Perspective: Magnetic skyrmions—Overview of recent progress in an active research field

Magnetic skyrmions possess topologically non-trivial particle-like nanoscale domain wall structures, which have reasonably good stability and unique dynamic properties and can be controlled by magnetic fields, electric fields, and electric currents. Therefore, magnetic skyrmions are expected to be used as novel information carriers in the next-generation high-density, low-energy-consumption, and non-volatile information storage and logic computing devices. Since the first experimental observation of magnetic skyrmions in 2009, a number of skyrmion-based device prototypes have been proposed. In this article, we review the recently proposed skyrmion-based devices and applications, including skyrmion-based racetrack memory, logic computing device, transistor-like functional device, and nano-oscillator. We first discuss advantages of skyrmion-based racetrack memory and solutions for some problems we are facing currently. We then introduce the duplication and merging of magnetic skyrmions and the skyrmion-based logic OR and AND gates. We also introduce the switch function of skyrmion-based transistor-like functional device. The switch function is realized via a voltage gate and controlled by the applied voltage as well as the driving spin current. Besides, a brief introduction of the skyrmion-based nano-oscillator is given. In addition, we introduce several possible methods to encode binary information in skyrmion-based devices. Finally, we discuss some possible future novel applications based on magnetic skyrmions.

Magnetic skyrmions are magnetic quasi-particles with a number of interesting properties for possible future applications in, memory storage devices, or non-conventional computing [1-7]. We have shown that in low energetic landscapes of thin film magnetic multilayers, skyrmions show Brownian-like diffusion [7], which can be influenced by magnetic fields, temperature, and the magnetic properties of the pinning site [8,9]. While the diffusive dynamics have experimentally been studied in the continuous film [7,8,10], the device application requires a fabrication process in general, which means that skyrmions move rather in confined geometry. Here we show that the diffusive dynamics of skyrmions can be significantly modified for the geometry of the confined system and the skyrmion density. It is experimentally shown that the critical factor to unravel the underlying physics is the commensurability effect which is corroborated with Molecular dynamics simulations, as well as the pinning effect. The combination of experiment and analysis enables us to reveal the intriguing behavior that pinning sites for magnetic skyrmion depends on the magnetic field strength of the order of μT. Our findings could pave the way to control the thermal dynamics of skyrmions and the pinning effect to realize novel skyrmionic device applications. Stable skyrmions are nucleated by applying a magnetic out-of-plane (OOP) field while pulsing once an in-plane field [10]. We study the skyrmion diffusion in confined geometries varying both the symmetry of the geometry as well as the number of skyrmions from a sparse population to a fully lattice-like situation [11]. Basic geometries like triangles and circles are used. By measuring the mean squared displacement (MSD) of the trajectories of the skyrmions in the structures, the diffusion coefficient is calculated. Figure 1 shows the thermal behavior of skyrmions as a function of the skyrmion density in triangular geometry [11]. As can be seen in Fig. 1(a), The number of skyrmions can be precisely controlled by varying the OOP field to allow us to investigate the skyrmion density dependence of the skyrmion diffusion in confined geometries. Figure 1(b) presents the time-averaged configurations over 9600 Kerr images, where some configurations exhibit blur skyrmions which move with arbitrary time scale. It is shown that the diffusion qualitatively depends on the commensurability of the skyrmion number. Also, we find that the states for skyrmion numbers of 1, 3, 6, and 10 commensurate with the geometry and lead to a saturation of the MSDs as a function of time. The MSDs for an incommensurate state exhibit a non-monotonic relation and do not saturate over the experimental timescale. As shown in Fig. 1(c), molecular simulations agree qualitatively with the experimental findings that corroborating the basic dependence of skyrmion numbers on the motion in triangular confinement [11]. The quantitative difference from the simulation could be related to the pinning effect on the magnetic skyrmion. To explore the behavior closely, we investigate the magnetic field dependence of the skyrmion diffusion under a simplified environment. Figure 2 shows the OOP magnetic field dependence of histograms of skyrmion center positions in the circular geometry. For eliminating the commensurability effect, and the symmetry breaking of magnetic potential, we nucleate a single skyrmion in a circular geometry. We can see not only the modification of the depth of the pinning potential but also the pinning site transition with a small magnetic field of the order of μT, where the size of the skyrmion is modified. More intriguingly, the behavior shows hysteresis to a magnetic field, on the other hand, the reproducibility confirmed after applying a large magnetic field of 8 T suggests that the pinning sites themselves are not linked with the magnetic origin of pinned spins. Thus, the possible origin could arise from the topological spin texture itself. In conclusion, we reveal that the skyrmion diffusion is governed by the commensurability in confined geometry, as well as the magnetic field-dependent skyrmion pinning. The results show that for any potential skyrmionic device based on thin magnetic layers the numbers of skyrmions in the structured geometry as well as the geometry itself influence not only the arrangement but also the thermal diffusive motion of the skyrmions. Also, the pinning effect remains significant however, our findings indicate that magnetic skyrmions could be a new useful tool for experimentally exploring the pinning effect, which is a critical factor for any magnetic objects, and the possibility that the pinning sites are able to be tailored even after film deposition and fabrication process. **

Microelectronic technologies have been developing rapidly in the past half-century following the famous Moore's Law. However, this tendency is beginning to break down due to the thermal effects induced by the leakage current and data traffic. Spintronics sheds light on eliminating this bottleneck by using the spin degree of electron, which attracts great attention from both the academia and industry. The magnetic skyrmion is a particle-like spin texture with topological protection, envisioned as an energy efficient spintronic information carrier due to its nanoscale size, ultra-low driven energy, and high thermal stability. Recent research progress shows that the nucleation, transportation, and detection of skyrmion in room temperature, which affirm its potential application in electronics, lead to a new research field called skyrmionics. In this review article, we first introduce the fundamental concepts and recent progress of magnetic skyrmions, from both the theoretical and experimental point of view. Different types of magnetic skyrmions have different properties due to their physical dynamics. We only focus on the skyrmions stabilized by Dzyaloshinskii-Moriya interaction (DMI) in the ultra-thin film structures as their small size, high mobility and room temperature stability can provide the perspectives for electronic devices. The skyrmions have already been extensively investigated from both the theoretical and experimental aspects in recent years. Micromagnetic simulation is the main approach to theoretically studying the dynamics of skyrmions and their applications. Most of the innovative skyrmionic devices have first been demonstrated by this method. Experimentally, skyrmions can be measured by various methods, such as the neutron scattering, Lorentz transmission electron microscopy, scanning X-ray transmission microscopy, polar magneto-optical Kerr effect microscope, etc. In the third part of this paper, we present four basic functions of skyrmionic devices ranging from nucleation, motion, detection, to manipulation. The nucleation of skyrmions, corresponding to the information writing in skyrmionic devices, has been widely investigated. A skyrmion can be nucleated by conversion from domain wall pairs, local spin injection, local heating, and spin waves. Then, we focus on the current induced skyrmion motion and compare the two different torques:the spin transfer torque and the spin orbit torque. To read the data, it is necessary to detect skyrmions electrically. One way is to measure the topological Hall effect in a Hall bar. More commonly, skyrmions can be detected through magnetoresistance effects, i.e., giant magnetoresistance/anisotropic magnetoresistance, tunnel magnetore sistance, and non-collinear magnetoresistance, in a junction geometry. For manipulation, it is mainly demonstrated by the voltage controlled magnetic anisotropy (VCMA). Finally we discuss several representative skyrmionic nano-devices in memory, logic, and neuromorphic applications. The magnetic tunnel junction and the racetrack are two common designs for skyrmionic memory devices. The former can store multiple values in one bit, and the latter can realize fast and efficient data transmission. To control the skyrmionic data in these memories, the VCMA effect is one of the promising approaches, which is used in several designs. For the skyrmionic logic devices, they can be divided into two main types:the transistor and the logic gate. However, until now, these ideas are only demonstrated in simulation, and more efforts in experiment are needed. Besides, novel devices such as artificial synapses and neurons can be realized more naturally by skyrmion due to its particle-like property. In summary, skyrmionics is promising in several aspects, including performance improvement, emerging function and architecture design, and bio-inspired computing. Remarkable progress has been made in the past few years, however the device integration, the materials, and the data transmission still restrict its application. We hope this overview article may present a clear picture about skyrmionics and receive more attention, thus promoting its fast research and development in the future.

Magnetic skyrmions are topological swirling spin textures objects that can be manipulated and employed as information carriers. This is accomplished based either on their ground-state properties or their thermodynamic properties. Landauer’s principle establishes an irreversible conversion from information to physics. The inverse mechanism, the inverse mechanism is proposed for magnetic topological defects forming in magnetic nanostructures that are regarded as closed thermodynamic systems confirming Szilard’s and Brillouin’s hypotheses. This mechanism consists of the creation of bits of information using a thermodynamic source having a form of negentropy. In this perspective article, the following are proved for magnetic skyrmions: 1) Landauer’s principle expressed in terms of negentropy and 2) the generalized second principle of thermodynamics based on Brillouin’s negentropy principle of information. The thermodynamic entropy is converted into information entropy at the expense of negentropy, “negative entropy” corresponding to the loss of thermodynamic entropy from the magnetic skyrmion itself. A recently proposed practical device enables the verification of points 1) and 2) and allows a full understanding of the interchange between thermodynamics and information and vice versa regarding skyrmions as information units and showing, in perspective, the considerable advantages offered by this type of storing and coding information.

Magnetic skyrmions [1] are promising candidates for next-generation spintronic devices. Their solitonic and chiral nature allows an efficient current-induced motion up to high velocities [2]. A fine tuning of their chirality would enable highly-manipulable magnetic skyrmions, which paves the way for new functionalities in spintronic memory, logic and neuromorphic devices [3,4]. This gives great importance to the control of the interfacial Dzyaloshinskii-Moriya interaction (iDMI) [5,6] strength and sign, at the origin of magnetic skyrmions and their chirality. In this study, we directly demonstrate magnetic skyrmion’s chirality switching in a Ta/FeCoB/TaOx trilayer. In fact, by varying the thickness of FeCoB and the oxidation state at the FeCoB/TaOx interface, we are able to obtain different regions in which magnetic skyrmions are right-handed (iDMI>0) or left-handed (iDMI<0) (resp. regions #4 and #2 on Fig.1). This material-dependent chirality switching brings a new degree of freedom to the exciting physics of magnetic skyrmions. For the first time, we show that the iDMI sign crossover in the different regions, as measured by Brillouin-Light-Scattering (BLS), is accompanied by a change of skyrmion chirality, as confirmed by the opposite direction of current-induced motion of magnetic skyrmions (See Fig. 2). Notably, between the two regions of opposite iDMI sign we have found, as expected, a region where iDMI∼0. In this region, the control of the iDMI with an electric field [7] may lead to a voltage-induced chirality switching, which hasn’t been observed yet. This all-electrical control of magnetic skyrmions represents a cornerstone towards power efficient spintronic devices and multidirectional logic functionnalities.

Magnetic skyrmions have been subject of growing interest in recent years for their very promising applications in spintronics, quantum computation and future low power information technology devices. In this book chapter, we use the field theory method and coherent spin state ideas to investigate the properties of magnetic solitons in spacetime while focussing on 2D and 3D skyrmions. We also study the case of a rigid skyrmion dissolved in a magnetic background induced by the spin-tronics; and derive the effective rigid skyrmion equation of motion. We examine as well the interaction between electrons and skyrmions; and comment on the modified Landau-Lifshitz-Gilbert equation. Other issues, including emergent electrodynamics and hot applications for next-generation high-density efficient information encoding, are also discussed.

Magnetic skyrmions are topologically nontrivial spin textures with envisioned applications in energy-efficient magnetic information storage. Toggling the presence of magnetic skyrmions via writing/deleting processes is essential for spintronics applications, which usually require the application of a magnetic field, a gate voltage or an electric current. Here we demonstrate the reversible field-free writing/deleting of skyrmions at room temperature, via hydrogen chemisorption/desorption on the surface of Ni and Co films. Supported by Monte-Carlo simulations, the skyrmion creation/annihilation is attributed to the hydrogen-induced magnetic anisotropy change on ferromagnetic surfaces. We also demonstrate the role of hydrogen and oxygen on magnetic anisotropy and skyrmion deletion on other magnetic surfaces. Our results open up new possibilities for designing skyrmionic and magneto-ionic devices.

Magnetic skyrmionics is an advanced and active research field, which involves fundamental physics, the creation of efficient next-generation high-density information devices, the formation and manipulation of nanometer-size skyrmions in devices, and the development of compatible materials at room temperature. The magnetic skyrmions found in magnetic materials exhibit spiral magnetism. This book presents a basic overview of magnetic skyrmions along with current research on magnetic skyrmions, emphasizing formation mechanisms and materials design strategies. This book is suitable for an interdisciplinary audience of undergraduates, graduates, engineers, scientists, and researchers in the development of the next generation of spintronic devices.

Magnetic skyrmions are topological solitons promising for applications as encoders for digital information. A number of different skyrmion-based memory devices have been recently proposed. In order to demonstrate a viable skyrmion-based memory device, it is necessary to reliably and reproducibly nucleate, displace, detect, and delete the magnetic skyrmions, possibly in the absence of external applied magnetic fields, which would needlessly complicate the device design. While the skyrmion displacement and detection have both been thoroughly investigated, much less attention has been dedicated to the study of the skyrmion nucleation process and its sub-nanosecond dynamics. In this study, we investigate the nucleation of magnetic skyrmions from a dedicated nanoengineered injector, demonstrating the reliable magnetic skyrmion nucleation at the remnant state. The sub-nanosecond dynamics of the skyrmion nucleation process were also investigated, allowing us to shine light on the physical processes driving the nucleation.

We propose an alternative route to stabilize magnetic skyrmion textures which does not require Dzyaloshinkii-Moriya interactions, magnetic anisotropy, or an external Zeeman field. Instead, it solely relies on the emergence of flux in the system's ground state. We discuss scenarios that lead to a nonzero flux and identify the magnetic skyrmion ground states which become accessible in its presence. Moreover, we explore the chiral superconductors obtained for the surface states of a topological crystalline insulator when two types of magnetic skyrmion crystals coexist with a pairing gap. Our work opens perspectives for engineering topological superconductivity in a minimal fashion and promises to unearth functional topological materials and devices which may be more compatible with electrostatic control than the currently explored skyrmion-Majorana platforms.

Magnetic skyrmions are topologically stable spin textures at the nanoscale that can be manipulated with low current densities. Owing to their stability and small size, they are considered promising candidates for high-density, energy-efficient spintronic applications such as racetrack memory and logic devices. The efficient transport of magnetic skyrmions is critical for the development of next-generation skyrmion-based information processing technologies. In this work, we present a micromagnetic simulation study of skyrmion motion in a ferromagnetic nanotrack, focusing on the effects of sinusoidal variation in either the Gilbert damping coefficient( α ) or the non-adiabatic spin-transfer torque (STT)( β ) along the transverse direction. The simulation is performed using a Micromagnetic module in COMSOL Multiphysics which is governed by the Landau–Lifshitz-Gilbert equation. By employing the Thiele equation with spatially sinusoidal variations of α and β along the transverse direction, we numerically and theoretically computed the Dissipative tensor and the Gyromagnetic coupling vector and also calculate transverse and longitudinal velocities which clearly explains that the skyrmion is pushed towards the nearest attractor-rail and moves linearly with no magnus force. Using micromagnetic simulation, the sinusoidally varying α along the transverse direction, the skyrmion drifts toward the nearest attractor-rail, depending on its initial position, where SkHE is zero and it moves linearly. The spatial varying α ( y ) with different amplitudes, the skyrmion starts at same position and reaches the same attractor-rail with different path at different time scales, whereas by fixing the amplitude and varying the wavelength of α ( y ), skyrmion starts at same position and moves in different path and reaches different attractor-rails which will be useful for designing skyrmion multi-rail in the nanotrack. Similar dynamics but with inverse direction of the motion of skyrmion are observed while varying β sinusoidally along the width of the nanotrack. This controlled guidance opens new avenues for manipulating skyrmion dynamics, offering promising strategies for the design and optimization of multi-rail skyrmion transport systems. These findings provide valuable insights into the development of advanced spintronic devices utilizing magnetic skyrmions.

Discovering compact, stable, and easily controllable nanoscale non-trivial topological magnetic structures, such as magnetic skyrmions, is the key to developing next-generation high-density, high-speed, and low-energy non-volatile information storage devices. Based on the topological generation mechanism, magnetic skyrmions can be generated through the Dzyaloshinskii–Moriya interaction (DMI) caused by breaking space-reversal symmetry. Two-dimensional (2D) non-centrosymmetric Janus structurecan generate vertical built-in electric fields to break spatial inversion symmetry. Therefore, seeking for 2D Janus material with intrinsic magnetism is fundamental to develop the novel chiral magnetic storage technologies. In this work, we combine detailed machine learning techniques and first-principle calculations to investigate the magnetism of the unexplored 2D Janus material. We first collect 1179 2D hexagonal ABC-type Janus materials based on the Materials Project database, and use elemental composition as feature descriptors to construct four machine learning models: random forest (RF), gradient boosting decision trees (GBDT), extreme gradient boosting (XGB), and extra trees (ET). These algorithms and models are constructed to predict lattice constants, formation energy, and magnetic moment, via hyperparameter optimization and ten-fold cross-validation. The GBDT exhibits the highest accuracy and best prediction performance for magnetic moment classification. Subsequently, the collected data of 82018 yet-undiscovered 2D Janus materials, are input into the trained models to generate 4024 high magnetic moment 2D Janus materials with thermal stability. First-principles calculations are employed to validate random sample of 13 Janus materials with high magnetic moment. This study provides an effective machine learning framework for classifying the magnetic moments and screening highthroughput 2D Janus structures, thereby accelerating the exploration of their magnetic properties. The datasets provided in this work are available from &lt;ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.57760/sciencedb.j00213.00072"&gt;https://doi.org/10.57760/sciencedb.j00213.00072&lt;/ext-link&gt;.

Magnetic skyrmions are topologically protected entities that are promising for information storage and processing. Currently, an essential challenge for future advances of skyrmionic devices lies in achieving effective control of skyrmion properties. Here, through first-principles and Monte-Carlo simulations, we report the identification of nontrivial topological magnetism in two-dimensional multiferroics of Co2NF2. Because of ferroelectricity, monolayer Co2NF2 exhibits a large Dzyaloshinskii-Moriya interaction. This together with exchange interaction can stabilize magnetic skyrmions with the size of sub-10 nm under a moderate magnetic field. Importantly, arising from the magnetoelectric coupling effect, the chirality of magnetic skyrmions is ferroelectrically tunable, producing the four-fold degenerate skyrmions. When interfacing with monolayer MoSe2, the creation and annihilation of magnetic skyrmions, as well as phase transition between skyrmion and skyrmion lattice, can be realized in a ferroelectrically controllable fashion. A dimensionless parameter κ' is further proposed as the criterion for stabilizing magnetic skyrmions in such multiferroic lattices. Our work greatly enriches the two-dimensional skyrmionics and multiferroics research.

Electronic Circuits made of 2D Materials.

Learning and pattern recognition inevitably requires memory of previous events, a feature that conventional CMOS hardware needs to artificially simulate. Dynamical systems naturally provide the memory, complexity, and nonlinearity needed for a plethora of different unconventional computing approaches. In this perspective article, we focus on the unconventional computing concept of reservoir computing and provide an overview of key physical reservoir works reported. We focus on the promising platform of magnetic structures and, in particular, skyrmions, which potentially allow for low-power applications. Moreover, we discuss skyrmion-based implementations of Brownian computing, which has recently been combined with reservoir computing. This computing paradigm leverages the thermal fluctuations present in many skyrmion systems. Finally, we provide an outlook on the most important challenges in this field.