high frequency, the IPMD model based on one-dimensional Maxwell diffusion equation is proposed in this paper. In the IPMD model, the influence of hysteresis on magnetic field distribution is considered by coupling the TLN model, and the influence of skin effect at high frequency is considered by using the nonlinear segmentation method. The segmentation method divides the analysis area of silicon steel lamination into several slices and realizes the uniform expression of the magnetic field on a single slice. According to the characteristics of slow change of magnetic field of inner slice and fast change of magnetic field of outer slice, the thickness of outer slice is appropriately reduced and the thickness of inner slice is appropriately increased, as shown in Fig.1. By using the piecewise constant function to approximate the magnetic field distribution of silicon steel lamination, the eddy current loss can be accurately predicted by the IPMD model, as shown in Fig.2. III Conclusion The IPMD model proposed in this paper can accurately predict the eddy current loss in a wide frequency range while considering the physical background, which has practical significance for the study of eddy current loss characteristics of soft magnetic materials.

![](https://assets.underline.io/uploads/markdown_image/1/image/3f29b24d3766d42592f6f99f46519de4.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d51ad658646887115e6a672e465bac31.jpg)

An Improved Eddy Current Loss Model Over Broadband Frequency Range

An Improved Eddy Current Loss Model Over Broadband Frequency Range

Recently, ferromagnetic resonance (FMR) in insulating YIG film was shown to be driven by microwave current in the Pt film deposited on the top of YIG film and detected as a dc voltage in the Pt layer due to spin Hall effect and/or spin rectification[1,2]. Here, we demonstrate an alternative method to study FMR in ceramic YIG. A polycrystalline pellet was made from YIG nanopowder by sintering in the air at 900oC for 12 hr. Magnetization at 300K, shown in the main panel of Fig.1(a), affirms the soft ferromagnetic nature of YIG. The upper inset in (a) illustrates the sketch of our experimental setup. Since the resistance of YIG could not be measured by the impedance analyzer, a layer of silver paint was coated on the top surface of the sample and at two ends to allow radio-frequency current to flow. The sample bridges the signal line and the ground plane of the sample stage, which is connected to the impedance analyzer via a rigid coaxial cable. A microwave signal is injected into the Ag paint layer through the signal line. Resistive and reactance of the Ag-paint were measured while sweeping frequency at different values of the dc magnetic field,H. The lower inset shows magnetoresistance MR(b) and magnetoreactance MX(c) for five frequencies (f) as H decreased from 3 kOe to 0 Oe. The MR of the Ag-paint for 3 GHz exhibits a prominent peak at H = Hr around which MX crosses zero. Both the amplitude of the peak in MR and Hr decreases as f decreases. We argue that the peak in MR is caused by FMR. The inset shows the dependence of Hr on f and we are able to fit the data with Kittel’s relation for in-plane FMR. The observed electrical detection of FMR in YIG with colloidal silver particles having weak spin-orbit coupling than Pt deserves an urgent understanding. R. M. thanks the Ministry of Education, Singapore for support (Grant no. R144-000-442-114).

![](https://assets.underline.io/uploads/markdown_image/1/image/ae1fde754d75a41639f3df99d02d023b.jpg)

Fig. 1 (a) M-H isotherm of YIG sample at 300 K(main panel) and the schematic diagram of the experimental setup (upper inset). Field dependence of (b) magnetoresistance MR)and (c) magnetoreactance MX at selected frequencies of current excitation (bottom inset). Inset in (b) shows the frequency dependence of the resonance field (symbols) and Kittel's fit for FMR.

Electrically detected ferromagnetic resonance in polycrystalline YIG covered with a layer of Ag paint

The prospect of thermal imaging and control in magnetic particle imaging (MPI) is an important advancement for non-invasive medical diagnostics and therapeutics. Current MPI systems focus mainly on imaging from measurement of nanoparticle concentrations. Accurate derivation of temperature relies on detailed understanding of magnetization dynamics in the presence of AC drive fields and variable temperature [1]. Here, we report measurements of nanosecond magnetization dynamics using both time and frequency domain techniques. It has been reported that the imaging resolution of MPI is critically impacted by nanoparticle relaxation dynamics [2]; specifically, spin relaxation results in image blurring. The dynamic response (e.g. Néel and Brownian relaxation) of magnetic nanoparticles in magnetic fields is intricate, depending strongly on the particles’ inherent magnetic and structural properties, inter-particle interactions, and the local environment. We have developed an arbitrary-wave magnetic particle spectrometer with magnetic field amplitude up to 10 mTPk for characterizing magnetization dynamics over a broad temperature range (200 K to 350 K). We have characterized the dynamic AC susceptibility of nanoparticles ranging in diameter from 10 nm to 70 nm and in composition and observed peaks in the imaginary component (χ’’) at frequencies from as low as 50 Hz to 50 MHz. Figure 1 show the χ’’ peak frequency for 11.5 nm cobalt-doped ferrite nanoparticles at different temperatures. This peak reveals the effective relaxation timescale (τ ~ 1 μs). Additionally, we used pulsed excitation to characterize the magnetization dynamics with and without magnetic fields. Figure 2 shows a magnetization response of 7.5 nm cobalt-doped ferrites to a magnetic field pulse with 20 ns rise time. Monte Carlo simulations are used for analyzing both time and frequency domain measurements. This knowledge will eventually inform strategies for design and synthesis of magnetic nanoparticles with properties targeted for accurate and sensitive thermal imaging using MPI.

![](https://assets.underline.io/uploads/markdown_image/1/image/c09e0bfc2893d134e13e9ccf078bc358.jpg)

The imaginary component of AC susceptibility for 11.5 nm ferrite nanoparticles

![](https://assets.underline.io/uploads/markdown_image/1/image/cab02aa8ffbaedf3c9a626601584bbd6.jpg)

Pulsed magnetic field (black). Magnetization step-response of 7.5 nm cobalt-doped ferrite (red).

Magnetization dynamics of magnetic nanoparticles for thermal and magnetic particle imaging

New physics emerge from the interplay between spin waves and magnetic topological objects. Excitation modes permit to exploit the full potential of topological objects and increase the range of applications, in particular in the field of insulator-based spintronics. Recently, the number of proposals leveraging excitation modes of topological objects is steadily increasing, such as in microwave generation and detection, spin-wave guides, parametrons and in neuromorphic spintronic devices. In this talk I will present three ways to exploit excitations of magnetic topological objects. First, I will show that domain walls in thin films behave as flexible strings with an extra internal degree of freedom1. A direct application is the use of domain walls as spin-wave guides and hosts of magnetic domain wall skyrmions. Moreover, by considering closed domain wall strings, I will derive analytically deformations, instabilities2,3, and excitation modes of skyrmions4. Second, I will propose the use of topological objects as tunable nanoscale in-materio frequency multipliers for spintronic systems5. I will show that the excitation of topological objects by fractions of the eigenfrequencies presents advantages compared to the well-known parametric excitation as it requires less energy input and does not generate instabilities away from the excited topological objects. Third, I will discuss a mechanism to controllably manipulate the direction and speed of domain walls in kagome antiferromagnets via a single linearly polarized spin-wave source6. In this case, the coupling of spin wave modes inside the non-collinear domain wall allows for a highly tunable spin-wave induced domain wall motion with a frequency dependent domain wall velocity.

Exploiting excitations of magnetic topological objects

The establishment of chiral coupling in thin magnetic films with inhomogeneous anisotropy has led to the development of novel artificial systems of fundamental and technological interest. The chiral coupling itself is enabled by the Dzyaloshinskii-Moriya interaction (DMI) enforced by the patterned non-collinear magnetization [1-4]. Here, we create a domain wall track with out-of-plane (OOP) magnetization coupled to OOP stripes on each side via narrow parallel strips with in-plane magnetization as shown in Fig.1 (a). Since the chiral coupling prefers antiparallel OOP magnetization configuration over the parallel case, the regions of noncollinear magnetization in a single magnetic layer can be used to bias the domain wall velocity, as shown in series of Kerr images in Fig.1 (b). To tune the chiral torques, the design of the magnetic racetracks can be modified by varying the width of the tracks or the width of the transition region between noncollinear magnetizations, reaching effective chiral magnetic fields of up to 8 mT. Furthermore, we show how the magnitude of the chiral torques can be estimated by measuring asymmetric domain wall velocities. We also demonstrate spontaneous domain wall motion propelled by intrinsic torques even in the absence of any external driving force, which is of high importance for domain wall motion-based neuromorphic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/630ddf8c04b523dac1399ba71d81db43.jpg)

Figure 1: (a) Schematic of a DW racetrack with OOP magnetization delimited by two strips with IP anisotropy. The energy landscape of the DW racetrack is monotonous, except for local DW pinning sites. (b) Sequence of Kerr images of asymmetric DW motion in a racetrack with wOOP = 950 nm. The dashed lines correspond to the position of the IP magnetized strip while the full lines correspond to the boundary of the magnetic track. 80 current pulses are applied between each image; the pulse duration is 50 ns and the current density is 3.6×1011 A/m2.

Engineering of intrinsic chiral torques in magnetic thin films based on the Dzyaloshinskii-Moriya interaction

Magnetic multilayers of Ir/Co/Pt with interfacial Dzyaloshinskii-Moriya interaction (IDMI) [1] were deposited by magnetron sputtering with Co thickness d=1.8nm and repetitions N=6. Ferromagnetic resonance spectroscopy was applied to determine the values of effective magnetic uniaxial anisotropy, Hu = -0.45 T. Exploiting magneto-optical Kerr effect in longitudinal mode microscopy, magnetic force microscopy and vibrating sample magnetometery the magnetic field driven evolution of domain structures and hysteresis loops have been studied. Existence of weak stripe domains structure was deduced – large micrometer size domains with in-plane "core" magnetization modulated by small nano-domains with out-of-plane magnetization. Quantitative evaluation of IDMI was carried out using Brillouin light scattering (BLS) spectroscopy [2,3] from the difference between Stokes and anti-Stokes peak frequencies Δf. Due to the additive nature of IDMI, the asymmetric combination of Ir and Pt covers led to large values of surface DMI energy density Ds. Fig. 1 shows Stokes and anti-Stokes peaks for magnon scattering. It was found that Stokes and anti-Stokes frequencies as well as Δf, measured as a function of in-plane applied magnetic field, show hysteresis. These results are explained under the consideration of the influence of IDMI on the dynamics of in-plane magnetized “core” with weak stripe domains. In order to understand the spatial magnetization distribution and magnetization process, the micro-magnetic simulations were performed. Our findings leverage the impact of IDMI on domain structure. Large values of Ds can be useful for the stabilization of skyrmions [1] and studying the dynamical behavior of magnetic skyrmions in the in-plane magnetized sample [4].

![](https://assets.underline.io/uploads/markdown_image/1/image/92e6a5942842efc48ac7a6e5bad30c22.jpg)

Fig. 1. BLS spectrum for d=1.8 nm where Stokes and anti-Stokes peaks are shown. Measurement was done for wavevector k=11.81 μm-1 and applied in-plane magnetic field µ0H=72.8 mT. Experimental data (black line) and its mirror curve (red line, for easy comparison) determine the frequency difference Δf ≈1.5 GHz.

Magnetization statics and dynamics in Ir/Co/Pt multilayers with Dzyaloshinskii-Moriya interaction

Microwave response of magnetic textures in ferromagnets offers rich physics and has been intensively investigated over the past decades for their potential application in magnonics. Eigenexcitations of films featuring bubble domains [1,2] and stripes [3] have been accounted for, broadly consisting of acoustic, optical and domain wall oscillation modes. Recently, topologically non-trivial chiral magnetic structures called skyrmions [4] have gathered a lot of interest owing to their robust, tiny and particle-like nature. They exhibit unique spectral signatures which have been observed mainly in bulk systems below room temperature [5,6]. The experimental observation and interpretation of their resonant dynamics in thin films remain elusive owing to high damping coefficients. Here we report room temperature investigation of resonant skyrmion dynamics in [Pt/CoFeB/AlOx]×20 multilayers. We optimize our sample by tuning the different layer thicknesses to host magnetic skyrmions at room temperature, along with a fairly low damping parameter α= 0.02. We use magnetic force microscopy to observe the static magnetic domain configuration consisting of randomly distributed skyrmions and dense skyrmion lattice as a function of an out-of-plane magnetic field. Broadband ferromagnetic resonance measurements are performed to study the dynamic response with an in-plane excitation field. Besides the Kittel mode (KM) above saturation, three distinct modes, a low frequency mode (LFM), an intermediate frequency mode (IFM) and a high frequency mode (HFM), appear with unique frequency-field dispersions in the non-saturated state (see Fig). Micromagnetic simulations reveal the characteristics of these modes, where the LFM features a mode localized in the skyrmion edges, while for the IFM skyrmion edge dynamics couples with the uniform background. In the HFM, the precession of skyrmion cores emits omnidirectional spin waves into uniform background, producing interference patterns in the lattice. Our results thus open up new avenues for skyrmion-based magnonic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/20e701a47ef97bc8c284fee76af80155.jpg)

Fig : Frequency-field dispersion map measured by FMR over a frequency range of 0.1 GHz to 20 GHz with an out-of-plane magnetic field swept from -500 mT to 500 mT.

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