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![Skyrmion lattice simulations exposing the delocalised HF resonance
We use a rectangular unit cell in a hexagonal skyrmion lattice containing two skyrmions, with area Suc=3a2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{{\mathrm{uc}}}=\sqrt{3}{a}^{2}$$\end{document}. The lattice constant a is adjusted such that the topological charge density ρtop=2Suc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{{\mathrm{top}}}=\frac{2}{{S}_{{\mathrm{uc}}}}$$\end{document} coincides with that of a large (2 × 2 μm²) relaxed sample at the same field (Supplementary section II.C, Fig. S9). a Equilibrium magnetisation at 200 mT for a unit cell size 222 × 128 nm². The colour scale and arrows represent the out-of-plane and in-plane magnetisations. b Simulated resonance spectra for the geometry described in (a). c Vertical linecut through the spectra in (b) at 200 mT, highlighting the relative intensity of the HF and LF modes. d, g Spatial distribution of the microwave absorption intensity during HF and LF resonances at 200 mT, excited at 10.6 and 2 GHz, respectively. While the distribution of the LF mode is localised close to the skyrmion core, the HF mode intensity is primarily concentrated in the inter-skyrmion area. Panels a–d and g are simulated with a spacer thickness L = 2 nm. Panels e, f and h, i depict the variation of the absorption intensities and resonant frequencies with L for the HF and LF modes, respectively. The red dashed line at L = 2 nm corresponds to the experimental layer separation.](publication/350415791/figure/fig5/AS:1005851250798599@1616825034595/Skyrmion-lattice-simulations-exposing-the-delocalised-HF-resonance-We-use-a-rectangular.png)
Skyrmion lattice simulations exposing the delocalised HF resonance We use a rectangular unit cell in a hexagonal skyrmion lattice containing two skyrmions, with area Suc=3a2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{{\mathrm{uc}}}=\sqrt{3}{a}^{2}$$\end{document}. The lattice constant a is adjusted such that the topological charge density ρtop=2Suc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{{\mathrm{top}}}=\frac{2}{{S}_{{\mathrm{uc}}}}$$\end{document} coincides with that of a large (2 × 2 μm²) relaxed sample at the same field (Supplementary section II.C, Fig. S9). a Equilibrium magnetisation at 200 mT for a unit cell size 222 × 128 nm². The colour scale and arrows represent the out-of-plane and in-plane magnetisations. b Simulated resonance spectra for the geometry described in (a). c Vertical linecut through the spectra in (b) at 200 mT, highlighting the relative intensity of the HF and LF modes. d, g Spatial distribution of the microwave absorption intensity during HF and LF resonances at 200 mT, excited at 10.6 and 2 GHz, respectively. While the distribution of the LF mode is localised close to the skyrmion core, the HF mode intensity is primarily concentrated in the inter-skyrmion area. Panels a–d and g are simulated with a spacer thickness L = 2 nm. Panels e, f and h, i depict the variation of the absorption intensities and resonant frequencies with L for the HF and LF modes, respectively. The red dashed line at L = 2 nm corresponds to the experimental layer separation.
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![Micromagnetic simulations of a [Ir1Fe0.5Co0.5Pt1]²⁰ multilayer
The...](publication/350415791/figure/fig3/AS:1005851250810898@1616825034310/Micromagnetic-simulations-of-a-Ir1Fe05Co05Pt1-multilayer-The-simulation-model_Q320.jpg)
Non-collinear magnets exhibit a rich array of dynamic properties at microwave frequencies. They can host nanometre-scale topological textures known as skyrmions, whose spin resonances are expected to be highly sensitive to their local magnetic environment. Here, we report a magnetic resonance study of an [Ir/Fe/Co/Pt] multilayer hosting Néel skyrmi...
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In this paper, we theoretically studied the tunable dynamic microwave properties of a magnetic skyrmion manipulated by strains through micromagnetic simulations. The strains are induced by voltage due to the converse piezoelectric effect and then applied to modulate the dynamic characteristics through the magneto-elastic coupling effect. The tunabl...
Citations
... Differently from other internal modes, i.e. clockwise (CW) and counterclockwise (CCW), the breathing mode can be excited via an out-of-plane field 37 and it has only been experimentally observed with skyrmion lattices in bulk materials at low temperature [38][39][40] . For skyrmion lattices in magnetic multilayers at room temperature, only signatures of the CW and CCW modes have been excited by an in-plane ac field 41,42 . ...
The growing market and massive use of Internet of Things nodes is placing unprecedented demands of energy efficient hardware for edge computing and microwave devices. In particular, magnetic tunnel junctions (MTJs), as main building blocks of spintronic microwave technology, can offer a path for the development of compact and high-performance microwave detectors. On the other hand, the fascinating field of skyrmionics is bridging together concepts from topology and spintronics. Here, we show the proof of concept of a topological spin-torque diode realized with an MTJ on top of a skyrmionic material at room temperature and for a wide region of applied fields, including the zero-field case. Our spin torque diode electrical measurements show the electrical excitation of a skyrmion resonant mode with frequencies near 4 GHz and a selectivity one order of magnitude smaller than the uniform modes excited in the same device. Micromagnetic simulations identify these dynamics with the excitation of the breathing mode and point out the role of thickness dependent magnetic parameters (magnetic anisotropy field and Dzyaloshinkii Moriya interaction) in both stabilizing and exciting the magnetic skyrmions. This work marks a milestone for the development of topological spin-torque diodes.
... Resonant modes detecting helicity shifts can be traced as a function of frequency, magnetic, and electric fields. Resonance probes can detect eigenstate transitions in individual skyrmions, either by magnetic resonance force microscopy (MRFM) 94,95 , or by using a magnetic force microscopy (MFM) tip as a local microwave probe [94][95][96][97][98][99] . ...
... Ferromagnetic Resonance (FMR) is a useful method to distinguish helicities, and detect gyration and breathing modes of skyrmions 98,99 , with a quantized level shift manifesting as a discontinuity in the resonance frequency in the millikelvin regime. For a skyrmion radius of only a few nanometers, it is challenging to probe single skyrmions, and therefore collective excitations need to be analyzed in a magnetically homogeneous material. ...
Magnetic nano-skyrmions develop quantized helicity excitations, and the quantum tunneling between nano-skyrmions possessing distinct helicities is indicative of the quantum nature of these particles. Experimental methods capable of nondestructively resolving the quantum aspects of topological spin textures, their local dynamical response, and their functionality now promise practical device architectures for quantum operations. With abilities to measure, engineer, and control matter at the atomic level, nano-skyrmions present opportunities to translate ideas into solid-state technologies. Proof-of-concept devices will offer electrical control over the helicity, opening a promising new pathway toward functionalizing collective spin states for the realization of a quantum computer based on skyrmions. This Perspective aims to discuss developments and challenges in this new research avenue in quantum magnetism and quantum information.
... Low frequency signal appearing in field range of − 20 mT to − 100 mT, can be owned to the magnetic response of vortex structure which remains stable in the similar field range. The appearance of such low frequency mode in ultrathin films has been discussed in literature for IDMI induced magnetic Skyrmions [24]. Similar as Fig. 2 (a), VNA-FMR measurements were done from negative magnetic field to positive magnetic field sweeping direction and the same value of switching frequency H Sw ≈ +35 mT was derived. ...
... The most common skyrmion detection scheme is based on the topological Hall effect [33]. Alternatively, spin Hall magnetoresistance [34] or FM resonance measurements were applied for skyrmion detection [35]. Imaging techniques like spin polarized scanning tunneling microscopy at a low temperature around 4 K [9], electron microscopy (Lorentz transmission electron microscopy or scanning electron microscopy), synchrotron-based techniques using magnetic dichroism in the x-ray range, and magneto-optical Kerr effect (MOKE) imaging give direct access for the detection and investigation of skyrmion and skyrmion motion in various material systems (see, e.g. ...
The controlled formation and adjustment of size and density of magnetic skyrmions in Ta/CoFeB/MgO trilayers with low Dzyaloshinskii-Moriya interaction is demonstrated. Close to the out-of-plane to in-plane magnetic spin reorientation transition, we find that small energy contributions enable skyrmion formation in a narrow window of 20 picometer in CoFeB thickness. Zero-field stable skyrmions are established with proper magnetic field initialization within a 10 picometer CoFeB thickness range. Using magneto-optical imaging with quantitative image processing, variations in skyrmion distribution and diameter are analyzed quantitively, the latter for sizes well below the optical resolution limit. We demonstrate the controlled merging of individual skyrmions. The overall demonstrated degree of comprehension of skyrmion control aids to the development of envisioned skyrmion based magnetic memory devices.
... We, thus, consider this unusual behavior most likely originates from the local absorption of magnetic quasiparticles, such as the skyrmion. 43,44 Magnetic skyrmions are vortex-like spin texture, which exhibit exotic topological characteristics, including localized particle properties with smaller magnetic domain sizes and its spin ordering can be manipulated via the chiral interfacial DMI. 45,46 More importantly, the critical zero-crossing wavelength is directly related to the skyrmion size and distribution, which is consistent with the magnitude of topological Hall effect exhibited in q H vs l 0 H Z curves. ...
Non-collinear antiferromagnets with a D0 19 hexagonal structure have attracted tremendous attention for their potential applications in topological spintronics. Exploring the relationship between spin texture and electronic band structure is crucial for understanding the physical nature of these chiral antiferromagnets. Here, we systematically investigated the variation of topological spin texture of the non-collinear antiferromagnet Mn3Sn film using magnetic circular dichroism (MCD) spectroscopy. The evolution of Mn spin texture from coplanar inverted triangular structure to swirling spin texture was achieved in Mn3Sn/Pt heterostructures through introducing an interfacial Dzyaloshinskii-Moriya interaction (DMI) at room temperature. Correspondingly, unconventional zero-crossing points in energy-resolved MCD spectra as well as a gradual shift of a zero-crossing point to longer wavelength were observed. Our work provides a spin texture modulation approach via interfacial DMI and an effective non-contact magneto-optical detection method to reveal the spin texture in the non-collinear antiferromagnet/heavy metal system.
... Only very recently, resonant dynamics with specific spectroscopic signatures of thin-film multilayers hosting skyrmions has been evidenced. 47,48 However, much remains to be explored and understood concerning their individual and collective resonant response to microwave excitations. ...
... Similar modes were previously described and reported in bulk crystals, 45,46 and lately in thin films. 47,48 Intriguingly, we also observe a well-defined mode at high frequency (>12 GHz), which corresponds to the in-phase precession of the magnetization within the skyrmion cores. The skyrmions here, have a distinct three-dimensional structure due to the competition between all the existing magnetic interactions in these multilayers, notably the interlayer dipolar effects. ...
... 56 We estimate by FMR a Gilbert damping constant of α = 0.022 and an inhomogeneous broadening of ∼18 mT (see Fig. 1 in the supplementary material) for our samples, which are relatively low for such multilayer systems. 47,56 The overall magnetic volume is enhanced with the 20 repetitions of the trilayer, which not only increases the thermal stability of the skyrmions 28 but also provides a larger signal-to-noise ratio for inductive measurements. Figure 1(b) shows the out-of-plane hysteresis curve of the sample measured by alternating gradient field magnetometer, which is characteristic of thin films hosting skyrmions. ...
Skyrmions are topological magnetic solitons that exhibit a rich variety of dynamics, such as breathing and gyration, which can involve collective behavior in arrangements like skyrmion lattices. However, such localized excitations typically lie in the gap of the spin wave spectrum and do not couple to propagating modes. By combining magnetic force microscopy, broadband ferromagnetic resonance, and micromagnetics simulations, we show that in thin-film multilayers of [Pt/FeCoB/AlOx]20 a high-frequency (>12 GHz) mode accompanies the skyrmion lattice phase, which involves the coherent precession of the skyrmion cores that results in the generation of 50–80 nm wavelength spin waves flowing into the uniformly magnetized background. This observation is made possible by a Gilbert damping constant of ∼0.02, which is nearly an order of magnitude lower than in similar ultrathin materials. The simulations also reveal a complex three-dimensional spin structure of the skyrmion cores, which plays a key role for spin wave generation.
... Excitation of short-wavelength magnons 31,32 ( 1 ≠ 0, specifically, 1 > 1 rad μm -1 ) in uniform spin alignment ( 0 = 0, Fig. 1b), is proved to be highly challenging and usually inefficient. Likewise, driving excitations in a non-uniform spin texture ( 0 ≠ 0) using uniform microwave perturbation ( 1 ≈ 0, namely, 1 ≪ 1 rad μm -1 ) is again inefficient [4][5][6][7] . In order to efficiently excite chaotic magnons, one would need to exert non-uniform excitation field ( 1 ≠ 0) on a static spin texture ( 0 ≠ 0) in the condition 1 ≈ 0 ≠ 0. In view of other prerequisites for chaos, e.g. ...
Topological spin textures such as magnetic skyrmions 1-7 are promising candidates as information carriers for next-generation memory-in-logic devices 8 . Antiferromagnetic spin textures 9-12 , compared to their ferromagnetic counterparts, innately possess high stability with respect to external disturbance 13,14 and high-frequency dynamics 15-18 compatible with ultrafast information processing. However, deterministic creation and reconfigurable switching of different antiferromagnetic spin textures have not been realized so far. Here, we demonstrate room-temperature deterministic switching between antiferromagnetic domain walls, Bloch bimerons and Néel bimerons in single-crystal hematite (α-Fe 2 O 3 ) 12,19-22 . All three topological states are found to be remarkably stable and fully controllable, as confirmed by 1’000 switching cycles. Their dynamics exhibit distinct resonance frequencies and magnetic field dependences. The switching from domain walls to Bloch bimerons requires only one microwave pulse (100 ns) with ultralow energy consumption (1 nJ). When the dynamic excitation wavevector approaches that of static spin textures, and the power lies beyond a threshold, chaotic magnons 23-26 are excited, which subsequently nucleate bimerons and finally lead to a deterministic switching, as unveiled by micromagnetic simulations. The progressive switching from Bloch-type to Néel-type bimerons imitates the weighted sum operation in neuromorphic computing 27,28 . Thus, our work points to the possibility of using spin textures in antiferromagnets for information processing.
... These modes are well understood both theoretically 17 and experimentally 18,19 in bulk systems and are used routinely to characterize the extent of the skyrmion pocket in phase space. 20 In thin film systems, this is much more difficult because of the lowered sensitivity of measurements and the reduced number of skyrmions in the system, 21,22 and so most work on these systems is theoretical. 23,24 It was recently shown that in synthetic antiferromagnets, the coupling between the skyrmions in each layer produces a splitting of both the rotational 25 and breathing 26 modes into in-phase (IP) and out-of-phase (OOP) modes. ...
Skyrmions are small topologically protected magnetic structures that hold promise for applications from data storage to neuromorphic computing and they have been shown to possess internal microwave frequency excitations. Skyrmions in a synthetic antiferromagnet have been predicted to be smaller and faster than their ferromagnetic equivalents and also shown to possess more internal modes. In this work, we consider the breathing modes of skyrmions in a four repetition synthetic antiferromagnetic multilayer by means of micromagnetic simulations and examine the further splitting of the modes into different arrangements of out-of-phase, in-phase, and modes with more complex phase relationships. This results in a lowering of frequencies, which is promising for skyrmion sensing applications in a synthetic antiferromagnet.
... 60,75,93,[166][167][168][169] While Néel skyrmion has been experimentally observed in heavy metal/ferromagnetic metal multilayer thin-films. 82,[170][171][172][173][174][175] The distinct configurations of skyrmion are due to different kinds of DM interaction: the bulk DM interaction prompts the emergence of Bloch type, and the interfacial DM interaction prompts the emergence of Néel type, as shown in Figs. 2(c) and 2(d). ...
In recent years, magnon and spin texture are attracting great interest in condensed matter physics and magnetism. Magnonics is aiming to use magnon as information carriers to realize functions for storage, transmission, and processing. Magnetic skyrmion is representative spin texture due to its topologically nontrivial properties. Since skyrmions are topologically protected, their transformation to other spin configurations requires overcoming additional topological energy barriers. Therefore, skyrmions are more stable than other trivial spin textures. In addition, the characters of nanoscale size, quasiparticle properties, and various excitation modes make them a potential candidate for spintronic application. Magnon and skyrmion, as two fundamental excitations, can coexist in magnetic systems and interplay with each other through direct exchange interactions. In this review, we provide an overview of recent theoretical and experimental studies on magnon–skyrmion interactions. We mainly focus on three kinds of magnon–skyrmion interactions: (i) magnon scattering by skyrmion, (ii) skyrmion motion driven by magnon, and (iii) coupling between magnon and skyrmion modes. The first two kinds of interactions could be clearly explained by the wave-particle interaction model on the classical level. Alternatively, the last kind of interaction could be understood by the coupled harmonic oscillator model on the quantum level, which indicates fast energy exchange and hybrid magnon states. The exploration focused on quantum phenomena of magnon has led to the emerging field of quantum magnonics and promoted applications of magnon in quantum information storage and processing. In the end, we give a perspective on the exploration of magnon–skyrmion interaction in quantum magnonics.
... [41,42] In recent years, the skyrmion-hosting thin-films in the form of [heavy-metal (HM)/ferromagneticmetal (FM)/heavy-metal (HM)] n multilayers are reported to show relatively low damping of less than 0.05. [37,43] These findings provide a promising platform for studying the dynamic spin wave modes of the skyrmion-hosting thin-film systems, and promotes the experimental realization of SMCs. ...
In this work, an interlayer perpendicular standing spin wave mode is observed in the skyrmion-hosting [Pt/Co/Ta] 10 multilayer by time-resolved magneto-optical Kerr effect measurements. The observed interlayer mode depends on the interlayer spinpumping and spin transfer torque among the neighboring Co layers. This mode shows monotone increasing frequency-field dependence which is similar to the ferromagnetic resonance mode, but with higher frequency range. Besides, the damping of the interlayer mode is found to be a relatively low constant value of 0.027 which is independent of the external field. This work expound the potential application of the [heavy-metal/ferromagnetic-metal] n multilayers for skyrmion-based magnonic devices which can provide multiple magnon modes, relatively low damping, and skyrmion states, simultaneously.
