Thermal skyrmion diffusion used in a reshuffler device

Fundamental theory of current-induced motion of magnetic skyrmions

Magnetic skyrmions are topological spin textures that appear in magnets with broken spatial inversion symmetry as a consequence of competition between the (anti)ferromagnetic exchange interactions and the Dzyaloshinskii-Moriya interactions in a magnetic field. In the research of spintronics, the current-driven dynamics of skyrmions has been extensively studied aiming at their applications to next-generation spintronic devices. However, current-induced skyrmion motion exhibits diverse behaviors depending on various factors and conditions such as the type of skyrmion, driving mechanism, system geometry, direction of applied current, and type of the magnet. While this variety attracts enormous research interest of fundamental science and enriches their possibilities of technical applications, it is, at the same time, a source of difficulty and complexity that hinders their comprehensive understandings. In this article, we discuss fundamental and systematic theoretical descriptions of current-induced motion of skyrmions driven by the spin-transfer torque and the spin-orbit torque. Specifically, we theoretically describe the behaviors of current-driven skyrmions depending on the factors and conditions mentioned above by means of analyses using the Thiele equation. Furthermore, the results of the analytical theory are visually demonstrated and quantitatively confirmed by micromagnetic simulations using the Landau-Lifshitz-Gilbert-Slonczewski equation. In particular, we discuss dependence of the direction and velocity of motion on the type of skyrmion (Bloch type and Néel type) and its helicity, the system geometry (thin plate and nanotrack), the direction of applied current (length and width direction of the nanotrack) and its spin-polarization orientation, and the type of magnet (ferromagnet and antiferromagnet). The comprehensive theory provided by this article is expected to contribute significantly to research on the manipulation and control of magnetic skyrmions by electric currents for future spintronics applications.

Rolling Motion of Rigid Skyrmion Crystallites Induced by Chiral Lattice Torque

Magnetic skyrmions are topologically protected spin textures with emergent particle-like behaviors. Their dynamics under external stimuli is of great interest and importance for topological physics and spintronics applications alike. So far, skyrmions are only found to move linearly in response to a linear drive, following the conventional model treating them as isolated quasiparticles. Here, by performing time and spatially resolved resonant elastic X-ray scattering of the insulating chiral magnet Cu2OSeO3, we show that for finite-sized skyrmion crystallites, a purely linear temperature gradient not only propels the skyrmions but also induces continuous rotational motion through a chiral lattice torque. Consequently, a skyrmion crystallite undergoes a rolling motion under a small gradient, while both the rolling speed and the rotational sense can be controlled. Our findings offer a new degree of freedom for manipulating these quasiparticles toward device applications and underscore the fundamental phase difference between the condensed skyrmion lattice and isolated skyrmions.

Imaging magnetic spiral phases, skyrmion clusters, and skyrmion displacements at the surface of bulk Cu2OSeO3

Surfaces - by breaking bulk symmetries, introducing roughness, or hosting defects - can significantly influence magnetic order in magnetic materials. Determining their effect on the complex nanometer-scale phases present in certain non-centrosymmetric magnets is an outstanding problem requiring high-resolution magnetic microscopy. Here, we use scanning SQUID microscopy to image the surface of bulk Cu2OSeO3 at low temperature and in a magnetic field applied along100 . Real-space maps measured as a function of applied field reveal the microscopic structure of the magnetic phases and their transitions. In low applied field, we observe a magnetic texture consistent with an in-plane stripe phase, pointing to the existence of a distinct surface state. In the low-temperature skyrmion phase, the surface is populated by clusters of disordered skyrmions, which emerge from rupturing domains of the tilted spiral phase. Furthermore, we displace individual skyrmions from their pinning sites by applying an electric potential to the scanning probe, thereby demonstrating local skyrmion control at the surface of a magnetoelectric insulator.

Confined antiskyrmion motion driven by electric current excitations

Current-driven dynamics of topological spin textures, such as skyrmions and antiskyrmions, have garnered considerable attention in condensed matter physics and spintronics. As compared with skyrmions, the current-driven dynamics of their antiparticles - antiskyrmions - remain less explored due to the increased complexity of antiskyrmions. Here, we design and employ fabricated microdevices of a prototypical antiskyrmion host, (Fe0.63Ni0.3Pd0.07)3P, to allow in situ current application with Lorentz transmission electron microscopy observations. The experimental results and related micromagnetic simulations demonstrate current-driven antiskyrmion dynamics confined within stripe domains. Under nanosecond-long current pulses, antiskyrmions exhibit directional motion along the stripe regardless of the current direction, while the antiskyrmion velocity is linearly proportional to the current density. Significantly, the antiskyrmion mobility could be enhanced when the current flow is perpendicular to the stripe direction. Our findings provide novel and reliable insights on dynamical antiskyrmions and their potential implications on spintronics.

Realization of skyrmion shift register

The big data explosion demands novel data storage technology. Among many different approaches, solitonic racetrack memory devices hold great promise for accommodating nonvolatile and low-power functionalities. As representative topological solitons, magnetic skyrmions are envisioned as potential information carriers for efficient information processing. While their advantages as memory and logic elements have been vastly exploited from theoretical perspectives, the corresponding experimental efforts are rather limited. These challenges, which are key to versatile skyrmionic devices, will be studied in this work. Through patterning concaved surface topography with designed arrays of indentations on standard Si/SiO2 substrates, we demonstrate that the resultant non-flat energy landscape could lead to the formation of hexagonal and square skyrmion lattices in Ta/CoFeB/MgO multilayers. Based on these films, one-dimensional racetrack devices are subsequently fabricated, in which a long-distance deterministic shifting of skyrmions between neighboring indentations is achieved at room temperature. Through separating the word line and the bit line, a prototype shift register device, which can sequentially generate and precisely shift complex skyrmionic data strings, is presented. The deterministic writing and long-distance shifting of skyrmionic bits can find potential applications in transformative skyrmionic memory, logic as well as the in-memory computing devices.

Influence of the Hall-bar geometry on texture-induced topological spin transport in two-dimensional Rashba spin-orbit ferromagnets

While the recent prediction and observation of magnetic skyrmions bears inspiring promise for next-generation spintronic devices, how to detect and track their position becomes an important issue. In this work, we investigate the spin transport in a two-dimensional magnetic nanoribbon with the Hall-bar geometry in the presence of Rashba spin-orbit coupling and magnetic skyrmions. We employ the Kwant tight-binding code to compute the Hall conductance and local spin-polarized current density. We consider two versions of the model: One with single skyrmion and one with two separate skyrmions. It is found that the size and position of the skyrmions strongly modulate the Hall conductance near the Hall-bar position. The geometry of the Hall bar also has a strong influence on the Hall conductance of the system. With the decreasing of the width of Hall leads, the peak of Hall conductance becomes sharper. We also show the spatial distribution of the spin-polarized current density around a skyrmion located at different positions. We extend this study toward two separate skyrmions, where the Hall conductance also reveals a sizable dependence on the position of the skyrmions and their distance. Our numerical analysis offers the possibility of electrically detecting the skyrmion position, which could have potential applications in ultrahigh-density storage design.

Topological Spin Textures: Basic Physics and Devices

In the face of escalating modern data storage demands and the constraints of Moore's Law, exploring spintronic solutions, particularly the devices based on magnetic skyrmions, has emerged as a promising frontier in scientific research. Since the first experimental observation of skyrmions, topological spin textures have been extensively studied for their great potential as efficient information carriers in spintronic devices. However, significant challenges have emerged alongside this progress. This review aims to synthesize recent advances in skyrmion research while addressing the major issues encountered in the field. Additionally, current research on promising topological spin structures in addition to skyrmions is summarized. Beyond 2D structures, exploration also extends to 1D magnetic solitons and 3D spin textures. In addition, a diverse array of emerging magnetic materials is introduced, including antiferromagnets and 2D van der Waals magnets, broadening the scope of potential materials hosting topological spin textures. Through a systematic examination of magnetic principles, topological categorization, and the dynamics of spin textures, a comprehensive overview of experimental and theoretical advances in the research of topological magnetism is provided. Finally, both conventional and unconventional applications are summarized based on spin textures proposed thus far. This review provides an outlook on future development in applied spintronics.

Bending skyrmion strings under two-dimensional thermal gradients

Magnetic skyrmions are topologically protected magnetization vortices that form three-dimensional strings in chiral magnets. With the manipulation of skyrmions being key to their application in devices, the focus has been on their dynamics within the vortex plane, while the dynamical control of skyrmion strings remained uncharted territory. Here, we report the effective bending of three-dimensional skyrmion strings in the chiral magnet MnSi in orthogonal thermal gradients using small angle neutron scattering. This dynamical behavior is achieved by exploiting the temperature-dependent skyrmion Hall effect, which is unexpected in the framework of skyrmion dynamics. We thus provide experimental evidence for the existence of magnon friction, which was recently proposed to be a key ingredient for capturing skyrmion dynamics, requiring a modification of Thiele's equation. Our work therefore suggests the existence of an extra degree of freedom for the manipulation of three-dimensional skyrmions.

Demonstration of Controlled Skyrmion Injection Across a Thickness Step

Spintronic devices incorporating magnetic skyrmions have attracted significant interest recently. Such devices traditionally focus on controlling magnetic textures in 2D thin films. However, enhanced performance of spintronic properties through the exploitation of higher dimensionalities motivates the investigation of variable-thickness skyrmion devices. We report the demonstration of a skyrmion injection mechanism that utilizes charge currents to drive skyrmions across a thickness step and, consequently, a metastability barrier. Our measurements show that under certain temperature and field conditions skyrmions can be reversibly injected from a thin region of an FeGe lamella, where they exist as an equilibrium state, into a thicker region, where they can only persist as a metastable state. This injection is achieved with a current density of 3 × 108 A m-2, nearly 3 orders of magnitude lower than required to move magnetic domain walls. This highlights the possibility to use such an element as a skyrmion source/drain within future spintronic devices.

Brownian Electric Bubble Quasiparticles

Recent works on electric bubbles (including the experimental demonstration of electric skyrmions) constitute a breakthrough akin to the discovery of magnetic skyrmions some 15 years ago. So far research has focused on obtaining and visualizing these objects, which often appear to be immobile (pinned) in experiments. Thus, critical aspects of magnetic skyrmions-e.g., their quasiparticle nature, Brownian motion-remain unexplored (unproven) for electric bubbles. Here we use predictive atomistic simulations to investigate the basic dynamical properties of these objects in pinning-free model systems. We show that it is possible to find regimes where the electric bubbles can present long lifetimes (∼ns) despite being relatively small (diameter <2  nm). Additionally, we find that they can display stochastic dynamics with large and highly tunable diffusion constants. We thus establish the quasiparticle nature of electric bubbles and put them forward for the physical effects and applications (e.g., in token-based probabilistic computing) considered for magnetic skyrmions.

Homochiral antiferromagnetic merons, antimerons and bimerons realized in synthetic antiferromagnets

The ever-growing demand for device miniaturization and energy efficiency in data storage and computing technology has prompted a shift towards antiferromagnetic topological spin textures as information carriers. This shift is primarily owing to their negligible stray fields, leading to higher possible device density and potentially ultrafast dynamics. We realize in this work such chiral in-plane topological antiferromagnetic spin textures namely merons, antimerons, and bimerons in synthetic antiferromagnets by concurrently engineering the effective perpendicular magnetic anisotropy, the interlayer exchange coupling, and the magnetic compensation ratio. We demonstrate multimodal vector imaging of the three-dimensional Néel order parameter, revealing the topology of those spin textures and a globally well-defined chirality, which is a crucial requirement for controlled current-induced dynamics. Our analysis reveals that the interplay between interlayer exchange and interlayer magnetic dipolar interactions plays a key role to significantly reduce the critical strength of the Dzyaloshinskii-Moriya interaction required to stabilize topological spin textures, such as antiferromagnetic merons, in synthetic antiferromagnets, making them a promising platform for next-generation spintronics applications.

Acoustic-driven magnetic skyrmion motion

Magnetic skyrmions have great potential for developing novel spintronic devices. The electrical manipulation of skyrmions has mainly relied on current-induced spin-orbit torques. Recently, it was suggested that the skyrmions could be more efficiently manipulated by surface acoustic waves (SAWs), an elastic wave that can couple with magnetic moment via the magnetoelastic effect. Here, by designing on-chip piezoelectric transducers that produce propagating SAW pulses, we experimentally demonstrate the directional motion of Néel-type skyrmions in Ta/CoFeB/MgO/Ta multilayers. We find that the shear horizontal wave effectively drives the motion of skyrmions, whereas the elastic wave with longitudinal and shear vertical displacements (Rayleigh wave) cannot produce the motion of skyrmions. A longitudinal motion along the SAW propagation direction and a transverse motion due to topological charge are simultaneously observed and further confirmed by our micromagnetic simulations. This work demonstrates that acoustic waves could be another promising approach for manipulating skyrmions, which could offer new opportunities for ultra-low power skyrmionics.

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).

Reconfigurable Neuromorphic Computing: Materials, Devices, and Integration

Neuromorphic computing has been attracting ever-increasing attention due to superior energy efficiency, with great promise to promote the next wave of artificial general intelligence in the post-Moore era. Current approaches are, however, broadly designed for stationary and unitary assignments, thus encountering reluctant interconnections, power consumption, and data-intensive computing in that domain. Reconfigurable neuromorphic computing, an on-demand paradigm inspired by the inherent programmability of brain, can maximally reallocate finite resources to perform the proliferation of reproducibly brain-inspired functions, highlighting a disruptive framework for bridging the gap between different primitives. Although relevant research has flourished in diverse materials and devices with novel mechanisms and architectures, a precise overview remains blank and urgently desirable. Herein, the recent strides along this pursuit are systematically reviewed from material, device, and integration perspectives. At the material and device level, one comprehensively conclude the dominant mechanisms for reconfigurability, categorized into ion migration, carrier migration, phase transition, spintronics, and photonics. Integration-level developments for reconfigurable neuromorphic computing are also exhibited. Finally, a perspective on the future challenges for reconfigurable neuromorphic computing is discussed, definitely expanding its horizon for scientific communities.

All-Electrical 9-Bit Skyrmion-Based Racetrack Memory Designed with Laser Irradiation

Racetrack memories with magnetic skyrmions have recently been proposed as a promising storage technology. To be appealing, several challenges must still be faced for the deterministic generation of skyrmions, their high-fidelity transfer, and accurate reading. Here, we realize the first proof-of-concept of a 9-bit skyrmion racetrack memory with all-electrical controllable functionalities implemented in the same device. The key ingredient is the generation of a tailored nonuniform distribution of magnetic anisotropy via laser irradiation in order to (i) create a well-defined skyrmion nucleation center, (ii) define the memory cells hosting the information coded as the presence/absence of skyrmions, and (iii) improve the signal-to-noise ratio of anomalous Hall resistance measurements. This work introduces a strategy to unify previous findings and predictions for the development of a generation of racetrack memories with robust control of skyrmion nucleation and position, as well as effective skyrmion electrical detection.

Electrically programmable magnetic coupling in an Ising network exploiting solid-state ionic gating

Two-dimensional arrays of magnetically coupled nanomagnets provide a mesoscopic platform for exploring collective phenomena as well as realizing a broad range of spintronic devices. In particular, the magnetic coupling plays a critical role in determining the nature of the cooperative behavior and providing new functionalities in nanomagnet-based devices. Here, we create coupled Ising-like nanomagnets in which the coupling between adjacent nanomagnetic regions can be reversibly converted between parallel and antiparallel through solid-state ionic gating. This is achieved with the voltage-control of the magnetic anisotropy in a nanosized region where the symmetric exchange interaction favors parallel alignment and the antisymmetric exchange interaction, namely the Dzyaloshinskii-Moriya interaction, favors antiparallel alignment of the nanomagnet magnetizations. Applying this concept to a two-dimensional lattice, we demonstrate a voltage-controlled phase transition in artificial spin ices. Furthermore, we achieve an addressable control of the individual couplings and realize an electrically programmable Ising network, which opens up new avenues to design nanomagnet-based logic devices and neuromorphic computers.

Survival of skyrmions along granular racetracks at room temperature

Skyrmions can be envisioned as bits of information that can be transported along nanoracetracks. However, temperature, defects, and/or granularity can produce diffusion, pinning, and, in general, modification in their dynamics. These effects may cause undesired errors in information transport. We present simulations of a realistic system where both the (room) temperature and sample granularity are taken into account. Key feasibility magnitudes, such as the success probability of a skyrmion traveling a given distance along the racetrack, are calculated. The results are evaluated in terms of the eventual loss of skyrmions by pinning, destruction at the edges, or excessive delay due to granularity. The model proposed is based on the Fokker-Planck equation resulting from Thiele's rigid model for skyrmions. The results could serve to establish error detection criteria and, in general, to discern the dynamics of skyrmions in realistic situations.

Enhanced thermally-activated skyrmion diffusion with tunable effective gyrotropic force

Magnetic skyrmions, topologically-stabilized spin textures that emerge in magnetic systems, have garnered considerable interest due to a variety of electromagnetic responses that are governed by the topology. The topology that creates a microscopic gyrotropic force also causes detrimental effects, such as the skyrmion Hall effect, which is a well-studied phenomenon highlighting the influence of topology on the deterministic dynamics and drift motion. Furthermore, the gyrotropic force is anticipated to have a substantial impact on stochastic diffusive motion; however, the predicted repercussions have yet to be demonstrated, even qualitatively. Here we demonstrate enhanced thermally-activated diffusive motion of skyrmions in a specifically designed synthetic antiferromagnet. Suppressing the effective gyrotropic force by tuning the angular momentum compensation leads to a more than 10 times enhanced diffusion coefficient compared to that of ferromagnetic skyrmions. Consequently, our findings not only demonstrate the gyro-force dependence of the diffusion coefficient but also enable ultimately energy-efficient unconventional stochastic computing.

Instability of Magnetic Skyrmion Strings Induced by Longitudinal Spin Currents

It is well established that spin-transfer torques exerted by in-plane spin currents give rise to a motion of magnetic skyrmions resulting in a skyrmion Hall effect. In films of finite thickness or in three-dimensional bulk samples the skyrmions extend in the third direction forming a string. We demonstrate that a spin current flowing longitudinally along the skyrmion string instead induces a Goldstone spin wave instability. Our analytical results are confirmed by micromagnetic simulations of both a single string as well as string lattices, suggesting that the instability eventually breaks the strings. A longitudinal current is thus able to melt the skyrmion string lattice via a nonequilibrium phase transition. For films of finite thickness or in the presence of disorder a threshold current will be required, and we estimate the latter assuming weak collective pinning.

Ordering of room-temperature magnetic skyrmions in a polar van der Waals magnet

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications.

Experimental demonstration of a skyrmion-enhanced strain-mediated physical reservoir computing system

Physical reservoirs holding intrinsic nonlinearity, high dimensionality, and memory effects have attracted considerable interest regarding solving complex tasks efficiently. Particularly, spintronic and strain-mediated electronic physical reservoirs are appealing due to their high speed, multi-parameter fusion and low power consumption. Here, we experimentally realize a skyrmion-enhanced strain-mediated physical reservoir in a multiferroic heterostructure of Pt/Co/Gd multilayers on (001)-oriented 0.7PbMg1/3Nb2/3O3-0.3PbTiO3 (PMN-PT). The enhancement is coming from the fusion of magnetic skyrmions and electro resistivity tuned by strain simultaneously. The functionality of the strain-mediated RC system is successfully achieved via a sequential waveform classification task with the recognition rate of 99.3% for the last waveform, and a Mackey-Glass time series prediction task with normalized root mean square error (NRMSE) of 0.2 for a 20-step prediction. Our work lays the foundations for low-power neuromorphic computing systems with magneto-electro-ferroelastic tunability, representing a further step towards developing future strain-mediated spintronic applications.

Solid-State Lithium Ion Supercapacitor for Voltage Control of Skyrmions

Ionic control of magnetism gives rise to high magnetoelectric coupling efficiencies at low voltages, which is essential for low-power magnetism-based nonconventional computing technologies. However, for on-chip applications, magnetoionic devices typically suffer from slow kinetics, poor cyclability, impractical liquid architectures, or strong ambient effects. As a route to overcoming these problems, we demonstrate a LiPON-based solid-state ionic supercapacitor with a magnetic Pt/Co₄₀Fe₄₀B₂₀/Pt thin-film electrode which enables voltage control of a magnetic skyrmion state. Skyrmion nucleation and annihilation are caused by Li ion accumulation and depletion at the magnetic interface under an applied voltage. The skyrmion density can be controlled through dc applied voltages or through voltage pulses. The skyrmions are nucleated by single 60 μs voltage pulses, and devices are cycled 750000 times without loss of electrical performance. Our results demonstrate a simple and robust approach to ionic control of magnetism in spin-based devices.

300-Times-Increased Diffusive Skyrmion Dynamics and Effective Pinning Reduction by Periodic Field Excitation

Thermally induced skyrmion dynamics, as well as skyrmion pinning effects, in thin films have attracted significant interest. While pinning poses challenges in deterministic skyrmion devices and slows down skyrmion diffusion, for applications in non-conventional computing, both pinning of an appropriate strength and skyrmion diffusion speed are key. Here, periodic field excitations are employed to realize an increase of the skyrmion diffusion by more than two orders of magnitude. Amplifying the excitation, a drastic reduction of the effective skyrmion pinning, is reported, and a transition from pinning-dominated diffusive hopping to dynamics approaching free diffusion is observed. By tailoring the field oscillation frequency and amplitude, a continuous tuning of the effective pinning and skyrmion dynamics is demonstrated, which is a key asset and enabler for non-conventional computing applications. It is found that the periodic excitations additionally allow stabilization of skyrmions at different sizes for field values that are inaccessible in static systems, opening up new approaches to ultrafast skyrmion motion by transiently exciting moving skyrmions.

Skyrmion Fluid and Bimeron Glass Protected by a Chiral Spin Liquid on a Kagome Lattice

Skyrmions are of interest both from a fundamental and technological point of view, due to their potential to act as information carriers. But one challenge concerns their manipulation, especially at high temperature where thermal fluctuations eventually disintegrate them. Here we study the competition between skyrmions and a chiral spin liquid, using the latter as an entropic buffer to impose a quasivacuum of skyrmions. As a result, the temperature becomes a knob to tune the skyrmion density from a dense liquid to a diluted gas, protecting the integrity of each skyrmion from paramagnetic disintegration. With this additional knob in hand, we find at high field a topological spin glass made of zero- and one-dimensional topological defects (respectively skyrmions and bimerons).

Magnetic Skyrmion Transistor Gated with Voltage-Controlled Magnetic Anisotropy

The paradigm shift of information carriers from charge to spin has long been awaited in modern electronics. The invention of the spin-information transistor is expected to be an essential building block for the future development of spintronics. Here, a proof-of-concept experiment of a magnetic skyrmion transistor working at room temperature, which has never been demonstrated experimentally, is introduced. With the spatially uniform control of magnetic anisotropy, the shape and topology of a skyrmion when passing the controlled area can be maintained. The findings will open a new route toward the design and realization of skyrmion-based spintronic devices in the near future.

Magnon scattering modulated by omnidirectional hopfion motion in antiferromagnets for meta-learning

Neuromorphic computing is expected to achieve human-brain performance by reproducing the structure of biological neural systems. However, previous neuromorphic designs based on synapse devices are all unsatisfying for their hardwired network structure and limited connection density, far from their biological counterpart, which has high connection density and the ability of meta-learning. Here, we propose a neural network based on magnon scattering modulated by an omnidirectional mobile hopfion in antiferromagnets. The states of neurons are encoded in the frequency distribution of magnons, and the connections between them are related to the frequency dependence of magnon scattering. Last, by controlling the hopfion's state, we can modulate hyperparameters in our network and realize the first meta-learning device that is verified to be well functioning. It not only breaks the connection density bottleneck but also provides a guideline for future designs of neuromorphic devices.

The PERCIVAL detector: first user experiments

The PERCIVAL detector is a CMOS imager designed for the soft X-ray regime at photon sources. Although still in its final development phase, it has recently seen its first user experiments: ptychography at a free-electron laser, holographic imaging at a storage ring and preliminary tests on X-ray photon correlation spectroscopy. The detector performed remarkably well in terms of spatial resolution achievable in the sample plane, owing to its small pixel size, large active area and very large dynamic range; but also in terms of its frame rate, which is significantly faster than traditional CCDs. In particular, it is the combination of these features which makes PERCIVAL an attractive option for soft X-ray science.

Coherent correlation imaging for resolving fluctuating states of matter

Fluctuations and stochastic transitions are ubiquitous in nanometre-scale systems, especially in the presence of disorder. However, their direct observation has so far been impeded by a seemingly fundamental, signal-limited compromise between spatial and temporal resolution. Here we develop coherent correlation imaging (CCI) to overcome this dilemma. Our method begins by classifying recorded camera frames in Fourier space. Contrast and spatial resolution emerge by averaging selectively over same-state frames. Temporal resolution down to the acquisition time of a single frame arises independently from an exceptionally low misclassification rate, which we achieve by combining a correlation-based similarity metric^1,2 with a modified, iterative hierarchical clustering algorithm^3,4. We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state with nanometre-scale resolution. We uncover an intricate network of transitions between more than 30 discrete states. Our spatiotemporal data enable us to reconstruct the pinning energy landscape and to thereby explain the dynamics observed on a microscopic level. CCI massively expands the potential of emerging high-coherence X-ray sources and paves the way for addressing large fundamental questions such as the contribution of pinning^5-8 and topology^9-12 in phase transitions and the role of spin and charge order fluctuations in high-temperature superconductivity^13,14.

Experimental Realization of a Skyrmion Circulator

Magnetic skyrmions are mobile topological spin textures that can be manipulated by different means. Their applications have been frequently discussed in the context of information carriers for racetrack memory devices, which on the other hand, exhibit a skyrmion Hall effect as a result of the nontrivial real-space topology. While the skyrmion Hall effect is believed to be detrimental for constructing racetrack devices, we show here that it can be implemented for realizing a three-terminal skyrmion circulator. In analogy to the microwave circulator, nonreciprocal transportation and circulation of skyrmions are studied both numerically and experimentally. In particular, successful control of the circulating direction of being either clockwise or counterclockwise is demonstrated, simply by changing the sign of the topological charge. Our studies suggest that the topological property of skyrmions can be incorporated for enabling novel spintronic functionalities; the skyrmion circulator is just one example.

Micromagnetic Design of Skyrmionic Materials and Chiral Magnetic Configurations in Patterned Nanostructures for Neuromorphic and Qubit Applications

Our study addresses the problematics of magnetic skyrmions, nanometer-size vortex-like swirling topological defects, broadly studied today for applications in classic, neuromorphic and quantum information technologies. We tackle some challenging issues of material properties versus skyrmion stability and manipulation within a multiple-scale modeling framework, involving complementary ab-initio and micromagnetic frameworks. Ab-initio calculations provide insight into the anatomy of the magnetic anisotropy, the Dzyaloshinskii-Moriya asymmetric exchange interaction (DMI) and their response to a gating electric field. Various multi-layered heterostructures were specially designed to provide electric field tunable perpendicular magnetization and sizeable DMI, which are required for skyrmion occurrence. Landau-Lifshitz-Gilbert micromagnetic calculations in nanometric disks allowed the extraction of material parameter phase diagrams in which magnetic textures were classified according to their topological charge. We identified suitable ranges of magnetic anisotropy, DMI and saturation magnetization for stabilizing skyrmionic ground states or writing/manipulating them using either a spin-transfer torque of a perpendicular current or the electric field. From analyzing the different contributions to the total magnetic free energy, we point out some critical properties influencing the skyrmions' stability. Finally, we discuss some experimental issues related to the choice of materials or the design of novel magnetic materials compatible with skyrmionic applications.

Brownian reservoir computing realized using geometrically confined skyrmion dynamics

Reservoir computing (RC) has been considered as one of the key computational principles beyond von-Neumann computing. Magnetic skyrmions, topological particle-like spin textures in magnetic films are particularly promising for implementing RC, since they respond strongly nonlinearly to external stimuli and feature inherent multiscale dynamics. However, despite several theoretical proposals that exist for skyrmion reservoir computing, experimental realizations have been elusive until now. Here, we propose and experimentally demonstrate a conceptually new approach to skyrmion RC that leverages the thermally activated diffusive motion of skyrmions. By confining the electrically gated and thermal skyrmion motion, we find that already a single skyrmion in a confined geometry suffices to realize nonlinearly separable functions, which we demonstrate for the XOR gate along with all other Boolean logic gate operations. Besides this universality, the reservoir computing concept ensures low training costs and ultra-low power operation with current densities orders of magnitude smaller than those used in existing spintronic reservoir computing demonstrations. Our proposed concept is robust against device imperfections and can be readily extended by linking multiple confined geometries and/or by including more skyrmions in the reservoir, suggesting high potential for scalable and low-energy reservoir computing.

Simulating anti-skyrmions on a lattice

Magnetic skyrmions are meta-stable spin structures that naturally emerge in magnetic materials. While a vast amount of effort has gone into the study of their properties, their counterpart of opposite topological charge, the anti-skyrmion, has not received as much attention. We aim to close this gap by deploying Monte Carlo simulations of spin-lattice systems in order to investigate which interactions support anti-skyrmions, as well as skyrmions of Bloch and Néel type. We find that the combination of ferromagnetic exchange and Dzyaloshinskii–Moriya (DM) interactions is able to stabilize each of the three types, depending on the specific structure of the DM interactions. Considering a three-dimensional spin lattice model, we provide a finite-temperature phase diagram featuring a stable anti-skyrmion lattice phase for a large range of temperatures. In addition, we also shed light on the creation and annihilation processes of these anti-skyrmion tubes and study the effects of the DM interaction strength on their typical size.

Magnetic Field Magnitudes Needed for Skyrmion Generation in a General Perpendicularly Magnetized Film

Due to its topological protection, the magnetic skyrmion has been intensively studied for both fundamental aspects and spintronics applications. However, despite recent advancements in skyrmion research, the deterministic creation of isolated skyrmions in a generic perpendicularly magnetized film is still one of the most essential and challenging techniques. Here, we present a method to create magnetic skyrmions in typical perpendicular magnetic anisotropy (PMA) films by applying a magnetic field pulse and a method to determine the magnitude of the required external magnetic fields. Furthermore, to demonstrate the usefulness of this result for future skyrmion research, we also experimentally study the PMA dependence on the minimum size of skyrmions. Although field-driven skyrmion generation is unsuitable for device application, this result can provide an easier approach for obtaining isolated skyrmions, making skyrmion-based research more accessible.

Magnetic-Field-Assisted Diffusion Motion of Magnetic Skyrmions

Studies of the diffusion dynamics of magnetic skyrmions have generated widespread interest in both fundamental physics and spintronics applications. Here we report the magnetic-field-assisted diffusion motion of skyrmions in a microstructured chiral FeGe magnet. We demonstrate the enhancement of diffusion motion of magnetic skyrmions that is manipulated and driven by an oscillatory magnetic field. Further, the directed diffusion of skyrmions is observed when an in-plane field was introduced to break the symmetry of the system. Finally, we demonstrate the application of a magnetic field can induce an arrangements transition of skyrmions assemble in microstructure, that is, from a stiff hexagonal lattice to a weak interactional isotropic state. By using a step-ascended magnetic field we finished the observation of a particle-like diffusive motion for magnetic skyrmions that transport from high-concentration regions to low-concentration regions and the diffusion flux is proportional to the concentration gradient followed Fick's law.

Universal Hopping Motion Protected by Structural Topology

A scaling law elucidates the universality in nature, presiding over many physical phenomena which seem unrelated. Thus, exploring the universality class of scaling law in a particular system enlightens its physical nature in relevance to other systems and sometimes unearths an unprecedented new dynamic phase. Here, the dynamics of weakly driven magnetic skyrmions are investigated, and its scaling law is compared with the motion of a magnetic domain wall (DW) creep. This study finds that the skyrmion does not follow the scaling law of the DW creep in 2D space but instead shows a hopping behavior similar to that of the particle-like DW in 1D confinement. In addition, the hopping law satisfies even when a topological charge of the skyrmion is removed. Therefore, the distinct scaling behavior between the magnetic skyrmion and the DW stems from a general principle beyond the topological charge. This study demonstrates that the hopping behavior of skyrmions originates from the bottleneck process induced by DW segments with diverging collective lengths, which is inevitable in any closed-shape spin structure in 2D. This work reveals that the structural topology of magnetic texture determines the universality class of its weakly driven motion, which is distinguished from the universality class of magnetic DW creep.

Pattern recognition with neuromorphic computing using magnetic field-induced dynamics of skyrmions

Nonlinear phenomena in physical systems can be used for brain-inspired computing with low energy consumption. Response from the dynamics of a topological spin structure called skyrmion is one of the candidates for such a neuromorphic computing. However, its ability has not been well explored experimentally. Here, we experimentally demonstrate neuromorphic computing using nonlinear response originating from magnetic field-induced dynamics of skyrmions. We designed a simple-structured skyrmion-based neuromorphic device and succeeded in handwritten digit recognition with the accuracy as large as 94.7% and waveform recognition. Notably, there exists a positive correlation between the recognition accuracy and the number of skyrmions in the devices. The large degrees of freedom of skyrmion systems, such as the position and the size, originate from the more complex nonlinear mapping, the larger output dimension, and, thus, high accuracy. Our results provide a guideline for developing energy-saving and high-performance skyrmion neuromorphic computing devices.

Confinement of Skyrmions in Nanoscale FeGe Device-like Structures

Skyrmion-based devices have been proposed as a promising solution for low-energy data storage. These devices include racetrack or logic structures and require skyrmions to be confined in regions with dimensions comparable to the size of a single skyrmion. Here we examine skyrmions in FeGe device shapes using Lorentz transmission electron microscopy to reveal the consequences of skyrmion confinement in a device-like structure. Dumbbell-shaped elements were created by focused ion beam milling to provide regions where single skyrmions are confined adjacent to areas containing a skyrmion lattice. Simple block shapes of equivalent dimensions were also prepared to allow a direct comparison with skyrmion formation in a less complex, yet still confined, device geometry. The impact of applying a magnetic field and varying the temperature on the formation of skyrmions within the shapes was examined. This revealed that it is not just confinement within a small device structure that controls the position and number of skyrmions but that a complex device geometry changes the skyrmion behavior, including allowing skyrmions to form at lower applied magnetic fields than in simple shapes. The impact of edges in complex shapes is observed to be significant in changing the behavior of the magnetic textures formed. This could allow methods to be developed to control both the position and number of skyrmions within device structures.

Skyrmion Echo in a System of Interacting Skyrmions

We consider helical rotation of skyrmions confined in the potentials formed by nanodisks. Based on numerical and analytical calculations we propose the skyrmion echo phenomenon. The physical mechanism of the skyrmion echo formation is also proposed. Because of the distortion of the lattice, impurities, or pinning effect, confined skyrmions experience slightly different local fields, which leads to dephasing of the initial signal. The interaction between skyrmions also can contribute to the dephasing process. However, switching the magnetization direction in the nanodiscs (e.g., by spin transfer torque) also switches the helical rotation of the skyrmions from clockwise to anticlockwise (or vice versa), and this restores the initial signal (which is the essence of skyrmion echo).

Spanning Fermi arcs in a two-dimensional magnet

The discovery of topological states of matter has led to a revolution in materials research. When external or intrinsic parameters break symmetries, global properties of topological materials change drastically. A paramount example is the emergence of Weyl nodes under broken inversion symmetry. While a rich variety of non-trivial quantum phases could in principle also originate from broken time-reversal symmetry, realizing systems that combine magnetism with complex topological properties is remarkably elusive. Here, we demonstrate that giant open Fermi arcs are created at the surface of ultrathin hybrid magnets where the Fermi-surface topology is substantially modified by hybridization with a heavy-metal substrate. The interplay between magnetism and topology allows us to control the shape and the location of the Fermi arcs by tuning the magnetization direction. The hybridization points in the Fermi surface can be attributed to a non-trivial mixed topology and induce hot-spots in the Berry curvature, dominating spin and charge transport as well as magneto-electric coupling effects.

It has been predicted that elemental Iron, with low dimensionality, will be a topological metal hosting Weyl nodes. Here, Chen et al. grow iron on tungsten, a heavy metal with a strong spin-orbit interaction, and using momentum microscopy, show the emergence of giant open Fermi arcs which can be shaped by varying the magnetization of the iron.

Current-driven dynamics and ratchet effect of skyrmion bubbles in a ferrimagnetic insulator

Magnetic skyrmions are compact chiral spin textures that exhibit a rich variety of topological phenomena and hold potential for the development of high-density memory devices and novel computing schemes driven by spin currents. Here, we demonstrate the room-temperature interfacial stabilization and current-driven control of skyrmion bubbles in the ferrimagnetic insulator Tm₃Fe₅O₁₂ coupled to Pt, showing the current-induced motion of individual skyrmion bubbles. The ferrimagnetic order of the crystal together with the interplay of spin-orbit torques and pinning determine the skyrmion dynamics in Tm₃Fe₅O₁₂ and result in a strong skyrmion Hall effect characterized by a negative deflection angle and hopping motion. Further, we show that the velocity and depinning threshold of the skyrmion bubbles can be modified by exchange coupling Tm₃Fe₅O₁₂ to an in-plane magnetized Y₃Fe₅O₁₂ layer, which distorts the spin texture of the skyrmions and leads to directional-dependent rectification of their dynamics. This effect, which is equivalent to a magnetic ratchet, is exploited to control the skyrmion flow in a racetrack-like device.

Degenerate skyrmionic states in synthetic antiferromagnets

Topological magnetic textures, characterized by integer topological chargeS, are potential candidates in future magnetic logic and memory devices, due to their smaller size and expected low threshold current density for their motion. An essential requirement to stabilize them is the Dzyaloshinskii-Moriya interaction (DMI) which promotes a particular chirality, leading to a unique value ofSin a given material. However, recently coexistence of skyrmions and antiskyrmions, with opposite topological charge, in frustrated ferromagnets has been predicted usingJ₁-J₂-J₃classical Heisenberg model, which opens new perspectives, to use the topological charge as an additional degree of freedom. In this work, we propose another approach of using a synthetic antiferromagnetic system, where one of the ferromagnetic (FM) layer has isotropic and the other FM layer has anisotropic DMI to promote the existence of skyrmions and antiskyrmions, respectively. A frustrated interaction arises due to the coupling between the magnetic textures in the FM layers, which enables the stabilization and coexistence of 6 novel elliptical topological textures.

Stabilizing magnetic skyrmions in constricted nanowires

Magnetic skyrmions are topologically-protected chiral nano-scale spin structures that offer low power and high-density functionalities for spintronic devices. They behave as particles that can be moved, created and annihilated. These characteristics make them promising information-carrying bits, hence a precise control of the skyrmion motion is essential. This study shows that stabilizing skyrmion is possible using a stepped nanowire geometry. The nanoconstriction dimension and materials properties are found to strongly affect the pinning, depinning and annihilation of the skyrmion. It is also observed that near the stepped region, the skyrmion slows down and its velocity changes direction before its stability. Moreover, a reduction of skyrmion size as it squeezes through the stepped region is observed. Our results will open a new strategy for the design and development of skyrmion-based devices.

Skyrmion pinning energetics in thin film systems

A key issue for skyrmion dynamics and devices are pinning effects present in real systems. While posing a challenge for the realization of conventional skyrmionics devices, exploiting pinning effects can enable non-conventional computing approaches if the details of the pinning in real samples are quantified and understood. We demonstrate that using thermal skyrmion dynamics, we can characterize the pinning of a sample and we ascertain the spatially resolved energy landscape. To understand the mechanism of the pinning, we probe the strong skyrmion size and shape dependence of the pinning. Magnetic microscopy imaging demonstrates that in contrast to findings in previous investigations, for large skyrmions the pinning originates at the skyrmion boundary and not at its core. The boundary pinning is strongly influenced by the very complex pinning energy landscape that goes beyond the conventional effective rigid quasi-particle description. This gives rise to complex skyrmion shape distortions and allows for dynamic switching of pinning sites and flexible tuning of the pinning.

Skyrmions, topological spin textures, can be pinned by defects present in the material that hosts them, influencing their motion. Here, Gruber et al show that the skyrmions are pinned at their boundary where the finite size of the skyrmions governs their pinning, and they demonstrate that certain pinning sites can switched on and off in-situ.

Deterministic Generation and Guided Motion of Magnetic Skyrmions by Focused He+-Ion Irradiation

Magnetic skyrmions are quasiparticles with nontrivial topology, envisioned to play a key role in next-generation data technology while simultaneously attracting fundamental research interest due to their emerging topological charge. In chiral magnetic multilayers, current-generated spin-orbit torques or ultrafast laser excitation can be used to nucleate isolated skyrmions on a picosecond time scale. Both methods, however, produce randomly arranged skyrmions, which inherently limits the precision on the location at which the skyrmions are nucleated. Here, we show that nanopatterning of the anisotropy landscape with a He⁺-ion beam creates well-defined skyrmion nucleation sites, thereby transforming the skyrmion localization into a deterministic process. This approach allows control of individual skyrmion nucleation as well as guided skyrmion motion with nanometer-scale precision, which is pivotal for both future fundamental studies of skyrmion dynamics and applications.

Topology dependence of skyrmion Seebeck and skyrmion Nernst effect

We explore the dynamics of skyrmions with various topological charges induced by a temperature gradient in an ultra-thin insulating magnetic film. Combining atomistic spin simulations and analytical calculations we find a topology-dependent skyrmion Seebeck effect: while skyrmions and antiskyrmions move to the hot regime, a topologically trivial localized spin structure moves to the cold regime. We further reveal the emergence of a skyrmion Nernst effect, i.e. finite, topology-dependent velocities transverse to the direction of the temperature gradient. These findings are in agreement with accompanying simulations of skyrmionic motion induced by monochromatic magnon currents, allowing us to demonstrate that the magnonic spin Seebeck effect is responsible for both, skyrmion Seebeck and Nernst effect. Furthermore we employ scattering theory together with Thiele's equation to identify linear momentum transfer from the magnons to the skyrmion as the dominant contribution and to demonstrate that the direction of motion depends on the topological magnon Hall effect and the topological charge of the skyrmion.

Controlled Switching of the Number of Skyrmions in a Magnetic Nanodot by Electric Fields

Magnetic skyrmions are topological swirling spin configurations that hold promise for building future magnetic memories and logic circuits. Skyrmionic devices typically rely on the electrical manipulation of a single skyrmion, but controllably manipulating a group of skyrmions can lead to more compact and memory-efficient devices. Here, an electric-field-driven cascading transition of skyrmion clusters in a nanostructured ferromagnetic/ferroelectric multiferroic heterostructure is reported, which allows a continuous multilevel transition of the number of skyrmions in a one-by-one manner. Most notably, the transition is non-volatile and reversible, which is crucial for multi-bit memory applications. Combined experiments and theoretical simulations reveal that the switching of skyrmion clusters is induced by the strain-mediated modification of both the interfacial Dzyaloshinskii-Moriya interaction and effective uniaxial anisotropy. The results not only open up a new direction for constructing low-power-consuming, non-volatile, and multi-bit skyrmionic devices, but also offer valuable insights into the fundamental physics underlying the voltage manipulation of skyrmion clusters.

Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation of an experimental physical system. Here we show that a dynamical neural network, trained on a minimal amount of data, can predict the behavior of spintronic devices with high accuracy and an extremely efficient simulation time, compared to the micromagnetic simulations that are usually employed to model them. For this purpose, we re-frame the formalism of Neural Ordinary Differential Equations to the constraints of spintronics: few measured outputs, multiple inputs and internal parameters. We demonstrate with Neural Ordinary Differential Equations an acceleration factor over 200 compared to micromagnetic simulations for a complex problem - the simulation of a reservoir computer made of magnetic skyrmions (20 minutes compared to three days). In a second realization, we show that we can predict the noisy response of experimental spintronic nano-oscillators to varying inputs after training Neural Ordinary Differential Equations on five milliseconds of their measured response to a different set of inputs. Neural Ordinary Differential Equations can therefore constitute a disruptive tool for developing spintronic applications in complement to micromagnetic simulations, which are time-consuming and cannot fit experiments when noise or imperfections are present. Our approach can also be generalized to other electronic devices involving dynamics.

Single skyrmion true random number generator using local dynamics and interaction between skyrmions

Magnetic skyrmions are of great interest to both fundamental research and applications in post-von-Neumann computing devices. The successful implementation of skyrmionic devices requires functionalities of skyrmions with effective controls. Here we show that the local dynamics of skyrmions, in contrast to the global dynamics of a skyrmion as a whole, can be introduced to provide effective functionalities for versatile computing. A single skyrmion interacting with local pinning centres under thermal effects can fluctuate in time and switch between a small-skyrmion and a large-skyrmion state, thereby serving as a robust true random number generator for probabilistic computing. Moreover, neighbouring skyrmions exhibit an anti-correlated coupling in their fluctuation dynamics. Both the switching probability and the dynamic coupling strength can be tuned by modifying the applied magnetic field and spin current. Our results could lead to progress in developing magnetic skyrmionic devices with high tunability and efficient controls.

Microdynamic Study of Spin-Lattice Coupling Effects on Skyrmion Transport

Skyrmion transport fundamentally determines the speed, energy consumption, and functionality of skyrmion-based spintronic devices, attracting considerable attention. Recent experimental studies found there is a migration barrier for the thermal activated transport of a skyrmion, which is speculated to be induced by the pinning effects of crystalline defects. In this Letter, we propose an alternative source of migration barrier for skyrmion transport, i.e., a local lattice distortion field due to spin-lattice coupling, which can lead to the same Arrhenius diffusion behavior in defect-free skyrmion materials. By performing spin-lattice dynamics simulations, we study the microdynamic insight into the influence of local lattice distortion field, which refreshes the mechanistic understanding on skyrmion transport.