Skyrmion lattices are present in many different chiral magnetic systems and their existence derives from a number of competing interactions. In a recent work [1], we showed that Pt/FeCoB/Al2O3 multilayers can host skyrmion lattices over a range of applied perpendicular fields. A particular feature of this material system is the presence of a "high-frequency" mode (HFM) under transverse field pumping, in the range of 12-18 GHz, which involves the coherent precession of the skyrmion cores and results in the generation of spin waves that flow into the uniform background region between skyrmions. Here, we discuss the results of micromagnetics simulations with the MuMax3 code [2] where we examine the role of spin wave interactions with the skyrmion cores. As the applied field increases and skyrmions begin to annihilate, leaving vacancies in the hexagonal lattice, the excitation of the HFM can serve to "anneal" the lattice, resulting in a glassy state as shown in the Figure. The spin wave interactions are found to provide a dynamical repulsive force between the skyrmion cores, which result in a more homogeneous arrangement in terms of density, but at the expense of crystalline order. These results also shed new light on how dynamical excitations can influence phase transitions associated with the melting of skyrmion lattices [3]. 

**References** 
[1] T. Srivastava et al, arXiv:2111.11797 (2021).
[2] A. Vansteenkiste et al, AIP Advances, vol. 4, 107133 (2014).
[3] P. Huang et al, Nat. Nanotechnol., vol. 15, 761 (2020). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/e72df4d60dcc344232ae5118adc7973d.png) 

Simulated MFM images of skyrmion lattices under different applied fields, before and after the excitation of a high-frequency mode (HFM) that generates spin waves. The insets show
discrete Fourier transforms of the spatial order.

Annealing a skyrmion lattice with spin wave excitations

One current goal of spintronics is the development of sustainable information technology based on pure spin currents. One promising way to do this is to use spin waves (SWs) in low damping insulating ferrimagnets like yttrium iron garnet (YIG) where relaxation can be controlled by spin orbit torque (SOT) at a heavy metal interface [1]. However, such metal/insulator hybrid devices exhibit saturation of SW amplification due to nonlinear coupling between modes [2]. Two strategies can be considered to overcome these issues. i) Nanopatterning leads to quantization of SW modes [3], thereby limiting the available nonlinear processes [4]. ii) Tuning the perpendicular magnetic anisotropy (PMA) can be used to control the sign of the nonlinear frequency shift [5]. Recently, the growth of ultra-thin films of bismuth doped YIG (BiYIG) with tunable PMA has been achieved [6], resulting in greatly improved characteristics of SOT emitted SWs [7]. Here, we study the magnetization dynamics in individual nanodisks patterned from such a 30 nm thick BiYIG film with submicron diameters. The static magnetic field is perpendicular to the plane. The in-plane microwave field is produced by an integrated antenna. To detect the FMR, we employ a magnetic resonance force microscope [8]. For the largest disks, the amplitude of the FMR peak quickly saturates as the excitation power is increased, which is accompanied by a strong distortion of the absorption line, that broadens and splits into several peaks (Fig1a). Micromagnetic simulations accurately reproduce these features and reveal that a dynamic instability is responsible for the observed behavior. To experimentally probe this complex dynamics, we apply a second, much weaker excitation field of varying frequency, in addition to the main driving field at high power. The frequency modulation spectrum obtained (Fig1b) reflects the existence of rich low-frequency temporal variations in the magnetization dynamics.

![](https://assets.underline.io/uploads/markdown_image/1/image/0f9922ccb39360e331cfbc33deb7fa05.jpg)

Fig 1. (a) Resonance line in the deeply nonlinear regime. (b) Two-tone spectroscopy performed inside the instability region, at μ0Hz = 165 mT.

Dynamic instabilitiy in high power FMR of BiYIG nanodisks

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.

Localized and propagating spin-wave modes in thin film multilayers hosting skyrmions

One current goal of spintronics is the development of a sustainable information technology based on the transport of pure spin currents. One promising way to do this is to use spin waves (SWs), the elementary excitations of magnetically ordered materials: by collective precession of magnetic moments, they can transport angular momentum. SW information processing also offers interesting alternatives to conventional microelectronics [1]. For this, yttrium iron garnet (YIG), an insulating ferrimagnet, is the ideal material because it has the lowest magnetic damping. Furthermore, thanks to the spin orbit torque (SOT), it is possible to control the relaxation time of SWs in YIG by an electric current injected into an adjacent platinum layer [2]. However, such metal/insulator hybrid devices presently have certain limitations, as a sudden drop in the amplitude of the main mode beyond a certain excitation threshold, which originates from nonlinear coupling with other SW modes [2]. Different strategies can be considered to overcome these issues. In nanopatterned samples the available SW modes become quantized, which severely limits the available nonlinear processes. As a result, nonlinear saturation thresholds are postponed, which allows to reach much higher amplitudes of single mode dynamics [3]. The perpendicular magnetic anisotropy (PMA) can also be used to control the sign of the nonlinear frequency shift. Recently, the growth of ultra-thin films of Bismuth doped YIG (BiYIG) with tunable PMA has been achieved while preserving a high dynamic quality [4]. It was shown that the emission characteristics of SWs emitted by SOT in thin BiYIG films where PMA compensates the in-plane shape anisotropy are greatly improved [5]. Here, we study the magnetization dynamics in individual nanodisks patterned from such a 30 nm thick BiYIG film, with diameters ranging from 1 µm down to 200 nm. The static magnetic field is applied perpendicularly to the sample plane. To excite the ferromagnetic resonance (FMR) of the BiYIG nanodisks, we use the spatially uniform in-plane microwave field produced by an antenna integrated on top. To detect it, we employ a magnetic resonance force microscope [6] in which a cobalt nanosphere grown at the tip of a soft cantilever [7] is dipolarly coupled to the longitudinal component of the magnetization of the nanodisk positioned underneath (Fig. 1). By studying the SW spectra of these BiYIG nanodisks in the linear regime, we find that their effective anisotropy field is weakly dependent of the diameter and negative, about -10 mT, which means that the PMA slightly overcompensates the shape anisotropy. The damping parameter is found to increase as the diameter is decreased and lies in the high 10-4 – low 10-3 range for all disks. We then perform measurement of the main resonance line, corresponding to the quasi-uniform mode, as a function of the microwave power injected into the antenna, which is varied by up to four orders of magnitude (excitation field ranging from 0.03 mT to 3 mT at 5 GHz). For all the disks, we observe a distortion of the resonance line at intermediate excitation power, corresponding to the onset of foldover. As expected, due to the negative effective anisotropy field, the resonance line shifts towards higher magnetic field as the precession angle increases, which is opposite to the behavior reported on undoped YIG nanodisks [3]. For the largest BiYIG disks, the dynamics witnessed at higher power is quite more complex and interesting, as shown in Fig. 2 for the 700 nm diameter nanodisk. We observe a rapid saturation of the peak amplitude, corresponding to average precession angles of the order of 10° to 20°, accompanied with a broadening of the line towards both lower and higher magnetic field. To understand this behavior, we perform extensive micromagnetic simulations. Using the magnetic parameters extracted in the linear regime and the nominal geometry of the nanodisks, these simulations reproduce the main characteristics of the measured FMR lines in the strongly nonlinear regime. They reveal that a dynamic instability is responsible of the observed behavior: as the amplitude of the quasi-uniform mode increases with the driving field, its precession profile gets more and more localized at the center of the disk, which eventually leads to the formation of a dynamic soliton similar to a wave bullet [8]. Moreover, this soliton is not stable over time, resulting in a rich temporal dynamics, which, depending on the exact driving conditions, can be quasi-periodic or intermittent. To experimentally access this complex temporal dynamics, we use the method introduced in [3], which consists in applying a second, much weaker excitation field of varying frequency, in addition to the main driving field at high power. The obtained frequency modulation spectra indeed reflect the existence of rich low-frequency temporal variations in the dynamics of the magnetization, as suggested by the simulations.

**References:**

[1] A. Chumak et al. Nat. Phys. 11, 453 (2015) [2] A. Hamadeh et al. Phys. Rev. Lett. 113, 197203 (2014); M. Evelt et al. Appl. Phys. Lett. 108, 172406 (2016) [3] Y. Li et al. Phys. Rev. X 9, 041036 (2019) [4] L. Soumah et al. Nat. Commun. 9, 3355 (2018) [5] M. Evelt et al. Phys. Rev. Appl. 10, 041002 (2018) [6] O. Klein et al. Phys. Rev. B 78, 144410 (2008) [7] S. Sangiao et al. Beilstein J. Nanotechnol. 8, 2106 (2017) [8] A. Slavin and V. Tiberkevich, Phys. Rev. Lett. 95, 237201 (2005)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4929da18838a5e687ca4c091422c4fa2.jpg)
Fig.1 - Schematics of the experiment. The microwave field supplied by the antenna drives the magnetization of a BiYIG nanodisk into FMR, opening a precession angle around the perpendicularly applied field, which is detected by the cantilever of a magnetic resonance force microscope.

![](https://assets.underline.io/uploads/markdown_image/1/image/4ea71d26a653b41e10c95b4dc047a304.jpg)
Fig.2 - Main resonance line of the 700 nm diameter nanodisk recorded at 5 GHz as a function of the driving power, increased by step of 1 dB from -8 dBm to 10 dBm. The spectra have been vertically offset for clarity.

 Strongly nonlinear ferromagnetic resonance of Bi-doped YIG nanodisks

Magnetic skyrmions are chiral whirling textures of magnetization with a non-trivial topology. Their nanometric size and particle-like behavior has engendered huge interest for their potential applications in memory and logic devices. The observation of magnetic skyrmions at room temperature has triggered extensive research to decipher their various static and dynamic properties which is crucial for their eventual implementation in spintronic devices [1]. In the case of ultra-thin multilayer films consisting of heavy metal_(HM)/ferromagnet_(FM)/insulator_(I), skyrmions are primarily stabilized by interfacial Dzyaloshinskii-Moriya interaction (iDMI) in combination with perpendicular anisotropy, dipolar, exchange and Zeeman energies, where each of these contributions can be finely tuned [2]. The non-trivial skyrmion topology and its emergent electrodynamics is at the heart of phenomena like the skyrmion Hall effect and the topological Hall effect. Another interesting consequence of the skyrmions topology is reflected in their unique spectral signatures given by the gyrotropic rotational modes [3] (clockwise and counter-clockwise) and the breathing mode [4], when excited by an in-plane or an out-of-plane rf magnetic field. These unique dynamics open up new prospects for skyrmion-based microwave detectors [5] and nano-oscillators [6]. However, the experimental observation of skyrmion resonance dynamics remains limited. So far, skyrmion eigen modes have been mainly observed at low temperature in bulk systems [7]. Only few studies have been carried out in thin films, but with zero iDMI [8]. The experimental observation of the excitation modes of homochiral skyrmions stabilized by iDMI at room temperature remains elusive and challenging owing to usually elevated damping parameter and material inhomogeneities in HM/FM/I systems. Here, we study the magnetization dynamics in a [Pt/CoFeB/AlOx]×20 multilayer deposited by sputtering. First, the system is optimized by tuning the Pt and CoFeB thicknesses to host magnetic skyrmions at room temperature, along with a minimized damping parameter α ~ 0.02, measured by ferromagnetic resonance (FMR). The quasi-static magnetic domain configuration is observed by magnetic force microscopy (MFM) where on sweeping an out-of-plane (OP) magnetic field from saturation to zero, random skyrmion nucleation occurs, forming a lattice structure which then breaks into a mixture of skyrmions and stripes at lower fields; finally transforming into labyrinthine domains as shown in Fig. 1. The dynamic response of the system is measured by Vector Network Analyser (VNA) FMR with an rf field applied in-plane and varied over a frequency (f) range of 0.1-20 GHz, and an OP dc magnetic field swept from -0.55 T to +0.55 T. The frequency-field dispersions indicated in Fig. 2 (a) show several resonant modes corresponding to the domain configurations observed by MFM at the respective applied fields. At fields above the saturation, the well-known Kittel mode is observed, pertaining to uniform precession. Below saturation, distinct modes arise in the resonance spectrum with both positive and negative dispersions at low (f&lt;2GHz), medium (2&lt;f&lt;7GHz) and high frequencies (f&gt;7). The low frequency mode is observed on increasing the field towards saturation as can be seen on comparing Fig. 2 (a) and (b). Micromagnetic simulations further give an insight into the mechanisms involved in the subsequent dynamic behavior of the skyrmions. We observe that the low frequency mode (LFM) is due to the excitations localized at the skyrmion edges, corresponding to the breathing dynamics. The medium frequency mode (MM), on the other hand, arises due to the localized excitations in the inter-skyrmion region, i.e. the non-reversed magnetic zone, and has a negative dispersion. The origin of the high frequency mode (HFM) lies in the excitations across the skyrmion lattice and corresponds to the spin waves travelling across both the reversed and non-reversed regions. These latter modes (MM and HFM) are hence attributed to the magnonic cystal modes of the skyrmion lattice. This observation opens up new possibilities of creating and designing dynamically modulable skyrmion-based magnonic crystals at room temperature.

**References:**

[1] A. Fert et al., Nat. Rev. Mater. 2, 17031 (2017) [2] W. Legrand et al., Sci Adv 4, 7, (2018) [3] M. Garst et al. J. Phys. D: Appl. Phys. 50, 293002 (2017) [4] J.-V. Kim, et al., Phys. Rev. B 90, 064410 (2014) [5] G. Finocchio et al., Appl. Phys. Lett. 107, 262401 (2015) [6] F. Garcia-Sanchez et al., New J. Phys. 18, 075011 (2016) [7] Onose et al. Phys. Rev. Lett. 109, 037603 (2012) [8] S. A. Montoya et al. Phys. Rev. B 95, 224405 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/85f55608a7a181b99a46e77d5eb4df88.jpg)
Fig. 1. Magnetic domain configurations: randomly distributed skyrmions, skyrmion lattice, skyrmion-stripe mix, and labyrinthine domains, measured by MFM under the application of OP magnetic field swept from negative to positive values. The OP hysteresis curve in blue is plotted below. The solid blue curve corresponds to the OP field sweep from negative to positive (NtoP) values and the dashed curve from positive to negative (PtoN). The corresponding skyrmion density (red spheres) determined from the MFM images is also plotted. A dense skyrmion lattice is seen to be stable between 0.18T and 0.32T. The dashed grey line indicates the possible extrapolation of the observed skyrmion density at higher field values in accordance with the OP hysteresis curve (NtoP).

![](https://assets.underline.io/uploads/markdown_image/1/image/d3c6b3fe1ca9c66501cb406ed6122b5f.jpg)
Fig. 2. (a) Frequency-field dispersion map (with dashed curves at HFM as a guide to the eye) measured by VNA-FMR by scanning over a frequency range of 0.1 GHz to 20 GHz with an applied OP field swept from -0.55 T to +0.55 T. (b) and (c) Zoom of the areas indicated by white squares in (a).

 Ferromagnetic resonance of skyrmions in thin film multilayers

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Presentations

Annealing a skyrmion lattice with spin wave excitations

Dynamic instabilitiy in high power FMR of BiYIG nanodisks

Localized and propagating spin-wave modes in thin film multilayers hosting skyrmions

Strongly nonlinear ferromagnetic resonance of Bi-doped YIG nanodisks

Ferromagnetic resonance of skyrmions in thin film multilayers

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