A reversible conversion between a skyrmion and a domain-wall pair in a junction geometry

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.

Generation of skyrmions by combining thermal and spin-orbit torque: breaking half skyrmions into skyrmions

Skyrmions, swirling spin textures with topologically protected stability and low critical driven-current density, can be generated from the stripe domain with current pulses, bringing them closer to practical applications in racetrack memory. However, the mechanism of this topological transition from the stripe domain to the skyrmion remains unclear because the transition process occurs at a nanosecond timescale, giving rise to difficulties in observing this process using imaging tools. In this study, we controlled the domain wall - skyrmion transition by combining Joule heating with spin-orbit torque (SOT) and experimentally observed the details of this process, by which we confirmed the mechanism: the spatial variation of the topological charge density induces half skyrmions branching from the stripe domains, and these half skyrmions overcome the surface tension and break away from the stripe domain, resulting in the generation of skyrmions. The details were observed by employing Joule heating to overcome the pinning effect and manipulating the strength of the SOT to induce the branching and breaking of half skyrmions. These findings offer new insights into skyrmion generation and serve as an important step towards the development of highly efficient devices for processing and computing based on skyrmionics.

Optimizing skyrmionium movement and stability via stray magnetic fields in trilayer nanowire constructs

Skyrmioniums, known for their unique transport and regulatory properties, are emerging as potential cornerstones for future data storage systems. However, the stability of skyrmionium movement faces considerable challenges due to the skyrmion Hall effect, which is induced by deformation. In response, our research introduces an innovative solution: we utilized micro-magnetic simulations to create a sandwiched trilayer nanowire structure augmented with a stray magnetic field. This combination effectively guides the skyrmionium within the ferromagnetic (FM) layer. Our empirical investigations reveal that the use of a stray magnetic field not only reduces the size of the skyrmionium but also amplifies its stability. This dual-effect proficiently mitigates the deformation of skyrmionium movement and boosts their thermal stability. We find these positive outcomes are most pronounced at a particular intensity of the stray magnetic field. Importantly, the required stray magnetic field can be generated using a heavy metal (HM1) layer of suitable thickness, rendering the practical application of this approach plausible in real-world experiments. Additionally, we analyze the functioning mechanism based on the Landau-Lifshitz-Gilbert (LLG) equation and energy variation. We also develop a deep spiking neural network (DSNN), which achieves a remarkable recognition accuracy of 97%. This achievement is realized through supervised learning via the spike timing dependent plasticity rule (STDP), considering the nanostructure as an artificial synapse device that corresponds to the electrical properties of the nanostructure. In conclusion, our study provides invaluable insights for the design of innovative information storage devices utilizing skyrmionium technology. By tackling the issues presented by the skyrmion Hall effect, we outline a feasible route for the practical application of this advanced technology. Our research, therefore, serves as a robust platform for continued investigations in this field.

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.

Reversible conversion between skyrmions and skyrmioniums

Skyrmions and skyrmioniums are topologically non-trivial spin textures found in chiral magnetic systems. Understanding the dynamics of these particle-like excitations is crucial for leveraging their diverse functionalities in spintronic devices. This study investigates the dynamics and evolution of chiral spin textures in [Pt/Co]₃/Ru/[Co/Pt]₃ multilayers with ferromagnetic interlayer exchange coupling. By precisely controlling the excitation and relaxation processes through combined magnetic field and electric current manipulation, reversible conversion between skyrmions and skyrmioniums is achieved. Additionally, we observe the topological conversion from a skyrmionium to a skyrmion, characterized by the sudden emergence of the skyrmion Hall effect. The experimental realization of reversible conversion between distinct magnetic topological spin textures represents a significant development that promises to expedite the advancement of the next generation of spintronic devices.

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.

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.

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.

Skyrmions-based logic gates in one single nanotrack completely reconstructed via chirality barrier

Logic gates based on magnetic elements are promising candidates for logic-in-memory applications with non-volatile data retention, near-zero leakage and scalability. In such spin-based logic devices, however, the multi-strip structure and fewer functions are obstacles to improving integration and reducing energy consumption. Here we propose a skyrmions-based single-nanotrack logic family including AND, OR, NOT, NAND, NOR, XOR and XNOR that can be implemented and reconstructed by building and switching the Dzyaloshinskii-Moriya interaction (DMI) chirality barrier on a racetrack memory. Besides the pinning effect of the DMI chirality barrier on skyrmions, the annihilation, fusion and shunting of two skyrmions with opposite chirality are also achieved and demonstrated via local reversal of the DMI, which are necessary for the design of an engineer programmable logic nanotrack, transistor and complementary racetrack memory.

Atomically Thin 2D van der Waals Magnetic Materials: Fabrications, Structure, Magnetic Properties and Applications

Two-dimensional (2D) van der Waals (vdW) magnetic materials are considered to be ideal candidates for the fabrication of spintronic devices because of their low dimensionality, allowing the quantization of electronic states and more degrees of freedom for device modulation. With the discovery of few-layer Cr2Ge2Te6 and monolayer CrI3 ferromagnets, the magnetism of 2D vdW materials is becoming a research focus in the fields of material science and physics. In theory, taking the Heisenberg model with finite-range exchange interactions as an example, low dimensionality and ferromagnetism are in competition. In other words, it is difficult for 2D materials to maintain their magnetism. However, the introduction of anisotropy in 2D magnetic materials enables the realization of long-range ferromagnetic order in atomically layered materials, which may offer new effective means for the design of 2D ferromagnets with high Curie temperature. Herein, current advances in the field of 2D vdW magnetic crystals, as well as intrinsic and induced ferromagnetism or antiferromagnetism, physical properties, device fabrication, and potential applications, are briefly summarized and discussed.

Transcription and logic operations of magnetic skyrmions in bilayer cross structures

Magnetic skyrmions are potential building blocks for future information storage and computing devices. Here, we computationally study the skyrmion dynamics in a cross structure made of two ferromagnetic nanotracks. We show that by controlling the skyrmion motion in the cross structure using spin currents, it is possible to realize the transcription of skyrmion at the intersection of the cross structure at certain conditions. Based on the transcription of skyrmion, we computationally demonstrate the AND, OR and NOT logical gates using the cross structures with modified geometries and appropriate magnetic parameters. Our results may provide guidelines to design future three-dimensional spintronics devices based on magnetic skyrmions.

Asymmetry in the propagation of vortex domain wall artificial skyrmion composite system

We studied the propagation of an artificial skyrmion coupled to the vortex domain wall (VDW). We discovered the following effect: depending on the propagation's direction, the dynamics of the coupled skyrmion VDW can be faster than the isolated VDW's velocity. The reason for such behavior is the structural distortion that occurs in the coupled system. We interpret the numerical results in terms of the modified Thiele's equation. In particular, increasing the Thiele's equation counteractive coefficient leads to the perfect fitting with the micromagnetic simulation results.

Scattering modes of skyrmions in a bilayer system with ferromagnetic coupling

Magnetic skyrmions are quasiparticle-like textures that are topologically different from a single domain magnetization state. Their topological protection, combined with the low current density needed to move them, make these objects relevant to be used as information storage structures. In such a context, the analysis of the interactions between skyrmions is interesting and relevant for future applications. In this work, through micromagnetic simulations and numerical calculations, we studied the interaction between two skyrmions living on different parallel ferromagnetic racetracks connected by an exchange-like interaction. The upper and lower racetracks are separated by a height offset and the interaction between the upper and the lower skyrmion is analyzed in terms of the magnetic and geometrical parameters. Three states are predicted, as a function of these parameters: scattered or free skyrmions, bound skymions, and annihilated skyrmions. Our results, presented in a phase diagram, demonstrate that even in the case here called free skyrmions, there is a small and brief interaction when both are close enough, but the skyrmion in the top layer does not drag the skyrmion in the bottom layer. For bound skyrmions, both keep linked during larger times. In the latter case, there are strong changes in the velocity of the skyrmions induced by the effect of a higher effective mass when both are coupled.

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.

Friedel Oscillations Induced by Magnetic Skyrmions: From Scattering Properties to All-Electrical Detection

Magnetic skyrmions are spin swirling solitonic defects that can play a major role in information technology. Their future in applications and devices hinges on their efficient manipulation and detection. Here, we explore from ab-initio their nature as magnetic inhomongeities in an otherwise unperturbed magnetic material, Fe layer covered by a thin Pd film and deposited on top of Ir(111) surface. The presence of skyrmions triggers scattering processes, from which Friedel oscillations emerge. The latter mediate interactions among skyrmions or between skyrmions and other potential surrounding defects. In contrast to their wavelengths, the amplitude of the oscillations depends strongly on the size of the skyrmion. The analogy with the scattering-off atomic defects enables the assignment of an effective scattering potential and a phase shift to the skyrmionic particles, which can be useful to predict their behavior on the basis of simple scattering frameworks. The induced charge ripples can be utilized for a noninvasive all-electrical detection of skyrmions located on a surface or even if buried a few nanometers away from the detecting electrode.

Magnon Landau Levels and Spin Responses in Antiferromagnets

We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose a model of an AFM topological insulator of magnons. In the long wavelength limit, the Landau levels induced by the inhomogeneous Dzyaloshinskii-Moriya interaction exhibit relativistic physics described by the Klein-Gordon equation. The spin Nernst response due to the formation of magnonic Landau levels is compared to similar topological responses in skyrmion and vortex-antivortex crystal phases of AFM insulators. Our studies show that AFM insulators exhibit rich physics associated with topological magnon excitations.

Multibit racetrack memory

We present a hybrid usage of domain walls and skyrmions in the same racetrack memory which can enable developing a platform for many-valued magnetic data storage technology, by numerically solving the Landau-Lifshitz-Gilbert equation. The conversion of domain-walls to magnetic skyrmions in a plain nanotrack without geometrical restrictions allowed us to realize a ternary racetrack memory. Annihilation, conversion, and passing over of the reverse domains are considered as the three-state of ternary logic. We anticipate that multibit racetrack memory will influence the development of data storage platforms for emergent computing technologies.

Role of higher-order exchange interactions for skyrmion stability

Transition-metal interfaces and multilayers are a promising class of systems to realize nanometer-sized, stable magnetic skyrmions for future spintronic devices. For room temperature applications, it is crucial to understand the interactions which control the stability of isolated skyrmions. Typically, skyrmion properties are explained by the interplay of pair-wise exchange interactions, the Dzyaloshinskii-Moriya interaction and the magnetocrystalline anisotropy energy. Here, we demonstrate that higher-order exchange interactions - which have so far been neglected - can play a key role for the stability of skyrmions. We use an atomistic spin model parametrized from first-principles and compare three different ultrathin film systems. We consider all fourth-order exchange interactions and show that, in particular, the four-site four spin interaction has a large effect on the energy barrier preventing skyrmion and antiskyrmion collapse into the ferromagnetic state. Our work opens perspectives to stabilize topological spin structures even in the absence of Dzyaloshinskii-Moriya interaction.

Sub-nanoscale atom-by-atom crafting of skyrmion-defect interaction profiles

Magnetic skyrmions are prime candidates as information carriers for spintronic devices due to their topological nature and nanometric size. However, unavoidable inhomogeneities inherent to any material leads to pinning or repulsion of skyrmions that, in analogy to biology concepts, define the phenotype of the skyrmion-defect interaction, generating complexity in their motion and challenging their application as future bits of information. Here, we demonstrate that atom-by-atom manufacturing of multi-atomic defects, being antiferromagnetic or ferromagnetic, permits the breeding of their energy profiles, for which we build schematically a Punnet-square. As established from first-principles for skyrmions generated in PdFe bilayer on Ir(111) surface, the resulting interaction phenotype is rich. It can be opposite to the original one and eventually be of dual pinning-repulsive nature yielding energy landscapes hosting multi-domains. This is dictated by the stacking site, geometry, size and chemical nature of the adsorbed defects, which control the involved magnetic interactions. This work provides new insights towards the development of disruptive device architectures incorporating defects into their design aiming to control and guide skyrmions.

Skyrmions and Spin Waves in Magneto-Ferroelectric Superlattices

We present in this paper the effects of Dzyaloshinskii–Moriya (DM) magneto–electric coupling between ferroelectric and magnetic interface atomic layers in a superlattice formed by alternate magnetic and ferroelectric films. We consider two cases: magnetic and ferroelectric films have the simple cubic lattice and the triangular lattice. In the two cases, magnetic films have Heisenberg spins interacting with each other via an exchange J and a DM interaction with the ferroelectric interface. The electrical polarizations of ±1 are assumed for the ferroelectric films. We determine the ground-state (GS) spin configuration in the magnetic film and study the phase transition in each case. In the simple cubic lattice case, in zero field, the GS is periodically non collinear (helical structure) and in an applied field H perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green’s function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperatures. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magneto–electric DM coupling and the applied magnetic field. Phase transition to the disordered phase is studied. In the case of the triangular lattice, we show the formation of skyrmions even in zero field and a skyrmion crystal in an applied field when the interface coupling between the ferroelectric film and the ferromagnetic film is rather strong. The skyrmion crystal is stable in a large region of the external magnetic field. The phase transition is studied.

A ferromagnetic skyrmion-based diode with a voltage-controlled potential barrier

Traditional electronic technologies face many challenges, such as the scalability of equipment and improvement of performance. Some novel spintronic objects are expected to improve electronic applications for the more-than-Moore era. For example, a magnetic skyrmion is a potential building block for the next generation of electronic devices due to its small size, good stability and low driving current threshold. However, the Magnus force acting on a ferromagnetic skyrmion can induce a transverse motion perpendicular to the driving force, which may lead to the destruction of skyrmions at sample edges. Here, we computationally demonstrate that the nanotrack edge with high magnetic perpendicular anisotropy (PMA), which is controlled by the voltage-controlled magnetic anisotropy (VCMA) effect, not only enables the reliable motion of skyrmions along the nanotrack, but also increases the skyrmion velocity. The one-way motion of skyrmions can be realized by applying voltage to create high PMA at a local area near the nanotrack edge. In addition, we show a feasible design of a skyrmion diode similar to the P-N junction. Our results may provide guidelines for designing skyrmion-based diodes.

Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications

The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last decades. In this topical review, we mainly review and discuss key results and findings in skyrmion research since the first experimental observation of magnetic skyrmions in 2009. We particularly focus on the theoretical, computational and experimental findings and advances that are directly relevant to the spintronic applications based on magnetic skyrmions, i.e. their writing, deleting, reading and processing driven by magnetic field, electric current and thermal energy. We then review several potential applications including information storage, logic computing gates and non-conventional devices such as neuromorphic computing devices. Finally, we discuss possible future research directions on magnetic skyrmions, which also cover rich topics on other topological textures such as antiskyrmions and bimerons in antiferromagnets and frustrated magnets.

Nonlocal accumulation, chemical potential, and Hall effect of skyrmions in Pt/Co/Ir heterostructure

Magnetic skyrmion is a swirling topological spin texture behaving as an individual particle. It shows a gyro-motion similarly to that of a charged particle under a magnetic field, being led to the transverse shift to the electric current, i.e., skyrmion Hall effect. With the open boundaries of a sample, this results in an accumulation of skyrmions on one side and their depletion on the other side. Here we demonstrate experimentally that this effect propagates non-locally over tens of micrometers even where the electric current is absent, when the narrow wires bridge bar-shaped Pt/Co/Ir heterostructure thin film systems. This nonlocality can be understood in terms of the “chemical potential” gradient for the skyrmion bubble induced by the skyrmion Hall effect in the nonequilibrium steady state under the electric current. The present result shows that the skyrmion Hall effect acts as the skyrmion pump and the thermodynamic concepts can be applied to the aggregate of skyrmion bubbles.

Statistical Properties and Configurational Entropy of a Two-Dimensional Néel Magnetic Skyrmions Population

The study of the thermodynamic properties of topological defects is important not only for understanding their magnetic properties but also for suggesting novel applications. In this paper, the statistical and statistical thermodynamic properties of a population of Néel magnetic skyrmion diameters hosted in an ultrathin cylindrical dot is determined within a two-dimensional analytical approach. The statistical properties such as the skyrmion size are calculated in the region of skyrmion metastability and are compared with the ones obtained using a recent three-dimensional analytical approach based on the analogy with the Maxwell–Boltzmann distribution of dilute gas molecules. The investigation of the statistical thermodynamic properties focus on the calculation of the configurational entropy at thermodynamic equilibrium determined in the continuous limit from the Boltzmann order function. While the statistical properties are quantitatively similar passing from the two-dimensional to the three-dimensional approach, the configurational entropy calculated from the two-dimensional skyrmions distribution is considerably lower than the one obtained from the three-dimensional skyrmions distribution. Because of the strong resemblance between the statistical configurational entropy and Jaynes’s information entropy, it is suggested to use magnetic skyrmions as temperature and external field dependent information entropy carriers for a future potential technological application in the field of low-dimensional magnetic systems and skyrmionics.

Direct current-tunable MHz to multi-GHz skyrmion generation and control

Skyrmions offer high density, low power, and nonvolatile memory functionalities due to their nanoscale and topologically-protected chiral spin structures. For integrated high-bandwidth devices, one needs to control skyrmion generation and propagation rates using current. Here, we introduce a skyrmion initialization and control method to generate periodic skyrmions from 114 MHz to 21 GHz using spin-polarized direct current. We first initialize a stable magnetic domain profile that is pinned between a notch and a rectangular constriction using a DC pulse. Next, we pass spin-polarized DC charge current to eject periodic skyrmions at a desired frequency. By changing the DC current density, we demonstrate in micromagnetic simulations that skyrmion generation frequencies can be controlled reversibly over more than seven octaves of frequencies. By using domain pinning and current-driven skyrmion motion, we demonstrate a highly tunable and DC-controlled skyrmion signal source, which pave the way towards ultra wideband, compact and integrated skyrmionic circuits.

Controlled modification of skyrmion information in a three-terminal racetrack memory

Manipulation of magnetic skyrmions has been generating considerable interest because of their potential applications in future spintronic devices. As an information carrier, a skyrmion is used to code a bit. In this work, we study via micromagnetic simulations a three-terminal racetrack memory, where an isolated skyrmion can be generated and annihilated by the gate voltage pulse. Thus, we can modify a train of skyrmion codes written at the generator in a controlled manner. The modified information is then detected at the collector. We have identified both gyration and breathing modes during skyrmion manipulation. The dynamics is analysed via a Thiele equation derived from the micromagnetic model. From the equation, the gyration mode of a skyrmion is suggested to be coupled to the breathing mode dynamics. This work proposes an effective method for controlled modification of skyrmion information in a potential energy-efficient racetrack memory, and provides a fundamental understanding of the intrinsic skyrmion dynamics during skyrmion manipulation.

Spin Torque Efficiency and Analytic Error Rate Estimates of Skyrmion Racetrack Memory

In this paper, the thermal stability of skyrmion bubbles and the critical currents to move them over pinning sites were investigated. For the used pinning geometries and the used parameters, the unexpected behavior is reported that the energy barrier to overcome the pinning site is larger than the energy barrier of the annihilation of a skyrmion. The annihilation takes place at boundaries by current driven motion, as well as due to the excitation over energy barriers, in the absence of currents, without forming Bloch points. It is reported that the pinning sites, which are required to allow thermally stable bits, significantly increase the critical current densities to move the bits in skyrmion-like structures to about jcrit = 0.62 TA/m². The simulation shows that the applied spin transfer model predicts experimentally obtained critical currents to move stable skyrmions at room temperature well, which is in contrast to simulations based on spin orbit torque that predict significantly too low critical currents. By calculating the thermal stability, as well as the critical current, we can derive the spin torque efficiency η = ΔE/Ic = 0.19 kBT300/μA, which is in a similar range to the simulated spin torque efficiency of MRAM structures. Finally, it is shown that the stochastic depinning process of any racetrack-like device requires an extremely narrow depinning time distribution smaller than ~6% of the current pulse length to reach bit error rates smaller than 10-9.

Current-driven coherent skyrmion generation

The next-generation logic and memory devices using magnetic skyrmions as spintronic information carriers are frequently studied, thanks to their remarkable magnetic stability, extremely compact size and very-low-cost driving forces within nanotracks. In order to realize skyrmion-based spintronic devices, understanding the skyrmion generation and their dynamics are essential. In this study, we have carried out a systematic micromagnetic simulation study on coherent magnetic skyrmion generation in which we theoretically engineered nanotracks by embedding an anti-notch to a channel of certain width. We found that the drift velocity and the skyrmion generation frequency can be tailored by the applied spin-polarized DC current density. Moreover, skyrmion generation is crucially affected by both damping and nonadiabaticity parameters, as well as the geometry of the anti-notch. We anticipate that our predictions provide rational basis for skyrmion-based devices in which skyrmions are used as information carriers, and influence future discussions.

Phase Transition in Frustrated Magnetic Thin Film-Physics at Phase Boundaries

In this review, we outline some principal theoretical knowledge of the properties of frustrated spin systems and magnetic thin films. The two points we would like to emphasize: (i) the physics in low dimensions where exact solutions can be obtained; (ii) the physics at phase boundaries where interesting phenomena can occur due to competing interactions of the two phases around the boundary. This competition causes a frustration. We will concentrate our attention on magnetic thin films and phenomena occurring near the boundary of two phases of different symmetries. Two-dimensional (2D) systems are in fact the limiting case of thin films with a monolayer. Naturally, we will treat this case at the beginning. We begin by defining the frustration and giving examples of frustrated 2D Ising systems that we can exactly solve by transforming them into vertex models. We will show that these simple systems already contain most of the striking features of frustrated systems such as the high degeneracy of the ground state (GS), many phases in the GS phase diagram in the space of interaction parameters, the reentrance occurring near the boundaries of these phases, the disorder lines in the paramagnetic phase, and the partial disorder coexisting with the order at equilibrium. Thin films are then presented with different aspects: surface elementary excitations (surface spin waves), surface phase transition, and criticality. Several examples are shown and discussed. New results on skyrmions in thin films and superlattices are also displayed. By the examples presented in this review we show that the frustration when combined with the surface effect in low dimensions gives rise to striking phenomena observed in particular near the phase boundaries.

Torsion-induced vortex switching and skyrmion-like state in ferroelectric nanodisks

The controllability of vortex state in ferroelectric nanodisks under the effect of external torsion is investigated in this work based on phase-field simulation. We discover a novel Bloch skyrmion-like state in ferroelectric nanodisks due to the combining effect of the torsion and the depolarization field. Moreover, a new strategy is proposed to achieve deterministic switching of the vortex chirality in the ferroelectric nanodisks. On the one hand, if a fixed external electric field is applied to the nanodisk, the vortex chirality can be switched by the torsion force. On the other hand, if we apply a fixed torsion force to the nanodisk, the vortex chirality can be readily switched by an external electric field. The feasibility of both mechanical and electrical switching of the vortex in the ferroelectric nanodisks is based on the trilinear coupling between the toroidization, polarization and shear strain of the system. The influences of temperature, electric field, torsion, and size of the nanodisk on the control of the vortex state are further revealed. Our findings shed light on the practical control and application of ferroelectric dipole vortices.

Skyrmions in the Moiré of van der Waals 2D Magnets

We explore the skyrmion formation and control possibilities in two-dimensional (2D) magnets from the ubiquitous moiré pattern in vdW heterostructures. Using the example of a ferromagnetic monolayer on an antiferromagnetic substrate, we demonstrate a new origin of skyrmions in the 2D magnets from the lateral modulation of interlayer magnetic coupling by the locally different atomic registries in moiré. The moiré skyrmions are doubly degenerate with opposite topological charge and trapped at an ordered array of sites with the moiré periodicity that can be dramatically tuned by strain and interlayer translation. At relatively strong interlayer coupling, the ground states are skyrmion lattices, where magnetic field can switch the skyrmion vorticity and location in the moiré. At weak interlayer coupling limit, we find metastable skyrmion excitations on the ferromagnetic ground state that can be deterministically moved between the ordered moiré trapping sites by current pulses. Our results point to potential uses of moiré skyrmions both as information carriers and as drastically tunable topological background of electron transport.

Universality of defect-skyrmion interaction profiles

Magnetic skyrmions are prime candidates for future spintronic devices. However, incorporating them as information carriers hinges on their interaction with defects ubiquitous in any device. Here we map from first-principles, the energy profile of single skyrmions interacting with single-atom impurities, establishing a generic shape as function of the defect’s electron filling. Depending on their chemical nature, foreign 3d and 4d transition metal adatoms or surface implanted defects can either repel or pin skyrmions in PdFe/Ir(111) thin films, which we relate to the degree of filling of bonding and anti-bonding electronic states inherent to the proximity of the non-collinear magnetic structure. Similarities with key concepts of bond theories in catalysis and surface sciences imbue the universality of the shape of the interaction profile and the potential of predicting its interaction. The resulting fundamental understanding may give guidance for the design of devices with surface implanted defects to generate and control skyrmions.

Clear understanding of the influence from material inhomogeneities and defects is one of the keys to achieve reliable Skyrmion based devices. Here the authors report their first principles studies on the interaction of single skyrmions with single-atom impurities and reveal its universal shape originated from the defect’s electron filling.

Skyrmion-Mediated Voltage-Controlled Switching of Ferromagnets for Reliable and Energy-Efficient Two-Terminal Memory

We propose a two-terminal nanomagnetic memory element based on magnetization reversal of a perpendicularly magnetized nanomagnet employing a unipolar voltage pulse that modifies the perpendicular anisotropy of the system. Our work demonstrates that the presence of Dzyaloshinskii-Moriya interaction can create an alternative route for magnetization reversal that obviates the need for utilizing precessional magnetization dynamics as well as a bias magnetic field that are employed in traditional voltage control of magnetic anisotropy (VCMA)-based switching of perpendicular magnetization. We show with extensive micromagnetic simulation, in the presence of thermal noise, that the proposed skyrmion-mediated VCMA switching mechanism is robust at room temperature leading to extremely low error switching while also being potentially 1-2 orders of magnitude more energy efficient than state-of-the-art spin transfer torque-based switching.

Spin-Wave-Driven Skyrmion Motion in Magnetic Nanostrip

The photon-assisted magnetic recording utilizes the ultrafast laser to excite the spin wave in the magnetic nanostructures and accordingly switch its magnetization state. Here, by means of micromagnetic simulation, the motion of magnetic skyrmions, a topologically protected chiral magnet with few nanometer size, induced by the spin wave is studied. It is found that the magnetic skyrmion can move in the same direction of spin-wave propagation, which is first accelerated and then decelerated exponentially. The magnetic skyrmion motion originated from the robust coupling of the spin waves with the skyrmion, through the SW’s linear momentum transfer torque acting on the skyrmion. Besides amplitude, the reflectivity of the spin wave by skyrmion has tremendous impact on the velocity of skyrmion motion. The skyrmion velocities are mainly determined by the reflectivity, when the spin-wave amplitude is almost identical. Our results give guidance for the design and development of spin-wave control spintronics.

Skyrmion electrical detection with the use of three-dimensional Topological Insulators/Ferromagnetic bilayers

The effect of the magnetic skyrmion texture on the electronic transport properties of the TI surface state coupled to a thin-film FM is numerically investigated. It is shown that both Bloch (vortex) and Néel (hedgehog) skyrmion textures induce additional scattering on top of a homogeneous background FM texture which can modify the conductance of the system. The change in conductance depends on several factors including the skyrmion size, the dimensions of the FM and the exchange interaction strength. For the Néel skyrmion, the result of the interaction strongly depends on the skyrmion number N sk and the skyrmion helicity h. For both skyrmion types, significant change of the resistance can be achieved, which is in the order of kΩ.

A nontrivial crossover in topological Hall effect regimes

We propose a new theory of the topological Hall effect (THE) in systems with non-collinear magnetization textures such as magnetic skyrmions. We solve the problem of electron scattering on a magnetic skyrmion exactly, for an arbitrary strength of exchange interaction and the skyrmion size. We report the existence of different regimes of THE and resolve the apparent contradiction between the adiabatic Berry phase theoretical approach and the perturbation theory for THE. We traced how the topological charge Hall effect transforms into the spin Hall effect upon varying the exchange interaction strength or the skyrmion size. This transformation has a nontrivial character: it is accompanied by an oscillating behavior of both charge and spin Hall currents. This hallmark of THE allows one to identify the chirality driven contribution to Hall response in the experiments.

Field-free deterministic ultrafast creation of magnetic skyrmions by spin-orbit torques

Magnetic skyrmions are stabilized by a combination of external magnetic fields, stray field energies, higher-order exchange interactions and the Dzyaloshinskii-Moriya interaction (DMI). The last favours homochiral skyrmions, whose motion is driven by spin-orbit torques and is deterministic, which makes systems with a large DMI relevant for applications. Asymmetric multilayers of non-magnetic heavy metals with strong spin-orbit interactions and transition-metal ferromagnetic layers provide a large and tunable DMI. Also, the non-magnetic heavy metal layer can inject a vertical spin current with transverse spin polarization into the ferromagnetic layer via the spin Hall effect. This leads to torques that can be used to switch the magnetization completely in out-of-plane magnetized ferromagnetic elements, but the switching is deterministic only in the presence of a symmetry-breaking in-plane field. Although spin-orbit torques led to domain nucleation in continuous films and to stochastic nucleation of skyrmions in magnetic tracks, no practical means to create individual skyrmions controllably in an integrated device design at a selected position has been reported yet. Here we demonstrate that sub-nanosecond spin-orbit torque pulses can generate single skyrmions at custom-defined positions in a magnetic racetrack deterministically using the same current path as used for the shifting operation. The effect of the DMI implies that no external in-plane magnetic fields are needed for this aim. This implementation exploits a defect, such as a constriction in the magnetic track, that can serve as a skyrmion generator. The concept is applicable to any track geometry, including three-dimensional designs.

Magnetic skyrmions without the skyrmion Hall effect in a magnetic nanotrack with perpendicular anisotropy

Magnetic skyrmions have potential applications in novel information devices with excellent energy efficiency. However, the skyrmion Hall effect (SkHE) could cause skyrmions moving in a nanotrack to get annihilated at the track edge. In this work, we discovered that the SkHE is depressed by modifying the magnetic structure at the edge of a track, and thus the skyrmion can move in almost a straight line at a high speed. Unlike the inner part of a track with perpendicular magnetic anisotropy, the edge layer exhibits in-plane magnetic anisotropy, and the orientation of edge moments is opposite that at the perimeter of skyrmions nearby. As a result, an enhanced repulsive force acts on the skyrmion to oppose the Magnus force that causes the SkHE. Additionally, the Dzyaloshinskii-Moriya interaction (DMI) constant of the edge layer also matters. When there is no DMI at the edge layer, the transverse displacement of the skyrmion can be depressed effectively when the width of the edge layer is sufficiently large. However, when the inner part and the edge share the same DMI constant, non-monotonically varied transverse displacement occurs because of the Néel-wall-like structure at the edge layer.

Quenching of Charge and Spin Degrees of Freedom in Condensed Matter

Electrons in condensed matter have internal degrees of freedom, such as charge, spin, and orbital, leading to various forms of ordered states through phase transitions. However, in individual materials, a charge/spin/orbital ordered state of the lowest temperature is normally uniquely determined in terms of the lowest-energy state, i.e., the ground state. Here, recent results are summarized showing that under rapid cooling, this principle does not necessarily hold, and thus, the cooling rate is a control parameter of the lowest-temperature state beyond the framework of the thermoequilibrium phase diagram. Although the cooling rate utilized in low-temperature experiments is typically 2 × 10^-3 to 4 × 10^-1 K s^-1 , the use of optical/electronic pulses facilitates rapid cooling, such as 10² -10³ K s^-1 . Such an unconventionally high cooling rate allows some systems to kinetically avoid a first-order phase transition, resulting in a quenched charge/spin state that differs from the ground state. It is also demonstrated that quenched states can be exploited as a non-volatile state variable when designing phase-change memory functions. The present findings suggest that rapid cooling is useful for exploring and controlling the metastable electronic/magnetic state, which is potentially hidden behind the ground state.

Self-consistent mean field theory studies of the thermodynamics and quantum spin dynamics of magnetic Skyrmions

A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S  =  1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.

An Improved Racetrack Structure for Transporting a Skyrmion

Magnetic skyrmions are promising building blocks for next generation data storage due to their stability, small size and extremely low currents to drive them, which can be used instead of traditional magnetic domain walls to store information as data bits in metalic racetrack memories. However, skyrmions can drift from the direction of electron flow due to the Magnus force and thus may annihilate at the racetrack edges, resulting in the loss of information. Here we propose a new skyrmion-based racetrack structure by adding high-K materials (materials with high magnetic crystalline anisotropy) at the edges, which confines the skyrmions in the center region of the metalic racetrack efficiently. This design can overcome both the clogging and annihilation of skyrmions according to our micromagnetic simulation, which occur normally for skyrmions moving on a racetrack under small and large driving currents, respectively. Phase diagrams for skyrmion motion on the proposed racetrack with various values of current density and racetrack edge width have been calculated and given, showing that skyrmions can be driven at a high speed (about 300 m/s) in the racetrack under relatively smaller driving currents. This design offers the possiblity of building an ultrafast and energy-efficient skyrmion transport device.

Observation of stable Néel skyrmions in cobalt/palladium multilayers with Lorentz transmission electron microscopy

Néel skyrmions are of high interest due to their potential applications in a variety of spintronic devices, currently accessible in ultrathin heavy metal/ferromagnetic bilayers and multilayers with a strong Dzyaloshinskii–Moriya interaction. Here we report on the direct imaging of chiral spin structures including skyrmions in an exchange-coupled cobalt/palladium multilayer at room temperature with Lorentz transmission electron microscopy, a high-resolution technique previously suggested to exhibit no Néel skyrmion contrast. Phase retrieval methods allow us to map the internal spin structure of the skyrmion core, identifying a 25 nm central region of uniform magnetization followed by a larger region characterized by rotation from in- to out-of-plane. The formation and resolution of the internal spin structure of room temperature skyrmions without a stabilizing out-of-plane field in thick magnetic multilayers opens up a new set of tools and materials to study the physics and device applications associated with chiral ordering and skyrmions.

Néel skyrmions are spin textures with a magnetization that rotates from in- to out-of-plane with distance from its centre. Here, the authors show that Lorentz transmission electron microscopy can be used to directly image Néel skyrmions with high resolution in thick exchange-coupled magnetic multilayers.

Room-Temperature Skyrmion Shift Device for Memory Application

Magnetic skyrmions are intensively explored for potential applications in ultralow-energy data storage and computing. To create practical skyrmionic memory devices, it is necessary to electrically create and manipulate these topologically protected information carriers in thin films, thus realizing both writing and addressing functions. Although room-temperature skyrmions have been previously observed, fully electrically controllable skyrmionic memory devices, integrating both of these functions, have not been developed to date. Here, we demonstrate a room-temperature skyrmion shift memory device, where individual skyrmions are controllably generated and shifted using current-induced spin-orbit torques. Particularly, it is shown that one can select the device operation mode in between (i) writing new single skyrmions or (ii) shifting existing skyrmions by controlling the magnitude and duration of current pulses. Thus, we electrically realize both writing and addressing of a stream of skyrmions in the device. This prototype demonstration brings skyrmions closer to real-world computing applications.

Controlling skyrmion helicity via engineered Dzyaloshinskii-Moriya interactions

Single magnetic skyrmion dynamics in chiral magnets with a spatially inhomogeneous Dzyaloshinskii-Moriya interaction (DMI) is considered. Based on the relation between DMI coupling and skyrmion helicity, it is argued that the latter must be included as an extra degree of freedom in the dynamics of skyrmions. An effective description of the skyrmion dynamics for an arbitrary inhomogeneous DMI coupling is obtained through the collective coordinates method. The resulting generalized Thiele equation is a dynamical system for the center of mass position and helicity of the skyrmion. It is found that the dissipative tensor and hence the Hall angle become helicity dependent. The skyrmion position and helicity dynamics are fully characterized by our model in two particular examples of engineered DMI coupling: half-planes with opposite-sign DMI and linearly varying DMI. In light of the experiment of Shibata et al (2013 Nat. Nanotechnol. 8 723) on the magnitude and sign of the DMI, our results constitute the first step toward a more complete understanding of the skyrmion helicity as a new degree of freedom that could be harnessed in future high-density magnetic storage and logic devices.

Skyrmions with Attractive Interactions in an Ultrathin Magnetic Film

We determined the parameters of a classical spin Hamiltonian describing an Fe monolayer on Pd(111) surface with a Pt_{1-x}Ir_{x} alloy overlayer from ab initio calculations. While the ground state of the system is ferromagnetic for x=0.00, it becomes a spin spiral state as Ir is intermixed into the overlayer. Although the Dzyaloshinsky-Moriya interaction is present in the system, we will demonstrate that the frustrated isotropic exchange interactions play a prominent role in creating the spin spiral state, and these frustrated couplings lead to an attractive interaction between Skyrmions at short distances. Using spin dynamics simulations, we show that under these conditions the individual Skyrmions form clusters, and that these clusters remain stable at finite temperature.

Magnetic Radial Vortex Stabilization and Efficient Manipulation Driven by the Dzyaloshinskii-Moriya Interaction and Spin-Transfer Torque

Solitons are very promising for the design of the next generation of ultralow power devices for storage and computation. The key ingredient to achieving this goal is the fundamental understanding of their stabilization and manipulation. Here, we show how the interfacial Dzyaloshinskii-Moriya Interaction (IDMI) is able to lift the energy degeneracy of a magnetic vortex state by stabilizing a topological soliton with radial chirality, hereafter called radial vortex. It has a noninteger Skyrmion number S (0.5<|S|<1) due to both the vortex core polarity and the magnetization tilting induced by the IDMI boundary conditions. Micromagnetic simulations predict that a magnetoresistive memory based on the radial vortex state in both free and polarizer layers can be efficiently switched by a threshold current density smaller than 10^{6}  A/cm^{2}. The switching processes occur via the nucleation of topologically connected vortices and vortex-antivortex pairs, followed by spin-wave emissions due to vortex-antivortex annihilations.

Electron Scattering on a Magnetic Skyrmion in the Nonadiabatic Approximation

We present a theory of electron scattering on a magnetic Skyrmion for the case when the exchange interaction is moderate so that the adiabatic approximation and the Berry phase approach are not applicable. The theory explains the appearance of a topological Hall current in the systems with magnetic Skyrmions, the special importance of which is its applicability to dilute magnetic semiconductors with a weak exchange interaction.