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Improvements in computing performance have significantly slowed down over the past few years owing to the intrinsic limitations of computing hardware. However, the demand for data computing has increased exponentially. To solve this problem, tremendous attention has been focused on the continuous scaling of Moore's Law as well as the advanced non-von Neumann computing architecture. A rich variety of unconventional computing paradigms has been raised with the rapid development of nanoscale devices. Magnetic skyrmions, spin swirling quasiparticles, have been endowed with great expectations for unconventional computing due to their potential as the smallest information carriers by exploiting their physics and dynamics. In this paper, we provide an overview of the recent progress of skyrmion-based unconventional computing from a joint device-application perspective. This paper aims to build up a panoramic picture, analyze the remaining challenges, and most importantly to shed light on the outlook of skyrmion based unconventional computing for interdisciplinary researchers., Comment: 9 Figure, 1 Table

Electrical manipulation of skyrmions attracts considerable attention for its rich physics and promising applications. To date, such a manipulation is realized mainly via spin-polarized current based on spin-transfer torque or spin-orbital torque effect. However, this scheme is energy-consuming and may produce massive Joule heating. To reduce energy dissipation and risk of heightened temperatures of skyrmion-based devices, an effective solution is to use electric field instead of current as stimulus. Here, we realize an electric-field manipulation of skyrmions in a nanostructured ferromagnetic/ferroelectrical heterostructure at room temperature via an inverse magneto-mechanical effect. Intriguingly, such a manipulation is non-volatile and exhibits a multi-state feature. Numerical simulations indicate that the electric-field manipulation of skyrmions originates from strain-mediated modification of effective magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Our results open a direction for constructing low-energy-dissipation, non-volatile, and multi-state skyrmion-based spintronic devices., Accepted by Nature Communications 11, 3577 (2020)

Frustrated topological spin textures have unique properties that may enable novel spintronic applications, such as helicity-based information storage and computing. Here, we report the statics and current-induced dynamics of two-dimensional (2D) pancake skyrmions in a stack of weakly coupled frustrated magnetic monolayers, which form a three-dimensional (3D) skyrmion string. The Bloch-type skyrmion string is energetically more stable than its N\'eel-type counterpart. It can be driven into translational motion by the dampinglike spin-orbit torque and shows the damping-dependent skyrmion Hall effect. Most notably, the skyrmion string can be transformed to a dynamically stable bimeron string by the dampinglike spin-orbit torque. The current-induced bimeron string rotates stably with respect to its center, which can spontaneously transform back to a skyrmion string when the current is switched off. Our results reveal unusual physical properties of 3D frustrated spin textures, and may open up different possibilities for spintronic applications based on skyrmion and bimeron strings., Comment: 6 pages, 3 figures

CeO2, TiO2, and CeO2–TiO2 layered thin films of different compositions were deposited on polished fused silica glass substrates using spin coating and then annealed at 550 °C for 1 h. Poorly crystalline fluorite-type CeO2 and anatase-type TiO2 were the only phases detected. The valence effects for Ce are attributed to intervalence charge transfer (IVCT) while those for TiO2 are attributed to simultaneous Ti4+ → Ti3+ redox and IVCT. Contamination of the grain boundaries by Si from the substrate is likely to have contributed to blockage of surface-active sites. While the roughnesses of the former thin films exhibited the expected direct correlation with the grain size, those of the latter two types of thin films showed a converse relation, suggesting that the grain boundaries of the layered TiO2 thin films included a recrystallized CeO2–TiO2 invariant point liquid and/or a CeO2–TiO2–SiO2 glass. These would have derived from the other sources of grain boundary contamination, which are Si contamination from the substrate and/or exsolved CeO2 beyond the solubility limit of TiO2. The UV–Vis spectra demonstrated two principal types of curves, with the CeO2 and higher TiO2 concentration giving typical spectra with sharp absorption edges while those of the lower TiO2 concentration indicated highly defective nanostructures with diffuse absorption edges. These data support the conclusion that CeO2 initially decreases the Eg by enhancing nucleation and recrystallization through defect formation but subsequently increases the Eg through supersaturation and consequent lattice distortion. The CeO2 thin films exhibited much worse photocatalytic performances than those of the TiO2 thin films, although no significant differences between the TiO2 thin films and the CeO2–TiO2 layered thin films were apparent, which probably resulted from the competing effects of blockage of the active sites on the grain boundaries and the extent of recrystallization of the thin film phases, the latter of which is more significant.

Racetrack memory (RM), a new storage scheme in which information flows along a nanotrack, has been considered as a potential candidate for future high-density storage device instead of hard disk drive (HDD). The first RM technology, which was proposed in 2008 by IBM, relies on a train of opposite magnetic domains separated by domain walls (DWs), named DW-RM. After 10 years of intensive research, a variety of fundamental advancements has been achieved; unfortunately, no product has been available until now. With increasing effort and resources dedicated to the development of DW-RM, it is likely that new materials and mechanisms will soon be discovered for practical applications. However, new concepts might also be on the horizon. Recently, an alternative information carrier, magnetic skyrmion, which was experimentally discovered in 2009, has been regarded as a promising replacement of DW for RM, named skyrmion-based RM (SK-RM). Intensive effort has been involved and amazing advances have been made in observing, writing, manipulating, and deleting individual skyrmions. So, what is the relationship between DW and skyrmion? What are the key differences between DW and skyrmion, or between DW-RM and SK-RM? What benefits could SK-RM bring and what challenges need to be addressed before application? In this review article, we intend to answer these questions through a comparative cross-layer study between DW-RM and SK-RM. This work will provide guidelines, especially for circuit and architecture researchers on RM.

In skyrmion-based racetrack memories, the information encoded by skyrmions may be destroyed due to the skyrmion Hall effect, which can be surmounted by using synthetic antiferromagnetic racetracks. Hence, the manipulation of skyrmions in synthetic antiferromagnetic racetracks is important for practical applications. Here, we computationally study the interaction between a pair of skyrmions and a locally modified region in a synthetic antiferromagnetic racetrack, where the perpendicular magnetic anisotropy or thickness is locally adjusted to be different from that of the rest region of the racetrack. It is found that the skyrmions can be attracted, repelled, and even trapped by the locally modified region in a controllable manner. Besides, we demonstrate that the skyrmion location can be precisely determined by the locally modified region. The possible manipulation of skyrmions by utilizing locally modified regions in a synthetic antiferromagnetic racetrack may be useful for future skyrmion-based applications., Comment: 5 pages, 4 figures

Topological spin textures can be found in both two-dimensional and three-dimensional nanostructures, which are of great importance to advanced spintronic applications. Here we report the current-induced skyrmion tube dynamics in three-dimensional synthetic antiferromagnetic (SyAF) bilayer and multilayer nanostructures. It is found that the SyAF skyrmion tube made of thinner sublayer skyrmions is more stable during its motion, which ensures that a higher speed of the skyrmion tube can be reached effectively at larger driving current. In the SyAF multilayer with a given total thickness, the current-induced deformation of the SyAF skyrmion tube decreases with an increasing number of interfaces; namely, the rigidity of the SyAF skyrmion tube with a given thickness increases with the number of ferromagnetic (FM) layers. For the SyAF multilayer with an even number of FM layers, the skyrmion Hall effect can be eliminated when the thicknesses of all FM layers are identical. Larger damping parameter leads to smaller deformation and slower speed of the SyAF skyrmion tube. Larger fieldlike torque leads to larger deformation and a higher speed of the SyAF skyrmion tube. Our results are useful for understanding the dynamic behaviors of three-dimensional topological spin textures and may provide guidelines for building SyAF spintronic devices., Comment: 8 pages, 6 figures

Magnetic skyrmionium can be used as a nanometer-scale non-volatile information carrier, which shows no skyrmion Hall effect due to its special structure carrying zero topological charge. Here, we report the static and dynamic properties of an isolated nanoscale skyrmionium in a frustrated magnetic monolayer, where the skyrmionium is stabilized by competing interactions. The frustrated skyrmionium has a size of about $10$ nm, which can be further reduced by tuning perpendicular magnetic anisotropy or magnetic field. It is found that the nanoscale skyrmionium driven by the damping-like spin-orbit torque shows directional motion with a favored Bloch-type helicity. A small driving current or magnetic field can lead to the transformation of an unstable N\'eel-type skyrmionium to a metastable Bloch-type skyrmionium. A large driving current may result in the distortion and collapse of the Bloch-type skyrmionium. Our results are useful for the understanding of frustrated skyrmionium physics, which also provide guidelines for the design of spintronic devices based on topological spin textures., Comment: 5 pages, 5 figures

Magnetic bimeron is a topological counterpart of skyrmions in in-plane magnets, which can be used as a spintronic information carrier. We report the static properties of bimerons with different topological structures in a frustrated ferromagnetic monolayer, where the bimeron structure is characterized by the vorticity $Q_{\text{v}}$ and helicity $\eta$. It is found that the bimeron energy increases with $Q_{\text{v}}$, and the energy of an isolated bimeron with $Q_{\text{v}}=\pm 1$ depends on $\eta$. We also report the dynamics of frustrated bimerons driven by the spin-orbit torques, which depend on the strength of the dampinglike and fieldlike torques. We find that the isolated bimeron with $Q_{\text{v}}=\pm 1$ can be driven into linear or elliptical motion when the spin polarization is perpendicular to the easy axis. We numerically reveal the damping dependence of the bimeron Hall angle driven by the dampinglike torque. Besides, the isolated bimeron with $Q_{\text{v}}=\pm 1$ can be driven into rotation by the dampinglike torque when the spin polarization is parallel to the easy axis. The rotation frequency is proportional to the driving current density. In addition, we numerically demonstrate the possibility of creating a bimeron state with a higher or lower topological charge by the current-driven collision and merging of bimeron states with different $Q_{\text{v}}$. Our results could be useful for understanding the bimeron physics in frustrated magnets., Comment: 13 pages, 12 figures

Magnetic skyrmion (Sk), instead of magnetic domain wall (DW), holds great promise as alternative information carriers in the future ultradense and low-power racetrack memory (RM). More importantly, by exploiting its unique properties, such as particle-like behavior and topological stability, Sk enables new functionalities that may be inaccessible to DW in RM applications. In this paper, we propose a complementary Sk-RM structure that enables voltage-controlled local data update functionality. Similar to our previous design in addressing the data representation issue, data information is represented in a robust way that both “0” and “1” are represented in the form of Sks and are moved synchronously by the spin Hall effect. Furthermore, this complementary Sk-RM structure can be developed for enabling local data update functionality, because Sks can be shifted between the two nanotracks by regulating the voltage-controlled gates. In this case, data bits “0” and “1” can be converted to each other freely within the nanotrack without being moved out of the nanotrack. This functionality brings great benefits in data access and management. Functionality and performance of the proposed design are studied with micromagnetic simulations.

The control of magnetic skyrmion creation and pinning through strain is studied by micromagnetic simulations. A single stable skyrmion can be created by a vertical strain pulse on Pd/Fe/Ir hybrid structure on Pb(Zr 1−x Ti x )O 3 nanowire with −1.8 V pulse voltage from 1.2 ns to 2.0 ns. Then the skyrmion is pinned by the vertical strain independent of the polarity during its propagation in the wire driven by the current. The proposed device integrates strain-controlled skyrmion creation and pinning in a single nanowire structure, which would open a new route for skyrmion-based memory and logic devices with ultra-low power consumption.

It is well known that magnetic domains in nanodisks can be used as storage units for computer memory. Using two quantum simulation approaches, we show here that spin vortices on magnetic monolayer nanodisks, which are chirality-free, can be induced by dipole-dipole interaction (DDI) on the disk-plane. When DDI is sufficiently strong, vortical and anti-vortical multi-domain textures can be generated simultaneously. Especially, a spin vortex can be easily created and deleted through either external magnetic or electrical signals, making them ideal to be used in nanomagnetic memory and logical devices. We demonstrate these properties in our simulations.

Racetrack memory (RM) has demonstrated great potential as nonvolatile mass storage in future advanced computer architectures. Domain wall (DW)-based RM first proposed in 2008 by IBM, however, suffers from challenges, such as storage density, scalability, and energy consumption. Recently, magnetic skyrmions, topologically protected particle-like spin textures, have expected to replace DWs as new information carriers in the RM design, owing to their superiorities to DWs in terms of topological stability, smaller size, as well as lower driving current density. Extensive investigations have been performed in skyrmion-based RM (Sky-RM) to date. Furthermore, skyrmions exhibits some unique properties that are inaccessible to DWs, thus enabling Sky-RM to explore some new functions that may be inaccessible to DW-RM. In this paper, a novel Sky-RM, capable of random information update/deletion/insertion, is proposed by exploiting the particle-like behaviors of skyrmions. Micromagnetic studies are performed to validate the function and performance of these novel data operations, which may bring performance benefits in data access operations and enable new applications.

Racetrack memory (RM) has been considered as one of the most attractive nonvolatile memories in the future advanced computer architectures. Current RM is based on domain wall (DW) motion, which, however, has some intrinsic limitations, such as scalability, density, and energy consumption owing to the physical property of DW. Recently, magnetic skyrmion, one new type of spintronic object, has emerged as an alternative of DW in RM application. The advantageous features of skyrmion, such as nanoscale size, topological stability, as well as ultralow depinning current density, make it promising as an information carrier in the future ultradense, high-speed, and low-power electronics in addition to RM design. In this paper, we primarily investigate the prospects of the skyrmion-based RM (Sky-RM). We developed a physics-based compact model for Sky-RM electronic design and performance evaluation. Experimentalmaterial parameterswere included and micromagnetic investigations were carried out simultaneously to calibrate the accuracy of the model. Using the developed model, hybrid simulations were performed to evaluate the Sky-RM performance, in comparison with the DW-based RM (DW-RM). Our results show that Sky-RM outperforms DW-RM in terms of storage density and energy efficiency.

Magnetic bimeron composed of two merons is a topological counterpart of magnetic skyrmion in in-plane magnets, which can be used as the nonvolatile information carrier in spintronic devices. Here we analytically and numerically study the dynamics of ferromagnetic bimerons driven by spin currents and magnetic fields. Numerical simulations demonstrate that two bimerons with opposite signs of topological numbers can be created simultaneously in a ferromagnetic thin film via current-induced spin torques. The current-induced spin torques can also drive the bimeron and its speed is analytically derived, which agrees with the numerical results. Since the bimerons with opposite topological numbers can coexist and have opposite drift directions, two-lane racetracks can be built in order to accurately encode the data bits. In addition, the dynamics of bimerons induced by magnetic field gradients and alternating magnetic fields are investigated. It is found that the bimeron driven by alternating magnetic fields can propagate along a certain direction. Moreover, combining a suitable magnetic field gradient, the Magnus-force-induced transverse motion can be completely suppressed, which implies that there is no skyrmion Hall effect. Our results are useful for understanding of the bimeron dynamics and may provide guidelines for building future bimeron-based spintronic devices., Comment: 8 pages, 8 figures

To enable functional skyrmion based spintronic devices, the controllable generation and manipulation of skyrmions is essential. While the generation of skyrmions by using a magnetic geometrical constriction has already been demonstrated, this approach is difficult to combine with a subsequent controlled manipulation of skyrmions. The high efficiency of skyrmion generation from magnetic constrictions limits the useful current density, resulting in stochastic skyrmion motion, which may obscure topological phenomena such as the skyrmion Hall effect. In order to address this issue, we designed a nonmagnetic conducting Ti/Au point contact in devices made of Ta/CoFeB/TaOx trilayer films. By applying high voltage pulses, we experimentally demonstrated that skyrmions can be dynamically generated. Moreover, the accompanied spin topology dependent skyrmion dynamics, the skyrmion Hall effect is also experimentally observed in the same devices. The creation process has been numerically reproduced through micromagnetic simulations in which the important role of skyrmion-antiskyrmion pair generation is identified. The motion and Hall effect of the skyrmions, immediately after their creation is described using a modified Thiele equation after taking into account the contribution from spatially inhomogeneous spin-orbit torques and the Magnus force. The simultaneous generation and manipulation of skyrmions using a nonmagnetic point contact could provide a useful pathway for designing novel skyrmion based devices., All comments are welcome

The antiferromagnetic skyrmion is a promising building block for future antiferromagnetic spintronic devices, which has several advantages, including ultrafast dynamics and zero skyrmion Hall angle. The understanding of the pinning and depinning of an antiferromagnetic skyrmion to defects is a prerequisite for skyrmion-based in-line motion applications, such as racetrack memory. Here, we numerically study the effect of two types of defects caused by the local decrease/increase of perpendicular magnetic anisotropy on the current-induced dynamics of an antiferromagnetic skyrmion, where the critical depinning current density of the skyrmion motion for different defects is determined under the framework of micromagnetics. We also provide an explanation for the complex behaviors of the antiferromagnetic skyrmion via energy landscape, which shows that the skyrmion always prefers to stay at a specific place with minimal energy. Furthermore, the current-induced motion of a skyrmion in an antiferromagnetic racetrack with defects is compared to that in a ferromagnetic racetrack. Our results are useful for the understanding of antiferromagnetic skyrmion physics at low temperatures and could provide guidelines for designing applications based on antiferromagnetic skyrmions.

Since the discovery of ferromagnetic two-dimensional (2D) van der Waals (vdW) crystals, significant interest on such 2D magnets has emerged, inspired by their appealing properties and integration with other 2D family for unique heterostructures. In known 2D magnets, spin-orbit coupling (SOC) stabilizes perpendicular magnetic anisotropy (PMA). Such a strong SOC could also lift the chiral degeneracy, leading to the formation of topological magnetic textures such as skyrmions through the Dzyaloshinskii-Moriya interaction (DMI). Here, we report the experimental observation of N\'eel-type chiral magnetic skyrmions and their lattice (SkX) formation in a vdW ferromagnet Fe3GeTe2 (FGT). We demonstrate the ability to drive individual skyrmion by short current pulses along a vdW heterostructure, FGT/h-BN, as highly required for any skyrmion-based spintronic device. Using first principle calculations supported by experiments, we unveil the origin of DMI being the interfaces with oxides, which then allows us to engineer vdW heterostructures for desired chiral states. Our finding opens the door to topological spin textures in the 2D vdW magnet and their potential device application., Comment: 26 pages, 5 figures

The direct imaging of inhomogeneous current distribution was demonstrated by using the polar magneto-optical Kerr microscopy., The direct imaging of current density vector distributions in thin films has remained a daring challenge. Here, we report that an inhomogeneous current distribution can be mapped directly by the trajectories of magnetic half-skyrmions driven by an electrical current in Pt/Co/Ta trilayer, using polar magneto-optical Kerr microscopy. The half-skyrmion carries a topological charge of 0.5 due to the presence of Dzyaloshinskii-Moriya interaction, which leads to the half-skyrmion Hall effect. The Hall angle of half-skyrmions is independent of current density and can be reduced to as small as 4° by tuning the thickness of the Co layer. The Hall angle is so small that the elongation path of half-skyrmion approximately delineates the invisible current flow as demonstrated in both a continuous film and a curved track. Our work provides a practical technique to directly map inhomogeneous current distribution even in complex geometries for both fundamental research and industrial applications.

A magnetic bimeron is a topologically non-trivial spin texture carrying an integer topological charge, which can be regarded as the counterpart of skyrmion in easy-plane magnets. The controllable creation and manipulation of bimerons are crucial for practical applications based on topological spin textures. Here, we analytically and numerically study the dynamics of an antiferromagnetic bimeron driven by a spin current. Numerical simulations demonstrate that the spin current can create an isolated bimeron in the antiferromagnetic thin film via the damping-like spin torque. The spin current can also effectively drive the antiferromagnetic bimeron without a transverse drift. The steady motion of an antiferromagnetic bimeron is analytically derived and is in good agreement with the simulation results. Also, we find that the alternating-current-induced motion of the antiferromagnetic bimeron can be described by the Duffing equation due to the presence of the nonlinear boundary-induced force. The associated chaotic behavior of the bimeron is analyzed in terms of the Lyapunov exponents. Our results demonstrate the inertial dynamics of an antiferromagnetic bimeron, and may provide useful guidelines for building future bimeron-based spintronic devices., 6 pages, 4 figures

We report the current-driven dynamics of frustrated skyrmions in an antiferromagnetically exchange coupled bilayer system, where the bilayer skyrmion consists of two monolayer skyrmions with opposite skyrmion numbers $Q$. We show that the in-plane current-driven bilayer skyrmion moves in a straight path, while the out-of-plane current-driven bilayer skyrmion moves in a circular path. It is found that the in-plane current-driven mobility of a bilayer skyrmion is much better than the monolayer one at a large ratio of $\beta/\alpha$, where $\alpha$ and $\beta$ denote the damping parameter and non-adiabatic spin transfer torque strength, respectively. Besides, the out-of-plane current-driven mobility of a bilayer skyrmion is much better than the monolayer one when $\alpha$ is small. We also reveal that one bilayer skyrmion (consisting of monolayer skyrmions with $Q=\pm 2$) can be separated to two bilayer skyrmions (consisting of monolayer skyrmions with $Q=\pm 1$) driven by an out-of-plane current. Our results may be useful for designing skyrmionic devices based on frustrated multilayer magnets., Comment: 7 pages, 4 figures

Magnetic skyrmions are topological quasiparticles with great potential for applications in future information storage and processing devices because of their nanoscale size, high stability, and large velocity. Recently, the high-frequency properties of skyrmions have been explored for magnon nanodevices. Here we systematically study the dynamics of an isolated skyrmion under voltage excitation through the voltage-controlled magnetic anisotropy effect in a circular thin film. A theoretical model considering the demagnetization energy, which has often been neglected or treated superficially in previous skyrmion research but is demonstrated to have importance in determining the skyrmion dynamic state, is developed. With our model, the periodic oscillation of the skyrmion radius can be solved numerically with similar precision compared to micromgnetic simulations, and the characteristic frequency of the skyrmion breathing can be determined analytically with greater precision than previous studies. Furthermore, we find that the breathing skyrmion can be analogized as a modulator by investigating its linear modulation functionality under sinusoidal-form voltage excitation. Different from the conventional modulation system with complex CMOS circuits, this skyrmion modulator device integrates with both the modulation and carrier wave generation functionality, thus showing greater convenience and efficiency in applications. Our findings can provide useful guidance for both theoretical and experimental skyrmions research as well as the development of skyrmion-based magnonic devices with significant potential applicability in future communication system., 29 pages, 8 figures

Perpendicular magnetic anisotropy can be induced when the atoms orbital anisotropy in the ultrathin ferromagnetic layer is reflected. Here, we computationally study a ferromagnetic skyrmion-based nano-oscillator model with a composite structure, where the skyrmion dynamics is controlled by modifying perpendicular magnetic anisotropy. The proposed nano-oscillator structure has two concentric circular areas with different anisotropy coefficients. When the anisotropy of the inner area is larger than that of the outer area, the inner area can provide a repulsive force acting on the skyrmion, leading to the motion of skyrmion along with the edge of the inner circular area. Three cases of skyrmion motion are found for different anisotropy coefficients. We also study the effects of each anisotropy coefficients and current density on the frequency of the skyrmion-based nano-oscillator. Our results provide a promising method to modulate the frequency of future skyrmion-based nano-oscillators.

Skyrmions in synthetic antiferromagnets (SAFs) could be immune to the skyrmion Hall effect and are, thus, promising in spintronics applications. We introduce breathing modes that can be realized by changing the magnetocrystalline anisotropy periodically in time to generate spin waves around a deformed SAF skyrmion. The net momentum transferred from the magnon spin currents results in a motion of the SAF skyrmion, which is two orders of magnitude faster than that of a ferromagnetic skyrmion. We also reveal that the velocity of the SAF skyrmion can be manipulated by the strength of antiferromagnetic coupling between layers, which is different from ferromagnetic and antiferromagnetic systems. This phenomenon originates from the damping-like character of the antiferromagnetic coupling and offers a dimension to optimize skyrmion dynamics in SAFs.

The magnetic skyrmionium can be seen as a coalition of two magnetic skyrmions with opposite topological charges and has potential applications in next-generation spintronic devices. Here, we report the current-driven dynamics of a skyrmionium in a ferromagnetic nanotrack with the voltage-controlled magnetic anisotropy. The pinning and depinning of a skyrmionium controlled by the voltage gate are investigated. The current-driven skyrmionium can be used to mimic the skyrmionium diode effect in the nanotrack with a voltage gate. We have further studied the skyrmionium dynamics in the nanotrack driven by a magnetic anisotropy gradient in the absence of spin current. The performance of a single wedge-shaped voltage gate at different temperatures is studied. Our results may provide useful guidelines for the design of voltage-controlled and skyrmionium-based spintronic devices.

Non-interacting particles exhibiting Brownian motion have been observed in many occasions of sciences, such as molecules suspended in liquids, optically trapped microbeads, and spin textures in magnetic materials. In particular, a detailed examination of Brownian motion of spin textures is important for designing thermally stable spintronic devices which motivates the present study. In this Letter, through using temporally and spatially resolved polar magneto-optic Kerr effect (MOKE) microscopy, we have experimentally observed the thermal fluctuation-induced random walk of a single isolated N\'eel-type magnetic skyrmion in an interfacially asymmetric Ta/CoFeB/TaOx multilayer. An intriguing topology dependent Brownian gyromotion behavior of skyrmions has been identified. The onset of Brownian gyromotion of a single skyrmion induced by the thermal effects, including a nonlinear temperature-dependent diffusion coefficient and topology-dependent gyromotion are further formulated based on the stochastic Thiele equation. The experimental and numerical demonstration of topology-dependent Brownian gyromotion of skyrmions can be useful for understanding the nonequilibrium magnetization dynamics and implementing spintronic devices.

Antiferromagnets are promising materials for future spintronic applications due to their unique properties including zero stray fields, robustness versus external magnetic fields and ultrafast dynamics, which have attracted extensive interest in recent years. In this work, we investigate the dynamics of isolated skyrmions in an antiferromagnetic nanotrack with a voltage-gated region. It is found that the skyrmion can be jointly controlled by the driving current and the voltage-controlled magnetic anisotropy gradient. We further propose a design of logic computing gates based on the manipulation of antiferromagnetic skyrmions, which is numerically realized combining several interactions and phenomena, including the spin Hall effect, voltage-controlled magnetic anisotropy effect, skyrmion-skyrmion interaction, and skyrmion-edge interaction. The proposed logic gates can perform the basic Boolean operations of the logic AND, OR, NOT, NAND and NOR gates. Our results may have a great impact on fundamental physics, and be useful for designing future non-volatile logic computing devices with ultra-low energy consumption and ultra-high storage density., Comment: 23 pages, 5 figures

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., Comment: 80 pages, 14 figures

Magnetic skyrmions are particle-like topological spin configurations, which can carry binary information and thus are promising building blocks for future spintronic devices. In this work, we investigate the relationship between the skyrmion dynamics and the characteristics of injected current in a skyrmion-based spin torque nano-oscillator, where the excitation source is introduced from a point nano-contact at the center of the nanodisk. It is found that the skyrmion will move away from the center of the nanodisk if it is driven by a spin-polarized current; however, it will return to the initial position in the absence of stimulus. Therefore, we propose a skyrmion-based artificial spiking neuron, which can effectively implement the leaky-integrate-fire operation. We study the feasibility of the skyrmion-based spiking neuron by using micromagnetic simulations. Our results may provide useful guidelines for building future magnetic neural networks with ultra-high density and ultra-low energy consumption., 5 pages, 5 figures

Magnetic skyrmions have attracted great interest in recent years due to their potential wide-scale applications in spintronic devices, such as the spin torque nano-oscillator (STNO) and racetrack memory. The spin-transfer torque can drive the motion of skyrmions on a ferromagnetic nanodisk, where skyrmions are stabilized by the Dzyaloshinskii-Moriya interaction (DMI). However, the Magnus force acted on a skyrmion can drive the skyrmion moving toward either the nanodisk center or edge, which may lead to the destruction of skyrmion at edge, and thus reduce the performance of skyrmion-based STNO. In order to overcome this problem, we designed a ferromagnet/spacer/ferromagnet/heavy metal STNO model, in which the inner and outer areas of the ferromagnetic nanodisk have different DMI, and those skyrmions could move along the boundary between inner and outer areas. We investigated the dynamics of skyrmions in such a STNO model by adjusting several geometrical and material parameters. We obtained an optimal frequency of skyrmion oscillation of 3.43 GHz. Our results may be useful for designing future STNOs based on skyrmions, where the Magnus-force-induced destruction of skyrmions can be effectively avoided.

Magnetic skyrmions could serve as information carriers in next-generation information storage and processing devices. Effective manipulation of the skyrmion motion is a vital task for realizing skyrmion-based applications. Skyrmion motion driven by voltage-controlled magnetic anisotropy (VCMA) has been proposed, of which the investigation is mostly focused on the dynamics of skyrmions. Here, using micromagnetic simulations we show that antiskyrmions can be effectively driven by the VCMA gradient in the presence of the anisotropic Dzyaloshinskii-Moriya interaction. We find that the antiskyrmion shows a transverse motion, i.e., the skyrmion Hall effect, induced by the VCMA gradient. As the skyrmion number of an antiskyrmion is opposite to that of a skyrmion, the anisotropy gradient-induced motion of ferromagnetically coupled skyrmion-antiskyrmion pair and antiferromagnetically coupled skyrmion-skyrmion and antiskyrmion-antiskyrmion pairs do not show the skyrmion Hall effect. We find that the velocity-driving force relations of these three combinations are different. Our results may provide guidelines for building future skyrmion-based information processing applications.

Skyrmion-based spin torque nano-oscillators are potential next-generation microwave signal generators. However, ferromagnetic skyrmion-based spin torque nano-oscillators cannot reach high oscillation frequencies. In this work, we propose to use the circular motion of an antiferromagnetic skyrmion to create the oscillation signal in order to overcome this obstacle. Micromagnetic simulations demonstrate that the antiferromagnetic skyrmion-based spin torque nano-oscillators can produce high frequencies (tens of GHz). Furthermore, the speed of the circular motion for an antiferromagnetic skyrmion in a nanodisk is analytically derived, which agrees well with the results of numerical simulations. Our findings are useful for the understanding of the inertial dynamics of an antiferromagnetic skyrmion and the development of future skyrmion-based spin torque nano-oscillators., 17 pages, 3 figures

The dynamics of antiferromagnets is a current hot topic in condensed matter physics and spintronics. However, the dynamics of insulating antiferromagnets cannot be excited by an electric current, which is a method usually used to manipulate ferromagnetic metals. Here, we propose to use the voltage-controlled magnetic anisotropy gradient as an excitation source to manipulate insulating antiferromagnetic textures. We analytically and numerically study the dynamics of an antiferromagnetic skyrmion driven by a magnetic anisotropy gradient. Our analytical calculations demonstrate that such a magnetic anisotropy gradient can effectively drive an antiferromagnetic skyrmion towards the area of lower magnetic anisotropy. The micromagnetic simulations are in good agreement with our analytical solution. Furthermore, the magnetic anisotropy gradient induced velocity of an antiferromagnetic skyrmion is compared with that of a ferromagnetic skyrmion. Our results are useful for the understanding of antiferromagnetic skyrmion dynamics and may open a new way for the design of antiferromagnetic spintronic devices., 19 pages, 3 figures

With the recent proposition of skyrmion utilization in racetrack memories at room temperature, skyrmionics has become a very attractive field. However, for the stability of skyrmions, it is essential to incorporate the Dzyaloshinskii-Moriya interaction (DMI) and the out-of-plane magnetic field into the system. In this work, we explore a system without these interactions. First, we propose a controlled way for the creation of magnetic skyrmions and skyrmioniums imprinted on a ferromagnetic nanotrack via a nanopatterned nanodisk with the magnetic vortex state. Then we investigate the detachment of the imprinted spin textures from the underneath of the nanodisk, as well as its transport by the spin-transfer torque imposed by spin-polarized current pulses applied in the nanotrack. A prominent feature of the moving imprinted spin texture is that its topological number Q is oscillating around the averaged value of Q=0 as if it is a resonant state between the skyrmions with Q= +/- 1 and the bubble with Q=0. We may call it a resonant magnetic soliton (RMS). A RMS moves along a straight line since it is free from the skyrmion Hall effect. In our studied device, the same electrodes are employed to realize the imprinted spin texture detachment and its transport. In addition, we have investigated the interaction between the RMS and a magnetic tunnel junction sensor, where the passing of the RMS in the nanotrack can be well detected. Our results would be useful for the development of novel spintronic devices based on moveable spin textures., 8 pages, 8 figures

In this work, we demonstrate that skyrmions can be nucleated in the free layer of a magnetic tunnel junction (MTJ) with Dzyaloshinskii-Moriya interactions (DMI) by a spin-polarized current with the assistance of stray fields from the pinned layer. The size, stability and number of created skyrmions can be tuned by either the DMI strength or the stray field distribution. The interaction between the stray field and the DMI effective field is discussed. A device with multi-level tunneling magnetoresistance is proposed, which could pave the ways for skyrmion-MTJ-based multi-bit storage and artificial neural network computation. Our results may facilitate the efficient nucleation and electrical detection of skyrmions., Comment: 4 figure in main text,14 figure in the supplementary information

Neuromorphic computing, which relies on a combination of a large number of neurons massively interconnected by an even larger number of synapses, has been actively studied for its characteristics such as energy efficiency, intelligence, and adaptability. To date, while the development of artificial synapses has shown great progress with the introduction of emerging nanoelectronic devices, e.g., memristive devices, the implementation of artificial neurons, however, depends mostly on semiconductor-based circuits via integrating many transistors, sacrificing energy efficiency and integration density. Here, we present a novel compact neuron device that exploits the current-driven magnetic skyrmion dynamics in a wedge-shaped nanotrack. Under the coaction of the exciting current pulse and the repulsive force exerted by the nanotrack edges, the dynamic behavior of the proposed skyrmionic artificial neuron device is in analogy to the leaky–integrate–fire (LIF) spiking function of a biological neuron. The tunable temporary location of the skyrmion in our artificial neuron behaves like the analog membrane potential of a biological neuron. The neuronal dynamics and the related physical interpretations of the proposed skyrmionic neuron device are carefully investigated via micromagnetic and theoretical methods. Such a compact artificial neuron enables energy-efficient and high-density implementation of neuromorphic computing hardware.

Magnetic skyrmions are promising information carriers for building future high-density and high-speed spintronic devices. However, to achieve a current-driven high-speed skyrmion motion, the required driving current density is usually very large, which could be energy inefficient and even destroy the device due to Joule heating. Here, we propose a voltage-driven skyrmion motion approach in a skyrmion shift device made of magnetic nanowires. The high-speed skyrmion motion is realized by utilizing the voltage shift, and the average skyrmion velocity reaches up to 259 m/s under 0.45 V applied voltage. In comparison with the widely studied vertical current-driven model, the energy dissipation is three orders of magnitude lower in our voltage-driven model, for the same speed motion of skyrmions. Our approach uncovers valuable opportunities for building skyrmion racetrack memories and logic devices with both ultra-low power consumption and ultra-high processing speed, which are appealing features for future spintronic applications.

The demagnetization process in hard/soft multilayer systems has been investigated systematically within a self-contained micromagnetic model when a deviation angle β between the easy axis and the applied field exists. Hysteresis loops, spin distributions and energy products have been calculated with a finite hard layer thickness t h . Both remanence and coercivity of the multilayer system decrease as β increases, leading to a significant decrease of the maximum energy product. A 30° deviation of the easy axis could result in a drop of the maximum energy product by more than 60%, which offers a possible explanation on the large discrepancy between the experimental and theoretical energy products. The effect of the finite hard layer thickness on the demagnetization process is important, which can only be ignored when t h is large enough.

Nd-Fe-B films with perpendicular magnetic anisotropy are important for various applications. Most common process to prepare Nd-Fe-B thin films with perpendicular magnetic anisotropy is the heteroepitaxy process. Here, Nd-Fe-B thin films with perpendicular magnetic anisotropy were prepared by a two-step process. Amorphous and magnetically soft thin films were first deposited. Crystallized, magnetic hard thin films were obtained by rapid thermal annealing of the as-deposited films. A clear correlation between perpendicular magnetic anisotropy of annealed state and the domain configuration in the as-deposited state was noticed. Films prepared without substrate heating, with additions of Tb show perpendicular coercivity which is larger than 24 kOe.

Magnetic skyrmions are promising candidates for future information technology. Here, we present a micromagnetic study of isolated skyrmions and skyrmion clusters in ferromagnetic nanodisks driven by the spin-polarized current with spatially varied polarization. The current-driven skyrmion clusters can be either dynamic steady or static, depending on the spatially varied polarization profile. For the dynamic steady state, the skyrmion cluster moves in a circle in the nanodisk, while for the static state, the skyrmion cluster is static. The frequency of the circular motion of skyrmion is also studied. Furthermore, the dependence of the skyrmion cluster dynamics on the magnetic anisotropy and Dzyaloshinskii-Moriya interaction is investigated. Our results may provide a pathway to realize magnetic skyrmion cluster based devices., Comment: 5 pages, 5 figures

The magnetic skyrmionium is a skyrmion-like structure but carries a zero net skyrmion number, which can be used as a building block for non-volatile information processing devices. Here, we study the dynamics of a magnetic skyrmionium driven by propagating spin waves. It is found that the skyrmionium can be effectively driven into motion by spin waves showing tiny skyrmion Hall effect, of which the mobility is much better than that of the skyrmion at the same condition. We also show that the skyrmionium mobility depends on the nanotrack width and damping coefficient, and can be controlled by an external out-of-plane magnetic field. Besides, we demonstrate the skyrmionium motion driven by spin waves is inertial. Our results indicate that the skyrmionium is a promising building block for building spin-wave spintronic devices., Comment: 5 pages, 6 figures

The helicity-orbital coupling is an intriguing feature of magnetic skyrmions in frustrated magnets. Here, we explore the skyrmion dynamics in a frustrated magnet based on the $J_{1}$-$J_{2}$-$J_{3}$ classical Heisenberg model explicitly by including the dipole-dipole interaction. The skyrmion energy acquires a helicity dependence due to the dipole-dipole interaction, resulting in the current-induced translational motion with a fixed helicity. The lowest energy states are the degenerate Bloch-type states, which can be used for building the binary memory. By increasing the driving current, the helicity locking-unlocking transition occurs, where the translational motion changes to the rotational motion. Furthermore, we demonstrate that two skyrmions can spontaneously form a bound state. The separation of the bound state forced by a driving current is also studied. In addition, we show the annihilation of a pair of skyrmion and antiskyrmion. Our results reveal the distinctive frustrated skyrmions may enable viable applications in topological magnetism., 10 pages, 10 figures

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.

Spintronic devices based on magnetic skyrmions are a promising candidate for next-generation memory applications due to their nanometre-size, topologically-protected stability and efficient current-driven dynamics. Since the recent discovery of room-temperature magnetic skyrmions, there have been reports of current-driven skyrmion displacement on magnetic tracks and demonstrations of current pulse-driven skyrmion generation. However, the controlled annihilation of a single skyrmion at room temperature has remained elusive. Here we demonstrate the deterministic writing and deleting of single isolated skyrmions at room temperature in ferrimagnetic GdFeCo films with a device-compatible stripline geometry. The process is driven by the application of current pulses, which induce spin-orbit torques, and is directly observed using a time resolved nanoscale X-ray imaging technique. We provide a current-pulse profile for the efficient and deterministic writing and deleting process. Using micromagnetic simulations, we also reveal the microscopic mechanism of the topological fluctuations that occur during this process., Comment: 27 pages, 4 figures

Nanoscale magnetic junction provides a useful approach to act as the building block for magnetoresistive random access memories (MRAM), where one of the key issues is to control the magnetic domain configuration. Here, we study the domain structure and the magnetic switching in the Permalloy (Fe20Ni80) nanoscale magnetic junctions with different thicknesses by using micromagnetic simulations. It is found that both the 90-degree and 45-degree domain walls can be formed between the junctions and the wire arms depending on the thickness of the device. The magnetic switching fields show distinct thickness dependencies with a broad peak varying from 7 nm to 22 nm depending on the junction sizes, and the large magnetic switching fields favor the stability of the MRAM operation., 9 pages,5 figures

Spin-Cherenkov effect enables strong excitations of spin waves (SWs) with nonlinear wave dispersions. The Dzyaloshinskii-Moriya interaction (DMI) results in anisotropy and nonreciprocity of SWs propagation. In this work, we study the effect of the interfacial DMI on SW Cherenkov excitations in permalloy thin-film strips within the framework of micromagnetism. By performing micromagnetic simulations, it is shown that coherent SWs are excited when the velocity of a moving magnetic source exceeds the propagation velocity of the SWs. Moreover, the threshold velocity of the moving magnetic source with finite DMI can be reduced compared to the case of zero DMI. It thereby provides a promising route towards efficient SW generation and propagation, with potential applications in spintronic and magnonic devices., 6 pages, 5 figures. To be published in Scientific Reports

Magnetic skyrmion, vortex-like swirling topologically stable spin configurations, is appealing as information carrier for future nanoelectronics, owing to the stability, small size and extremely low driving current density. One of the most promising applications of skyrmion is to build racetrack memory (RM). Compared to domain wall-based RM (DW-RM), skyrmion-based RM (Sky-RM) possesses quite a few benefits in terms of energy, density and speed etc. Until now, the fundamental behaviors, including nucleation/annihilation, motion and detection of skyrmion have been intensively investigated. However, one indispensable function, i.e., pinning/depinning of skyrmion still remains an open question and has to be addressed before applying skyrmion for RM. Furthermore, Current research mainly focuses on physical investigations, whereas the electrical design and evaluation are still lacking. In this work, we aim to promote the development of Sky-RM from fundamental physics to realistic electronics. First, we investigate the pinning/depinning characteristics of skyrmion in a nanotrack with the voltage-controlled magnetic anisotropy (VCMA) effect. Then, we propose a compact model and design framework of Sky-RM for electrical evaluation. This work completes the elementary memory functionality of Sky-RM and fills the technical gap between the physicists and electronic engineers, making a significant step forward for the development of Sky-RM., Comment: 10 pages, 8 figures

A magnetic skyrmion is a topological magnetization structure with a nanometric size and a well-defined swirling spin distribution, which is anticipated to be an essential building block for novel skyrmion-based device applications. We study the motion of magnetic skyrmions in multilayer synthetic antiferromagnetic (SAF) racetracks as well as in conventional monolayer ferromagnetic (FM) racetracks at finite temperature. There is an odd-even effect of the constituent FM layer number on the skyrmion Hall effect (SkHE). Namely, due to the suppression of the SkHE, the magnetic skyrmion has no transverse motion in multilayer SAF racetracks packed with even FM layers. It is shown that a moving magnetic skyrmion is stable even at room temperature ($T=300$ K) in a bilayer SAF racetrack but it is destructed at $T=100$ K in a monolayer FM racetrack. Our results indicate that the SAF structures are reliable and promising candidates for future applications in skyrmion-electronics and skyrmion-spintronics., 12 pages, 8 figures

Magnetic skyrmions might be used as information carriers in future advanced memories, logic gates and computing devices. However, there exists an obstacle known as the skyrmion Hall effect (SkHE), that is, the skyrmion trajectories bend away from the driving current direction due to the Magnus force. Consequently, the skyrmions in constricted geometries may be destroyed by touching the sample edges. Here we theoretically propose that the SkHE can be suppressed in the antiferromagnetically exchange-coupled bilayer system, since the Magnus forces in the top and bottom layers are exactly cancelled. We show that such a pair of SkHE-free magnetic skyrmions can be nucleated and be driven by the current-induced torque. Our proposal provides a promising means to move magnetic skyrmions in a perfectly straight trajectory in ultra-dense devices with ultra-fast processing speed., Magnetic skyrmions propagating under an applied current along a nanowire experience the magnus force, deflecting them towards the edges where they may be destroyed, potentially hindering their applications. Here, the authors propose a method to surpass this issue utilizing magnetic bilayers systems.

A magnetic skyrmionium is a nontopological soliton, which has a doughnut-like out-of-plane spin texture in thin films, and can be phenomenologically viewed as a coalition of two topological magnetic skyrmions with opposite topological numbers. Due to its zero topological number ($Q=0$) and doughnut-like structure, the skyrmionium has its distinctive characteristics as compared to the skyrmion with $Q=\pm 1$. Here we systematically study the generation, manipulation and motion of a skyrmionium in ultrathin magnetic nanostructures by applying a magnetic field or a spin-polarized current. It is found that the skyrmionium moves faster than the skyrmion when they are driven by the out-of-plane current, and their velocity difference is proportional to the driving force. However, the skyrmionium and skyrmion exhibit an identical current-velocity relation when they are driven by the in-plane current. It is also found that a moving skyrmionium is less deformed in the current-in-plane geometry compared with the skyrmionum in the current-perpendicular-to-plane geometry. Furthermore we demonstrate the transformation of a skyrmionium with $Q=0$ into two skyrmions with $Q=+1$ in a nanotrack driven by a spin-polarized current, which can be seen as the unzipping process of a skyrmionium. We illustrate the energy and spin structure variations during the skyrmionium unzipping process, where linear relations between the spin structure and energies are found. These results could have technological implications in the emerging field of skyrmionics., Comment: 14 pages, 15 figures