Observation of magnetic excitations of Skyrmion crystal in a helimagnetic insulator Cu2OSeO3

Topological Spin Textures in an Insulating van der Waals Ferromagnet

Generation and control of topological spin textures constitutes one of the most exciting challenges of modern spintronics given their potential applications in information storage technologies. Of particular interest are magnetic insulators, which due to low damping, absence of Joule heating and reduced dissipation can provide energy-efficient spin-textures platform. Here, it is demonstrated that the interplay between sample thickness, external magnetic fields, and optical excitations can generate a prolific paramount of spin textures, and their coexistence in insulating CrBr3 van der Waals (vdW) ferromagnets. Using high-resolution magnetic force microscopy and large-scale micromagnetic simulation methods, the existence of a large region in T-B phase diagram is demonstrated where different stripe domains, skyrmion crystals, and magnetic domains exist and can be intrinsically selected or transformed to each-other via a phase-switch mechanism. Lorentz transmission electron microscopy unveils the mixed chirality of the magnetic textures that are of Bloch-type at given conditions but can be further manipulated into Néel-type or hybrid-type via thickness-engineering. The topological phase transformation between the different magnetic objects can be further inspected by standard photoluminescence optical probes resolved by circular polarization indicative of an existence of exciton-skyrmion coupling mechanism. The findings identify vdW magnetic insulators as a promising framework of materials for the manipulation and generation of highly ordered skyrmion lattices relevant for device integration at the atomic level.

The influence of antiferromagnetic spin cantings on the magnetic helix pitch in cubic helimagnets

In cubic helimagnets MnSi and Cu2OSeO3with their nearly isotropic magnetic properties, the magnetic structure undergoes helical deformation, which is almost completely determined by the helicoid wavenumberk=D/J, where magnetization field stiffnessJis associated with isotropic spin exchange, andDis a pseudoscalar value characterizing the antisymmetric Dzyaloshinskii-Moriya (DM) interaction. Another magnetic feature of these crystals, also caused by the DM interactions, are antiferromagnetic spin cantings, similar to the ferromagnetic cantings responsible for the phenomenon of weak ferromagnetism. Here we show that cantings can strongly influence the helical order through the value of the parameterD. Changing the cantings in a strong magnetic field is predicted to affect the magnon spectrum of the crystals.

Task-adaptive physical reservoir computing

Reservoir computing is a neuromorphic architecture that may offer viable solutions to the growing energy costs of machine learning. In software-based machine learning, computing performance can be readily reconfigured to suit different computational tasks by tuning hyperparameters. This critical functionality is missing in 'physical' reservoir computing schemes that exploit nonlinear and history-dependent responses of physical systems for data processing. Here we overcome this issue with a 'task-adaptive' approach to physical reservoir computing. By leveraging a thermodynamical phase space to reconfigure key reservoir properties, we optimize computational performance across a diverse task set. We use the spin-wave spectra of the chiral magnet Cu2OSeO3 that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to different computational reservoir responses. The task-adaptive approach is applicable to a wide variety of physical systems, which we show in other chiral magnets via above (and near) room-temperature demonstrations in Co8.5Zn8.5Mn3 (and FeGe).

Broadband magnetic resonance spectroscopy in MnSc[Formula: see text]S[Formula: see text]

Recent neutron scattering experiments suggested that frustrated magnetic interactions give rise to antiferromagnetic spiral and fractional skyrmion lattice phases in MnSc[Formula: see text]S[Formula: see text] . Here, to trace the signatures of these modulated phases, we studied the spin excitations of MnSc[Formula: see text]S[Formula: see text] by THz spectroscopy at 300 mK and in magnetic fields up to 12 T and by broadband microwave spectroscopy at various temperatures up to 50 GHz. We found a single magnetic resonance with frequency linearly increasing in field. The small deviation of the Mn[Formula: see text] ion g-factor from 2, g = 1.96, and the absence of other resonances imply very weak anisotropies and negligible contribution of higher harmonics to the spiral state. The significant difference between the dc magnetic susceptibility and the lowest-frequency ac susceptibility in our experiment implies the existence of mode(s) outside of the measured frequency windows. The combination of THz and microwave experiments suggests a spin gap opening below the ordering temperature between 50 GHz and 100 GHz.

Topological Equivalence of Stripy States and Skyrmion Crystals

Stripy states, consisting of a collection of stripy spin textures, are the precursors of skyrmion crystals (SkXs). The common belief is that stripy states and SkXs are topologically unconnected and that transitions between SkXs and stripy states are phase transitions. Here, we show that both stripy states and SkXs are skyrmion condensates and they are topologically equivalent. By gradually tuning the stripe whose width goes from smaller than to larger than skyrmion-skyrmion separation, the structure of a skyrmion condensate transforms smoothly and continuously from various stripy phases, including helical states and mazes, to crystals, showing that stripy states are topologically connected to SkXs.

Voltage-Controlled Dzyaloshinskii-Moriya Interaction Torque Switching of Perpendicular Magnetization

Magnetization switching is the most important operation in spintronic devices. In modern nonvolatile magnetic random-access memory (MRAM), it is usually realized by spin-transfer torque (STT) or spin-orbit torque (SOT). However, both STT and SOT MRAM require current to drive magnetization switching, which will cause Joule heating. Here, we report an alternative mechanism, Dzyaloshinskii-Moriya interaction (DMI) torque, that can realize magnetization switching fully controlled by voltage pulses. We find that a consequential voltage-controlled reversal of DMI chirality in multiferroics can lead to continued expansion of a skyrmion thanks to the DMI torque. Enough DMI torque will eventually make the skyrmion burst into a quasiuniform ferromagnetic state with reversed magnetization, thus realizing the switching of a perpendicular magnet. The discovery is demonstrated in two-dimensional multiferroics, CuCrP_{2}Se_{6} and CrN, using first-principles calculations and micromagnetic simulations. As an example, we applied the DMI torque for simulating leaky-integrate-fire functionality of biological neurons. Our discovery of DMI torque switching of perpendicular magnetization provides tremendous potential toward magnetic-field-free and current-free spintronic devices, and neuromorphic computing as well.

Instability of skyrmion lattice under microwave magnetic field due to single-qhelimagnetic excitation mode

Composed of the three spiral magnetic vectors, the structure of skyrmion lattice (SkL) can be destructed by spin excitations in possibly two ways: one is to make decoherence of all the helices through the phase change of a certain spiral magnetic vector, and the other is to inhibit one or two spiral components while enhancing the others so that it becomes a magnetic structure of single or double magnetic vectors. Here, we present a micromagnetic study on the spin excitations of a two-dimensional SkL under the in-plane microwave magnetic field. By calculating the parameters describing the in-plane spin excitations mode, we find that the spin configuration tends to be an enhanced single-vector spiral magnetic structure due to the excitation modes under some specific frequencies so that the SkL will collapse to the topologically trivial state. Our results help to form a deeper understanding of the spin excitation in SkL under an ac magnetic field.

Adaptive cognition implemented with a context-aware and flexible neuron for next-generation artificial intelligence

Neuromorphic computing mimics the organizational principles of the brain in its quest to replicate the brain's intellectual abilities. An impressive ability of the brain is its adaptive intelligence, which allows the brain to regulate its functions "on the fly" to cope with myriad and ever-changing situations. In particular, the brain displays three adaptive and advanced intelligence abilities of context-awareness, cross frequency coupling, and feature binding. To mimic these adaptive cognitive abilities, we design and simulate a novel, hardware-based adaptive oscillatory neuron using a lattice of magnetic skyrmions. Charge current fed to the neuron reconfigures the skyrmion lattice, thereby modulating the neuron's state, its dynamics and its transfer function "on the fly." This adaptive neuron is used to demonstrate the three cognitive abilities, of which context-awareness and cross-frequency coupling have not been previously realized in hardware neurons. Additionally, the neuron is used to construct an adaptive artificial neural network (ANN) and perform context-aware diagnosis of breast cancer. Simulations show that the adaptive ANN diagnoses cancer with higher accuracy while learning faster and using a more compact and energy-efficient network than a nonadaptive ANN. The work further describes how hardware-based adaptive neurons can mitigate several critical challenges facing contemporary ANNs. Modern ANNs require large amounts of training data, energy, and chip area, and are highly task-specific; conversely, hardware-based ANNs built with adaptive neurons show faster learning, compact architectures, energy-efficiency, fault-tolerance, and can lead to the realization of broader artificial intelligence.

Magnetic Skyrmionic Bubbles at Room Temperature and Sign Reversal of the Topological Hall Effect in a Layered Ferromagnet Cr0.87Te

The search for materials that exhibit topologically protected spin configurations, such as magnetic skyrmions, continues to be fueled by the promise of outstanding candidate components for spin-based applications. In this study, in situ Lorentz transmission electron microscopy directly images Bloch-type magnetic skyrmionic bubbles in a layered ferromagnet Cr_0.87Te single crystal. Owing to the competition between a magnetic dipole interaction and uniaxial easy axis anisotropy, nanoscale magnetic bubbles with random chirality can be observed in a wide temperature range covering room temperature when the external magnetic field is applied along the out-of-plane direction. Moreover, high-density and stable skyrmionic bubbles are successfully realized at zero magnetic field by appropriate field-cooling manipulation. Additionally, a sign reversal of the Hall effect and the derived topological Hall effect is observed and discussed. As quasi-two-dimensional materials, the binary chromium tellurides hosting magnetic skyrmions could have many applications in low-dimensional skyrmion-based spintronic devices in an ambient atmosphere.

Slowdown of photoexcited spin dynamics in the non-collinear spin-ordered phases in skyrmion host GaV4S8

Formation of magnetic order alters the character of spin excitations, which then affects transport properties. We investigate the photoexcited ultrafast spin dynamics in different magnetic phases in Néel-type skyrmion host GaV₄S₈ with time-resolved magneto-optical Kerr effect experiments. The coherent spin precession, whose amplitude is enhanced in the skyrmion-lattice phase, shows a signature of phase coexistence across the magnetic phase transitions. The incoherent spin relaxation dynamics slows down by a factor of two in the skyrmion-lattice/cycloid phases, indicating significant decrease in thermal conductivity triggered by a small change of magnetic field. The slow heat diffusion in the skyrmion-lattice/cycloid phases is attributed to the stronger magnon scattering off the domain walls formed in abundance in the skyrmion-lattice/cycloid phase. These results highlight the impact of spatial spin structure on the ultrafast heat transport in spin systems, providing a useful insight for the step toward ultrafast photocontrol of the magnets with novel spin orders.

Skyrmions are a topological magnetic texture that have garnered considerable interest for various technological applications. Here, Sekiguchi et al. investigate the ultrafast optical response of GaV4S6, and find a significant reduction in the thermal conductivity in the skyrmion phase.

Laser-Controlled Real- and Reciprocal-Space Topology in Multiferroic Insulators

Magnetic materials in which it is possible to control the topology of their magnetic order in real space or the topology of their magnetic excitations in reciprocal space are highly sought after as platforms for alternative data storage and computing architectures. Here we show that multiferroic insulators, owing to their magnetoelectric coupling, offer a natural and advantageous way to address these two different topologies using laser fields. We demonstrate that via a delicate balance between the energy injection from a high-frequency laser and dissipation, single skyrmions-archetypical topological magnetic textures-can be set into motion with a velocity and propagation direction that can be tuned by the laser field amplitude and polarization, respectively. Moreover, we uncover an ultrafast Floquet magnonic topological phase transition in a laser-driven skyrmion crystal and we propose a new diagnostic tool to reveal it using the magnonic thermal Hall conductivity.

Tunable gigahertz dynamics of low-temperature skyrmion lattice in a chiral magnet

Recently, it has been shown that the chiral magnetic insulator Cu₂OSeO₃hosts skyrmions in two separated pockets in temperature and magnetic field phase space. It has also been shown that the predominant stabilization mechanism for the low-temperature skyrmion (LTS) phase is via the crystalline anisotropy, opposed to temperature fluctuations that stabilize the well-established high-temperature skyrmion (HTS) phase. Here, we report on a detailed study of LTS generation by field cycling, probed by GHz spin dynamics in Cu₂OSeO₃. LTSs are populated via a field cycling protocol with the static magnetic field applied parallel to the ⟨100⟩ crystalline direction of plate and cuboid-shaped bulk crystals. By analyzing temperature-dependent broadband spectroscopy data, clear evidence of LTS excitations with clockwise (CW), counterclockwise (CCW), and breathing mode (BR) character at temperatures belowT= 40 K are shown. We find that the mode intensities can be tuned with the number of field-cycles below the saturation field. By tracking the resonance frequencies, we are able to map out the field-cycle-generated LTS phase diagram, from which we conclude that the LTS phase is distinctly separated from the high-temperature counterpart. We also study the mode hybridization between the dark CW and the BR modes as a function of temperature. By using two Cu₂OSeO₃crystals with different shapes and therefore different demagnetization factors, together with numerical calculations, we unambiguously show that the magnetocrystalline anisotropy plays a central role for the mode hybridization.

Nanoscale Magnetization and Current Imaging Using Time-Resolved Scanning-Probe Magnetothermal Microscopy

Magnetic microscopy that combines nanoscale spatial resolution with picosecond scale temporal resolution uniquely enables direct observation of the spatiotemporal magnetic phenomena that are relevant to future high-speed, high-density magnetic storage and logic technologies. Magnetic microscopes that combine these metrics has been limited to facility-level instruments. To address this gap in lab-accessible spatiotemporal imaging, we develop a time-resolved near-field magnetic microscope based on magnetothermal interactions. We demonstrate both magnetization and current density imaging modalities, each with spatial resolution that far surpasses the optical diffraction limit. In addition, we study the near-field and time-resolved characteristics of our signal and find that our instrument possesses a spatial resolution on the scale of 100 nm and a temporal resolution below 100 ps. Our results demonstrate an accessible and comparatively low-cost approach to nanoscale spatiotemporal magnetic microscopy in a table-top form to aid the science and technology of dynamic magnetic devices with complex spin textures.

Microwave resonances of magnetic skyrmions in thin film multilayers

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 skyrmions at room temperature. Experiments reveal two distinct resonances of the skyrmion phase during in-plane ac excitation, with frequencies between 6-12 GHz. Complementary micromagnetic simulations indicate that the net magnetic dipole moment rotates counterclockwise (CCW) during both resonances. The magnon probability distribution for the lower-frequency resonance is localised within isolated skyrmions, unlike the higher-frequency mode which principally originates from areas between skyrmions. However, the properties of both modes depend sensitively on the out-of-plane dipolar coupling, which is controlled via the ferromagnetic layer spacing in our heterostructures. The gyrations of stable isolated skyrmions reported in this room temperature study encourage the development of new material platforms and applications based on skyrmion resonances. Moreover, our material architecture enables the resonance spectra to be tuned, thus extending the functionality of such applications over a broadband frequency range.

Chiral Emission of Exchange Spin Waves by Magnetic Skyrmions

Spin waves or their quanta magnons raise the prospect to act as information carriers in the absence of Joule heating. The challenge to excite spin waves with nanoscale wavelengths free of nanolithography becomes a critical bottleneck for the application of nanomagnonics. Magnetic skyrmions are chiral magnetic textures at the nanoscale. In this work, short-wavelength exchange spin waves are demonstrated to be chirally emitted in a low damping magnetic insulating thin film by magnetic skyrmions. The spin-wave chirality originates from the chiral spin pumping effect and is determined by the cross product of the magnetization orientation and the film normal direction. The Halbach effect explains the enhancement or attenuation of the spin-wave amplitude with a reversed sign of the Dyzaloshinskii-Moriya interaction. Controllable spin-wave propagation is demonstrated by rotating a moderate applied field. Our findings are key for building compact low-power nanomagnonic devices based on intrinsic nanoscale magnetic textures.

Magnetic Skyrmion Materials

Skyrmion, a concept originally proposed in particle physics half a century ago, can now find the most fertile field for its applicability, that is, the magnetic skyrmion realized in helimagnetic materials. The spin swirling vortex-like texture of the magnetic skyrmion can define the particle nature by topology; that is, all the constituent spin moments within the two-dimensional sheet wrap the sphere just one time. Such a topological nature of the magnetic skyrmion can lead to extraordinary metastability via topological protection and the driven motion with low electric-current excitation, which may promise future application to spintronics. The skyrmions in the magnetic materials frequently show up as the crystal lattice form, e.g., hexagonal lattice, but sometimes as isolated or independent particles. These skyrmions in magnets were initially found in acentric magnets, such as chiral, polar, and bilayered magnets endowed with antisymmetric spin exchange interaction, while the skyrmion host materials have been explored in a broader family of compounds including centrosymmetric magnets. This review describes the materials science and materials chemistry of magnetic skyrmions using the classification scheme of the skyrmion forming microscopic mechanisms. The emergent phenomena and functions mediated by skyrmions are described, including the generation of emergent magnetic and electric field by statics and dynamics of skrymions and the inherent magnetoelectric effect. The other important magnetic topological defects in two or three dimensions, such as biskyrmions, antiskyrmions, merons, and hedgehogs, are also reviewed in light of their interplay with the skyrmions.

Néel-Type Elliptical Skyrmions in a Laterally Asymmetric Magnetic Multilayer

Magnetic skyrmions, topological-chiral spin textures, have potential applications in next-generation high-density and energy-efficient spintronic devices for information storage and logic technologies. Tailoring the detailed spin textures of skyrmions is of pivotal importance for tuning skyrmion dynamics, which is one of the key factors for the design of skyrmionic devices. Here, the direct observation of parallel aligned elliptical magnetic skyrmions in Pt/Co/Ta multilayers with an oblique-angle deposited Co layer is reported. Domain wall velocity and spin-orbit-torque-induced out-of-plane effective field analysis demonstrate that the formation of unusual elliptical skyrmions is correlated to the anisotropic effective perpendicular magnetic anisotropy energy density (K^eff _u ) and Dzyaloshinskii-Moriya interaction (DMI) in the film plane. Structural analysis and first-principles calculations further show that the anisotropic K^eff _u and DMI originate from the interfacial anisotropic strain introduced by the oblique-angle deposition. The work provides a method to tune the spin textures of skyrmions in magnetic multilayers and, thereby, a new degree of freedom for the design of skyrmionic devices.

Nonreciprocity of spin waves in the conical helix state

Nonreciprocity emerges in nature and in artificial objects from various physical origins, being widely utilized in contemporary technologies as exemplified by diode elements in electronics. While most of the nonreciprocal phenomena are realized by employing interfaces where the inversion symmetry is trivially lifted, nonreciprocal transport of photons, electrons, magnons, and possibly phonons also emerge in bulk crystals with broken space inversion and time reversal symmetries. Among them, directional propagation of bulk magnons (i.e., quanta of spin wave excitation) is attracting much attention nowadays for its potentially large nonreciprocity suitable for spintronic and spin-caloritronic applications. Here, we demonstrate nonreciprocal propagation of spin waves for the conical spin helix state in Cu₂OSeO₃ due to a combination of dipole and Dzyaloshinskii-Moriya interactions. The observed nonreciprocal spin dispersion smoothly connects to the hitherto known magnetochiral nonreciprocity in the field-induced collinear spin state; thus, all the spin phases show diode characteristics in this chiral insulator.

Intrinsic DMI-free skyrmion formation and robust dynamic behaviors in magnetic hemispherical shells

We performed finite-element micromagnetic simulations to examine the formation of skyrmions without intrinsic Dzyaloshinskii–Moriya interaction (DMI) in magnetic hemispherical shells. We found that curvature-induced DM-like interaction allows for further stabilization of skyrmions without the DMI in curved-geometry hemispherical shells for a specific range of uniaxial perpendicular magnetic anisotropy (PMA) constant K_u. The larger the curvature of the shell, the higher the K_u value required for the formation of the skyrmions. With well-stabilized skyrmions, we also found in-plane gyration modes and azimuthal spin-wave modes as well as an out-of-plane breathing mode, similarly to previously found modes for planar geometries. Furthermore, additional higher-frequency hybrid modes were observed due to coupling between the gyration and azimuthal modes. This work provides further physical insight into the static and dynamic properties of intrinsic DMI-free skyrmions formed in curved-geometry systems.

Tunable interfacial Dzyaloshinskii-Moriya interaction in symmetrical Au/[Fe/Au]n multilayers

The interfacial Dzyaloshinskii-Moriya interaction (i-DMI) has been exploited in as-made symmetrical Au/[Fe/Au]n structures. By tailoring the chirality of the i-DMI at the Au/Fe interface, an overall enhancement of the i-DMI can be obtained in such a symmetrical structure. Furthermore, the tunability of the i-DMI was realized by changing the stacking number n. Compared to the top of Fe, a large tensile stress at the bottom of Fe due to lattice mismatch was responsible for the chirality change in the sub/Au/Fe system. Layer-resolved DMI calculations revealed that the sign of the spin-orbit coupling (SOC) energy was changed for Au near the interface of Au/Fe under tensile stress, subsequently reversing the chirality of the i-DMI from left-handed to right-handed. Our findings provide a simplest way to tune the i-DMI in a multilayer system, further benefiting the application of skyrmion-based devices.

Microwave Spectroscopy of the Low-Temperature Skyrmion State in Cu_{2}OSeO_{3}

In the cubic chiral magnet Cu_{2}OSeO_{3} a low-temperature skyrmion state (LTS) and a concomitant tilted conical state are observed for magnetic fields parallel to ⟨100⟩. Here, we report on the dynamic resonances of these novel magnetic states. After promoting the nucleation of the LTS by means of field cycling, we apply broadband microwave spectroscopy in two experimental geometries that provide either predominantly in-plane or out-of-plane excitation. By comparing the results to linear spin-wave theory, we clearly identify resonant modes associated with the tilted conical state, the gyrational and breathing modes associated with the LTS, as well as the hybridization of the breathing mode with a dark octupole gyration mode mediated by the magnetocrystalline anisotropies. Most intriguingly, our findings suggest that under decreasing fields the hexagonal skyrmion lattice becomes unstable with respect to an oblique deformation, reflected in the formation of elongated skyrmions.

Spin waves in skyrmionic structures with various topological charges

Equilibrium properties and localized magnon excitations are investigated in topologically distinct skyrmionic textures. The observed shape of the structures and their orientation on the lattice is explained based on their vorticities and the symmetry of the crystal. The transformation between different textures and their annihilation as a function of magnetic field is understood based on the energy differences between them. The angular momentum spin-wave eigenmodes characteristic of cylindrically symmetric structures are combined in the distorted spin configurations, leading to avoided crossings in the magnon spectrum. The susceptibility of the skyrmionic textures to homogeneous external fields is calculated, revealing that a high number of modes become detectable due to the hybridization between the angular momentum eigenmodes. These findings should contribute to the observation of spin waves in distorted skyrmionic structures via experiments and numerical simulations, widening the range of their possible applications in magnonic devices.

Effect of chemical substitution on the skyrmion phase in Cu2OSeO3

Magnetic skyrmions have been the focus of intense research due to their unique qualities which result from their topological protections. Previous work on Cu2OSeO3, the only known insulating multiferroic skyrmion material, has shown that chemical substitution alters the skyrmion phase. We chemically substitute Zn, Ag, and S into powdered Cu2OSeO3 to study the effect on the magnetic phase diagram. In both the Ag and the S substitutions, we find that the skyrmion phase is stabilized over a larger temperature range, as determined via magnetometry and small-angle neutron scattering (SANS). Meanwhile, while previous magnetometry characterization suggests two high temperature skyrmion phases in the Zn-substituted sample, SANS reveals the high temperature phase to be skyrmionic while we are unable to distinguish the other from helical order. Overall, chemical substitution weakens helical and skyrmion order as inferred from neutron scattering of the q ≈ 0.01 Å - 1 magnetic peak.

Electron Beam Lithography of Magnetic Skyrmions

The emergence of magnetic skyrmions, topological spin textures, has aroused tremendous interest in studying the rich physics related to their topology. While skyrmions promise high-density and energy-efficient magnetic memory devices for information technology, the manifestation of their nontrivial topology through single skyrmions and ordered and disordered skyrmion lattices could also give rise to many fascinating physical phenomena, such as chiral magnon and skyrmion glass states. Therefore, generating skyrmions at designated locations on a large scale, while controlling the skyrmion patterns, is the key to advancing topological magnetism. Here, a new, yet general, approach to the "printing" of skyrmions with zero-field stability in arbitrary patterns on a massive scale in exchange-biased magnetic multilayers is presented. By exploiting the fact that the antiferromagnetic order can be reconfigured by local thermal excitations, a focused electron beam with a graphic pattern generator to "print" skyrmions is used, which is referred to as skyrmion lithography. This work provides a route to design arbitrary skyrmion patterns, thereby establishing the foundation for further exploration of topological magnetism.

Spin Wave Radiation by a Topological Charge Dipole

The use of spin waves (SWs) as data carriers in spintronic and magnonic logic devices offers operation at low power consumption, free of Joule heating. Nevertheless, the controlled emission and propagation of SWs in magnetic materials remains a significant challenge. Here, we propose that skyrmion-antiskyrmion bilayers form topological charge dipoles and act as efficient sub-100 nm SW emitters when excited by in-plane ac magnetic fields. The propagating SWs have a preferred radiation direction, with clear dipole signatures in their radiation pattern, suggesting that the bilayer forms a SW antenna. Bilayers with the same topological charge radiate SWs with spiral and antispiral spatial profiles, enlarging the class of SW patterns. We demonstrate that the characteristics of the emitted SWs are linked to the topology of the source, allowing for full control of the SW features, including their amplitude, preferred direction of propagation, and wavelength.

Giant Topological Hall Effect and Superstable Spontaneous Skyrmions below 330 K in a Centrosymmetric Complex Noncollinear Ferromagnet NdMn2Ge2

Skyrmions with topologically nontrivial spin textures are promising information carriers in next-generation ultralow power consumption and high-density spintronic devices. To promote their further development and utilization, the search for new room temperature skyrmion-hosting materials is crucial. Considering that most of the previous skyrmion-hosting materials are noncollinear magnets, here, the detection of the topological Hall effect (THE) and the discovery of skyrmions at room temperature are first reported in a centrosymmetric complex noncollinear ferromagnet NdMn₂Ge₂. Below 330 K, the compound can host stable Bloch-type skyrmions with about 75 nm diameter in a wide window of magnetic field and temperature, including zero magnetic field and room temperature. Moreover, the skyrmions can induce a giant topological Hall effect in a wide temperature range with a maximum value of -2.05 μΩ cm. These features make the compound attractive for both fundamental research and potential application in novel spintronic devices.

Cryogenic frequency-domain electron spin resonance spectrometer based on coplanar waveguides and field modulation

We present an instrument to perform frequency-domain electron spin resonance experiments that is based on coplanar waveguides and field modulation. A large parameter space in frequency (up to 25 GHz), magnetic field (up to 8 T), and temperature (down to 1.6 K) is accessible. We performed experiments on DPPH (2,2-diphenyl-1-picrylhydrazyl) as a standard to calibrate the field modulation as well as on a carbon fiber sample to estimate the overall sensitivity of the instruments. Spectra of a ruby sample in a broad frequency and field range at cryogenic temperatures are recorded with and without field modulation. The comparison reveals the improved signal-to-noise ratio achieved by field modulation.

Propagation dynamics of spin excitations along skyrmion strings

Magnetic skyrmions, topological solitons characterized by a two-dimensional swirling spin texture, have recently attracted attention as stable particle-like objects. In a three-dimensional system, a skyrmion can extend in the third dimension forming a robust and flexible string structure, whose unique topology and symmetry are anticipated to host nontrivial functional responses. Here we experimentally demonstrate the coherent propagation of spin excitations along skyrmion strings for the chiral-lattice magnet Cu₂OSeO₃. We find that this propagation is directionally non-reciprocal and the degree of non-reciprocity, as well as group velocity and decay length, are strongly dependent on the character of the excitation modes. These spin excitations can propagate over a distance exceeding 50 μm, demonstrating the excellent long-range ordered nature of the skyrmion-string structure. Our combined experimental and theoretical analyses offer a comprehensive account of the propagation dynamics of skyrmion-string excitations and suggest the possibility of unidirectional information transfer along such topologically protected strings.

Ferromagnetic Resonance with Magnetic Phase Selectivity by Means of Resonant Elastic X-Ray Scattering on a Chiral Magnet

Cubic chiral magnets, such as Cu_{2}OSeO_{3}, exhibit a variety of noncollinear spin textures, including a trigonal lattice of spin whirls, the so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at gigahertz frequencies, we probe the ferromagnetic resonance (FMR) modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS FMR, is carried out at distinct positions in reciprocal space, it allows us to distinguish contributions originating from different magnetic states, providing information on the precise character, weight, and mode mixing as a prerequisite of tailored excitations for applications.

Electrically driven spin torque and dynamical Dzyaloshinskii-Moriya interaction in magnetic bilayer systems

Efficient control of magnetism with electric means is a central issue of current spintronics research, which opens an opportunity to design integrated spintronic devices. However, recent well-studied methods are mostly based on electric-current injection, and they are inevitably accompanied by considerable energy losses through Joule heating. Here we theoretically propose a way to exert spin torques into magnetic bilayer systems by application of electric voltages through taking advantage of the Rashba spin-orbit interaction. The torques resemble the well-known electric-current-induced torques, providing similar controllability of magnetism but without Joule-heating energy losses. The torques also turn out to work as an interfacial Dzyaloshinskii-Moriya interaction which enables us to activate and create noncollinear magnetism like skyrmions by electric-voltage application. Our proposal offers an efficient technique to manipulate magnetizations in spintronics devices without Joule-heating energy losses.

Experimental Observation of Single Skyrmion Signatures in a Magnetic Tunnel Junction

We have deterministically created a stable topological spin texture in magnetic tunnel junctions (MTJ) by using pulsed or microwave currents. The spin texture is characterized by a field-dependent intermediate resistance state and a new magnetic resonance. Micromagnetic simulations show that the observations are consistent with the nucleation of a single skyrmion, facilitated by a spatially nonuniform stray field. The unique resonance spectrum is identified as the skyrmion breathing mode and a skyrmion diameter of 75 nm is estimated. This work shows the possibility to create skyrmions in MTJs without the Dzyaloshinskii-Moriya interaction and could lead to noninvasive, on-chip skyrmion measurement.

A sum rule of uniaxial anisotropy and external magnetic field for formation of Néel-type skyrmion lattices in two-dimensional ferromagnets

It is generally believed that the perpendicular magnetic anisotropy (PMA) plays an important role in stabilizing skyrmion lattices (SkL) in two-dimensional (2D) magnetic systems in which both Heisenberg exchange and Dzyaloshinskii-Moriya interactions co-exist, and the skyrmion sizes in SkLs are mainly determined by the strengths of these two intrinsic interactions. To investigate the details, we employ here a quantum computational approach we develop in recent years to simulate the Néel-type skyrmion lattices formed on a 2D PdFe/Ir(1 1 1)-like film. From our simulated results, we find that: within an external magnetic field applied normal to the film plane, the PMA is indeed able to help induce Néel-type SkLs in a wider field range; however, to stabilize the SkLs, the PMA cannot be too strong, the strengths of the external magnetic field and the maximal PMA must satisfy a sum rule since the effective perpendicular magnetic field generated by these two interactions cannot exceed a largest value. We also notice that the periodical boundary condition imposed on the FM system in simulations is able to facilitate SkL formations, and it can also modify the skyrmion size in a certain extend.

Observation of Nanoscale Skyrmions in SrIrO3/SrRuO3 Bilayers

Skyrmion imaging and electrical detection via topological Hall (TH) effect are two primary techniques for probing magnetic skyrmions, which hold promise for next-generation magnetic storage. However, these two kinds of complementary techniques have rarely been employed to investigate the same samples. We report the observation of nanoscale skyrmions in SrIrO₃/SrRuO₃ (SIO/SRO) bilayers in a wide temperature range from 10 to 100 K. The SIO/SRO bilayers exhibit a remarkable TH effect, which is up to 200% larger than the anomalous Hall (AH) effect at 5 K, and zero-field TH effect at 90 K. Using variable-temperature, high-field magnetic force microscopy (MFM), we imaged skyrmions as small as 10 nm, which emerge in the same field ranges as the TH effect. These results reveal a rich space for skyrmion exploration and tunability in oxide heterostructures.

Phonon Magnetochiral Effect

The magnetochiral effect (MCE) of phonons, a nonreciprocal acoustic propagation arising due to symmetry principles, is demonstrated in the chiral-lattice ferrimagnet Cu_{2}OSeO_{3}. Our high-resolution ultrasound experiments reveal that the sound velocity differs for parallel and antiparallel propagation with respect to the external magnetic field. The sign of the nonreciprocity depends on the chirality of the crystal in accordance with the selection rule of the MCE. The nonreciprocity is enhanced below the magnetic ordering temperature and at higher ultrasound frequencies, which is quantitatively explained by a proposed magnon-phonon hybridization mechanism.

Note: Derivative divide, a method for the analysis of broadband ferromagnetic resonance in the frequency domain

Broadband ferromagnetic resonance (bbFMR) spectroscopy is an established experimental tool to quantify magnetic properties. Due to frequency-dependent transmission of the microwave setup, bbFMR measurements in the frequency domain require a suitable background removal method. Here, we present a measurement and data analysis protocol that allows us to perform quantitative frequency-swept bbFMR measurements without the need for a calibration of the microwave setup. We furthermore compare the results of the proposed frequency space analysis and a conventional analysis in field-space of bbFMR data obtained from a permalloy thin film. The very good agreement of the extracted parameters using the two methods shows the reliability of our method.

Tunable surface configuration of skyrmion lattices in cubic helimagnets

In bulk helimagnets, the presence of magnetic skyrmion lattices is always accompanied by a periodic stress field due to the intrinsic magnetoelastic coupling. The release of this nontrivial stress field at the surface causes a periodic displacement field, which characterizes a novel particle-like property of skyrmion: its surface configuration. Here, we derive the analytical solution of this displacement field for semi-infinite cubic helimagnet with the skyrmion magnetization approximated by the triple-Q representation. For MnSi, we show that the skyrmion lattices have a bumpy surface configuration characterized by periodically arranged peaks with a characteristic height of about 10^-13 m. The pattern of the peaks can be controlled by varying the strength of the applied magnetic field. Moreover, we prove that the surface configuration varies together with the motion and deformation of the skyrmion lattices. As a result, the surface configuration can be tuned by application of electric current, mechanical loads, as well as any other effective external fields for skyrmion lattices.

Skyrmions Driven by Intrinsic Magnons

We study the dynamics of a Skyrmion in a magnetic insulating nanowire in the presence of time-dependent oscillating magnetic field gradients. These ac fields act as a net driving force on the Skyrmion via its own intrinsic magnetic excitations. In a microscopic quantum field theory approach, we include the unavoidable coupling of the external field to the magnons, which gives rise to time-dependent dissipation for the Skyrmion. We demonstrate that the magnetic ac field induces a super-Ohmic to Ohmic crossover behavior for the Skyrmion dissipation kernels with time-dependent Ohmic terms. The ac driving of the magnon bath at resonance results in a unidirectional helical propagation of the Skyrmion in addition to the otherwise periodic bounded motion.

Direct Observation of Twisted Surface skyrmions in Bulk Crystals

Magnetic skyrmions in noncentrosymmetric helimagnets with D_{n} symmetry are Bloch-type magnetization swirls with a helicity angle of ±90°. At the surface of helimagnetic thin films below a critical thickness, a twisted skyrmion state with an arbitrary helicity angle has been proposed; however, its direct experimental observation has remained elusive. Here, we show that circularly polarized resonant elastic x-ray scattering is able to unambiguously measure the helicity angle of surface skyrmions, providing direct experimental evidence that a twisted skyrmion surface state also exists in bulk systems. The exact surface helicity angles of twisted skyrmions for both left- and right-handed chiral bulk Cu_{2}OSeO_{3}, in the single as well as in the multidomain skyrmion lattice state, are determined, revealing their detailed internal structure. Our findings suggest that a skyrmion surface reconstruction is a universal phenomenon, stemming from the breaking of translational symmetry at the interface.

Laser-Induced Skyrmion Writing and Erasing in an Ultrafast Cryo-Lorentz Transmission Electron Microscope

We demonstrate that light-induced heat pulses of different duration and energy can write Skyrmions in a broad range of temperatures and magnetic field in FeGe. Using a combination of camera-rate and pump-probe cryo-Lorentz transmission electron microscopy, we directly resolve the spatiotemporal evolution of the magnetization ensuing optical excitation. The Skyrmion lattice was found to maintain its structural properties during the laser-induced demagnetization, and its recovery to the initial state happened in the sub-μs to μs range, depending on the cooling rate of the system.

Helimagnon Resonances in an Intrinsic Chiral Magnonic Crystal

We experimentally study magnetic resonances in the helical and conical magnetic phases of the chiral magnetic insulator Cu_{2}OSeO_{3} at the temperature T=5  K. Using a broadband microwave spectroscopy technique based on vector network analysis, we identify three distinct sets of helimagnon resonances in the frequency range 2  GHz≤f≤20  GHz with low magnetic damping α≤0.003. The extracted resonance frequencies are in accordance with calculations of the helimagnon band structure found in an intrinsic chiral magnonic crystal. The periodic modulation of the equilibrium spin direction that leads to the formation of the magnonic crystal is a direct consequence of the chiral magnetic ordering caused by the Dzyaloshinskii-Moriya interaction. The mode coupling in the magnonic crystal allows excitation of helimagnons with wave vectors that are multiples of the spiral wave vector.

Inertia-driven resonant excitation of a magnetic skyrmion

Topological spin structures such as magnetic domain walls, vortices, and skyrmions, have been receiving great interest because of their high potential application in various spintronic devices. To utilize them in the future spintronic devices, it is first necessary to understand the dynamics of the topological spin structures. Since inertial effect plays a crucial role in the dynamics of a particle, understanding the inertial effect of topological spin structures is an important task. Here, we report that a strong inertial effect appears steadily when a skyrmion is driven by an oscillating spin-Hall-spin-torque (SHST). We find that the skyrmion exhibits an inertia-driven hypocycloid-type trajectory when it is excited by the oscillating SHST. This motion has not been achieved by an oscillating magnetic field, which only excites the breathing mode without the inertial effect. The distinct inertial effect can be explained in terms of a spin wave excitation in the skyrmion boundary which is induced by the non-uniform SHST. Furthermore, the inertia-driven resonant excitation provides a way of experimentally estimating the inertial mass of the skyrmion. Our results therefore pave the way for the development of skyrmion-based device applications.

Magnetic Skyrmions and Skyrmion Clusters in the Helical Phase of Cu_{2}OSeO_{3}

Skyrmions are nanometric spin whirls that can be stabilized in magnets lacking inversion symmetry. The properties of isolated Skyrmions embedded in a ferromagnetic background have been intensively studied. We show that single Skyrmions and clusters of Skyrmions can also form in the helical phase and investigate theoretically their energetics and dynamics. The helical background provides natural one-dimensional channels along which a Skyrmion can move rapidly. In contrast to Skyrmions in ferromagnets, the Skyrmion-Skyrmion interaction has a strong attractive component and thus Skyrmions tend to form clusters with characteristic shapes. These clusters are directly observed in transmission electron microscopy measurements in thin films of Cu_{2}OSeO_{3}. Topological quantization, high mobility, and the confinement of Skyrmions in channels provided by the helical background may be useful for future spintronics devices.

Nonlinear Ultrafast Spin Scattering in the Skyrmion Phase of Cu_{2}OSeO_{3}

Ultrafast x-ray scattering studies of the topological Skyrmion phase in Cu_{2}OSeO_{3} show the dynamics to be strongly dependent on the excitation energy and fluence. At high photon energies, where the electron-spin scattering cross section is relatively high, the excitation of the topological Skyrmion phase shows a nonlinear dependence on the excitation fluence, in contrast to the excitation of the conical phase which is linearly dependent on the excitation fluence. The excitation of the Skyrmion order parameter is nonlinear in the magnetic excitation resulting from scattering during electron-hole recombination, indicating different dominant scattering processes in the conical and Skyrmion phases.

Nanosecond X-Ray Photon Correlation Spectroscopy on Magnetic Skyrmions

We report an x-ray photon correlation spectroscopy method that exploits the recent development of the two-pulse mode at the Linac Coherent Light Source. By using coherent resonant x-ray magnetic scattering, we studied spontaneous fluctuations on nanosecond time scales in thin films of multilayered Fe/Gd that exhibit ordered stripe and Skyrmion lattice phases. The correlation time of the fluctuations was found to differ between the Skyrmion phase and near the stripe-Skyrmion boundary. This technique will enable a significant new area of research on the study of equilibrium fluctuations in condensed matter.

Linearly polarized GHz magnetization dynamics of spin helix modes in the ferrimagnetic insulator Cu2OSeO3

Linear dichroism - the polarization dependent absorption of electromagnetic waves- is routinely exploited in applications as diverse as structure determination of DNA or polarization filters in optical technologies. Here filamentary absorbers with a large length-to-width ratio are a prerequisite. For magnetization dynamics in the few GHz frequency regime strictly linear dichroism was not observed for more than eight decades. Here, we show that the bulk chiral magnet Cu₂OSeO₃ exhibits linearly polarized magnetization dynamics at an unexpectedly small frequency of about 2 GHz at zero magnetic field. Unlike optical filters that are assembled from filamentary absorbers, the magnet is shown to provide linear polarization as a bulk material for an extremely wide range of length-to-width ratios. In addition, the polarization plane of a given mode can be switched by 90° via a small variation in width. Our findings shed a new light on magnetization dynamics in that ferrimagnetic ordering combined with antisymmetric exchange interaction offers strictly linear polarization and cross-polarized modes for a broad spectrum of sample shapes at zero field. The discovery allows for novel design rules and optimization of microwave-to-magnon transduction in emerging microwave technologies.

Observation of Various and Spontaneous Magnetic Skyrmionic Bubbles at Room Temperature in a Frustrated Kagome Magnet with Uniaxial Magnetic Anisotropy

The quest for materials hosting topologically protected skyrmionic spin textures continues to be fueled by the promise of novel devices. Although many materials have demonstrated the existence of such spin textures, major challenges remain to be addressed before devices based on magnetic skyrmions can be realized. For example, being able to create and manipulate skyrmionic spin textures at room temperature is of great importance for further technological applications because they can adapt to various external stimuli acting as information carriers in spintronic devices. Here, the first observation of skyrmionic magnetic bubbles with variable topological spin textures formed at room temperature in a frustrated kagome Fe₃ Sn₂ magnet with uniaxial magnetic anisotropy is reported. The magnetization dynamics are investigated using in situ Lorentz transmission electron microscopy, revealing that the transformation between different magnetic bubbles and domains is via the motion of Bloch lines driven by an applied external magnetic field. These results demonstrate that Fe₃ Sn₂ facilitates a unique magnetic control of topological spin textures at room temperature, making it a promising candidate for further skyrmion-based spintronic devices.

Noncentrosymmetric Magnets Hosting Magnetic Skyrmions

The concept of a skyrmion, which was first introduced by Tony Skyrme in the field of particle physics, has become widespread in condensed matter physics to describe various topological orders. Skyrmions in magnetic materials have recently received particular attention; they represent vortex-like spin structures with the character of nanometric particles and produce fascinating physical properties rooted in their topological nature. Here, a series of noncentrosymmetric ferromagnets hosting skyrmions is reviewed: B20 metals, Cu₂ OSeO₃ , Co-Zn-Mn alloys, and GaV₄ S₈ , where Dzyaloshinskii-Moriya interaction plays a key role in the stabilization of skyrmion spin texture. Their topological spin arrangements and consequent emergent electromagnetic fields give rise to striking features in transport and magnetoelectric properties in metals and insulators, such as the topological Hall effect, efficient electric-drive of skyrmions, and multiferroic behavior. Such electric controllability and nanometric particle natures highlight magnetic skyrmions as a potential information carrier for high-density magnetic storage devices with excellent energy efficiency.

Antiferromagnetic spin cantings as a driving force of ferroelectricity in multiferroic Cu2OSeO3

Ferroelectric properties of cubic chiral magnet Cu₂OSeO₃ can emerge due to the spin noncollinearity induced by antiferromagnetic cantings. The cantings are the result of the Dzyaloshinskii-Moriya interaction and in many ways similar to the ferromagnetic cantings in weak ferromagnets. An expression for the local electric polarization is derived, including terms with gradients of magnetization [Formula: see text]. When averaged over the crystal the electric polarization has a non-vanishing part associated with the anisotropy of the crystal point group 23. In the framework of the microscopic theory, it is shown that both scalar and vector products of spins, [Formula: see text] and [Formula: see text], can give contributions of the same order of magnitude into the electric polarization.

Interfacial Dzyaloshinskii-Moriya Interaction in Pt/CoFeB Films: Effect of the Heavy-Metal Thickness

We report the observation of a Pt layer thickness dependence on the induced interfacial Dzyaloshinskii-Moriya interaction in ultrathin Pt(d_{Pt})/CoFeB films. Taking advantage of the large spin-orbit coupling of the heavy metal, the interfacial Dzyaloshinskii-Moriya interaction is quantified by Brillouin light scattering measurements of the frequency nonreciprocity of spin waves in the ferromagnet. The magnitude of the induced Dzyaloshinskii-Moriya coupling is found to saturate to a value of 0.45  mJ/m^{2} for Pt thicknesses larger than ∼2  nm. The experimental results are explained by analytical calculations based on the three-site indirect exchange mechanism that predicts a Dzyaloshinskii-Moriya interaction at the interface between a ferromagnetic thin layer and a heavy metal. Our findings open up a way to control and optimize chiral effects in ferromagnetic thin films through the thickness of the heavy-metal layer.