Skyrmion Motion Research Articles

Design of a novel bilayered structure of ferromagnetic metal and nonmagnetic insulator wires while maintaining the distance between the constituent skyrmions

Magnetic-skyrmion-based racetrack memory is a high-density memory for storing information driven by low-power, wherein the arrangement of skyrmions is stored in the form of binary digit combinations. This arrangement is altered based on the skyrmion motion resulting from the influence of the spin-transfer torque. We propose a novel layered structure of a ferromagnetic metal (FM) wire/nonmagnetic insulator wire/FM wire in which the skyrmions move while maintaining the arrangement. It consists of two FM wires that are perpendicularly magnetized. One of these comprises several skyrmions, which act as binary digits (data skyrmions). The other wire constitutes a sufficient number of skyrmions that are closely packed and allow the spin-polarized current to flow. A dipole–dipole interaction acts between these two FM wires. The motion of the data skyrmion is induced by the current-induced motion of the packed skyrmion. The motion of skyrmions is simulated via micromagnetic approaches. The data skyrmions move while maintaining the distance between each skyrmion. The analog position of the data skyrmion is controlled by the current flowing through another wire. The stable data skyrmion motion has a threshold current. When the current is larger than the threshold current, the skyrmion breaks, and/or the distance between skyrmions breaks. The threshold current density is found to decrease with an increasing vacuum layer thickness and increase with increasing thickness of the FM wire flowing current. Our results show that the skyrmion motion in the proposed structure can drive skyrmions with a spin-current density lower than that of the coupled granular/continuous structure and the edge-notched nanowire structure. This structure can be used in developing low-power operational devices based on skyrmion motion.

Skyrmion motion and partitioning of domain wall velocity driven by repulsive interactions

Magnetic skyrmions, as a whirling spin texture with axisymmetry, cannot be propelled directly by a uniform perpendicular magnetic field. Therefore, reported skyrmion motions have been induced using other sorts of stimuli — typically, electric currents in magnetic metals. Here, we propose to drive skyrmion motion, in a uniform perpendicular field, by intrinsic repulsive interactions among an outer domain wall (DW) and magnetic skyrmions. Through micromagnetic simulations, we demonstrate that the uniform perpendicular magnetic field can indeed displace magnetic skyrmions alongside the leading DW. At a fixed field strength, the velocity of the skyrmion train evolves according to a 1 / (Ns + 1) relation with Ns denoting the number of skyrmions. Based on the Thiele equation, we elucidate, analytically, the mechanism of the driven magnetic skyrmion motion as well as the velocity equipartition phenomenon and reveal that the skyrmion–DW and inter-skyrmion repulsive interactions offer the driving force for skyrmion motion. This study underlines the role of spin textures’ interaction in skyrmion dynamics, and opens an alternative route for skyrmion manipulation especially relevant to insulating magnets. Given the correspondence between ferromagnetism and ferroelectricity, we anticipate that the scheme should also work for polar skyrmions in ferroelectrics.

Universal Hopping Motion Protected by Structural Topology (Adv. Mater. 40/2022)

Skyrmion Motion Understanding skyrmion motion is essential for the efficient operation of skyrmionic devices. In article number 2203275, Chanyong Hwang, Kyoung-Whan Kim, Albert Min Gyu Park, Kab-Jin Kim, and co-workers uncover a universal scaling behavior in the current-driven motion of skyrmions. The topology of the shape of the interface drags the skyrmions and causes them to show hopping properties distinct from the creep motion expected for magnetic domains. The universal scaling can provide insights for implementing skyrmion devices and understanding the dynamics of moving bodies with a closed interface.

Magnetic-Field-Assisted Diffusion Motion of Magnetic Skyrmions.

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

Statics and dynamics of skyrmions interacting with disorder and nanostructures

Magnetic skyrmions are topologically stable nanoscale particle-like objects that were discovered in 2009. Since that time, intense research interest has led to the identification of numerous compounds that support skyrmions over a range of conditions spanning cryogenic to room temperatures. Skyrmions can be set into motion under various types of driving, and the combination of their size, stability, and dynamics makes them ideal candidates for numerous applications. Skyrmions represent a new class of system in which the energy scales of the skyrmion-skyrmion interactions, sample disorder, temperature, and drive can compete. A growing body of work indicates that the static and dynamic states of skyrmions can be influenced strongly by pinning or disorder in the sample; thus, an understanding of such effects is essential for the eventual use of skyrmions in applications. In this article we review the current state of knowledge regarding individual skyrmions and skyrmion assemblies interacting with quenched disorder or pinning. We outline the microscopic mechanisms for skyrmion pinning, including the repulsive and attractive interactions that can arise from impurities, grain boundaries, or nanostructures. This is followed by descriptions of depinning phenomena, sliding states over disorder, the effect of pinning on the skyrmion Hall angle, the competition between thermal and pinning effects, the control of skyrmion motion using ordered potential landscapes such as one- or two-dimensional periodic asymmetric substrates, the creation of skyrmion diodes, and skyrmion ratchet effects. We highlight the distinctions arising from internal modes and the strong gyroscopic or Magnus forces that cause the dynamical states of skyrmions to differ from those of other systems with pinning. We also discuss future directions and open questions related to the pinning and dynamics in skyrmion systems.

Nucleation and manipulation of single skyrmions using spin-polarized currents in antiferromagnetic skyrmion-based racetrack memories

In this work, an ultrafast nucleation of an isolated anti-ferromagnetic (AFM) skyrmion was reported in an AFM layer with DMi strengths of 0.47-0.32 mathrm{mJ}/{mathrm{m}}^{2} using spin-transfer torque by locally injecting pure spin currents into magnetic tracks. Besides, we revealed the key advantages of AFM skyrmion-based racetrack memories by comparing the motion of AFM and FM skyrmions driven by spin–orbit torques (SOTs) for different skyrmion sizes along racetrack memories with various notch sizes. Our results indicate that for AFM skyrmion, the skyrmion Hall effect does not exist during the skyrmion motion, therefore at small skyrmion sizes, we succeeded to overcome the repulsive forces developed in the notch area for low and large SOTs. The obtained findings were carefully analyzed by computing the variation of energy barriers associated with the notch for different skyrmion sizes using minimum energy path (MEP) calculations. We showed that the larger the skyrmion size, the harder it is to shrink the skyrmion in the notch which produces a high energy barrier (Eb) for large skyrmion sizes. Moreover, as the notch size increases, the skyrmion size shrinks further, and hence Eb increases proportionally. Nevertheless, we proved that AFM skyrmions are more efficient and flexible than FM skyrmions against boundary forces.

Ultra-Low-Power Reservoir Computing Based on Synthetic Antiferromagnetic Skyrmion Pairs

Reservoir computing (RC) is a promising method to realize the universal learning system. However, the complexity and power consumption limit its application. In this letter, we propose an ultra-low power RC device based on Synthetic antiferromagnetic skyrmion pairs (SAFSPs). By leveraging the Ruderman-Kittel-Kasuya- Yosida (RKKY) effect and spin-orbital torque, skyrmion pendulum motion can be realized. Furthermore, periodic oscillations can be achieved through magnetic anisotropy engineering. Based on this nonlinear motion of magnetic skyrmions, a RC system can be built. Our results show that the cognitive task of nonlinear time series can be carried out by a network of the proposed device and the power consumption can be reduced to 466nW.

Tailoring skyrmion motion dynamics via magnetoelectric coupling: Toward highly energy-efficient and reliable non-volatile memory applications

Owing to the intriguing physical properties and significant spintronic applications, magnetic skyrmions have recently drawn intensive attention. Particularly, the skyrmion-based non-volatile memory (Sky-NVM) devices promise to be spintronic building blocks with high efficiency. However, tailoring Sky-NVM to achieve an energy-efficient and reliable operation in a synthetic, CMOS compatible, and magnetic-field-free integration is a challenging issue. Here, we report a new type of compact Sky-NVM with tailored skyrmion motion dynamics via in-plane strain gradient engineering. The skyrmion motion is merely driven by an in-plane electric field utilizing the magnetoelectric coupling effect, and the programmable switching is realized by gate biasing the potential barrier height via a voltage-controlled magnetic anisotropy. The proposed device is CMOS process compatible, and the comprehensive micromagnetic simulation results demonstrate that by applying a 0.3 V in-plane voltage combined with −0.17 V gate voltage, its write latency and the energy consumption reach 5.85 ns and 4.77 aJ/bit, respectively, superior to the state-of-the-art counterparts. Our work paves a new path toward ultra-low-power spintronic memory devices.

Spin-wave-driven skyrmion dynamics in ferrimagnets: Effect of net angular momentum

Searching for low-power-consuming and highly efficient methods for well-controllable driving of skyrmion motion is one of the most concerning issues for future spintronic applications, raising high concern with the choice of magnetic media and driving scenario. In this work, we propose a scenario of spin-wave-driven skyrmion motion in a ferrimagnetic (FiM) lattice with the net angular momentum ${\ensuremath{\delta}}_{s}$. We investigate theoretically the effect of both ${\ensuremath{\delta}}_{s}$ and the circular polarization of the spin wave on the skyrmion dynamics. It is revealed that the momentum onto the skyrmion imposed by the excited spin wave can be partitioned into a ferromagnetic term plus an antiferromagnetic term. The ratio of these two terms and consequently the Hall angle of skyrmion motion can be formulated as the functions of ${\ensuremath{\delta}}_{s}$, demonstrating the key role of ${\ensuremath{\delta}}_{s}$ as an effective control parameter for the skyrmion motion. Moreover, the spin wave frequency and chirality dependent skyrmion motion are discussed, predicting the frequency enhanced skyrmion Hall motion. This work thus represents an essential contribution to understanding the skyrmion dynamics in a FiM lattice.

Inhibition of Skyrmion Hall Effect by a Stripe Domain Wall

Magnetic skyrmions are topologically protected particlelike spin textures initially discovered in chiral magnetic materials. When driven by an electric current, magnetic skyrmions move at a certain angle (i.e., skyrmion Hall angle) with respect to the driving current due to the Magnus force, giving rise to the so-called skyrmion Hall effect (SHE). The SHE often leads to skyrmion annihilation at the sample edge, which is detrimental for practical applications. In this work, we study, experimentally and through micromagnetic simulations, the current-driven dynamics of skyrmion bubbles (SBs) in $\mathrm{Pt}/\mathrm{Co}/\mathrm{Ru}$ multilayer stacks. It is observed that, under certain circumstances, a long stripe domain will form and align along the sample edge, which separates the skyrmion bubbles from the edge and avoids their annihilation at the edge. Furthermore, the velocity of the skyrmion bubbles can be increased by the stripe domain wall (DW) through the DW-SB interaction, as predicted in our early theory. Our results deepen our understanding of skyrmion dynamics and pave the way to the realization of highly efficient information processing and computing devices based on ultrafast skyrmion motion.

Zero-Field Nucleation and Fast Motion of Skyrmions Induced by Nanosecond Current Pulses in a Ferrimagnetic Thin Film.

Skyrmion racetrack memories are highly attractive for next-generation data storage technologies. Skyrmions are noncollinear spin textures stabilized by chiral interactions. To achieve a fast-operating memory device, it is critical to move skyrmions at high speeds. The skyrmion dynamics induced by spin-orbit torques (SOTs) in the commonly studied ferromagnetic films is hindered by strong pinning effects and a large skyrmion Hall effect causing deflection of the skyrmion toward the racetrack edge, which can lead to information loss. Here, we investigate the current-induced nucleation and motion of skyrmions in ferrimagnetic Pt/CoGd/(W or Ta) thin films. We first reveal field-free skyrmion nucleation mediated by Joule heating. We then achieve fast skyrmion motion driven by SOTs with velocities as high as 610 m s-1 and a small skyrmion Hall angle |θSkHE| ≲ 3°. Our results show that ferrimagnets are better candidates for fast skyrmion-based memory devices with low risk of information loss.

Realization of the skyrmionic logic gates and diodes in the same racetrack with enhanced and modified edges

Magnetic skyrmions are topological quasiparticles with nanoscale size and high mobility, which have potential applications in information storage and spintronic devices. Here, we computationally investigate the dynamics of isolated skyrmions in a ferromagnetic racetrack, where magnetic properties of the edges are enhanced and modified, forming a channel with lower magnetic anisotropy for skyrmion motion. It is found that the rectangular notch at the edge can have a pinning effect on the skyrmion and enrich the dynamics of the skyrmion. Based on the racetrack with modified edges and the notch, we design a racetrack that realizes the skyrmionic logic AND, OR, and NOT gates as well as the diode in the same magnetic racetrack. It is found that the driving current density could be much smaller than those used in previous designs of skyrmion-based logic gates. By slightly altering the shape of the racetrack, we also design the NAND and NOR gates. Finally, we study the feasibility of our design at finite temperatures. Our results may contribute to the design of nonvolatile spintronic devices with integrated multiple functions and ultra-low energy consumption.

Mechanical Acceleration and Control of the Thermal Motion of a Magnetic Skyrmion

Engineering the kinetic motion of magnetic skyrmions shows great potential in spintronics. Particularly, as a natural property, temperature plays a significant role in the dynamics of skyrmions. For instance, the nonlinear and the rectilinear motions of skyrmions driven by spin-transfer torque and local energy imbalance in temperature gradients, respectively, have been explored. Although existing studies have already implied the multiphysics field-controlled property of skyrmion thermal motion, the investigation of mechanically controlled skyrmion motions in temperature gradients is absent, and the kinematic equation is unclear. Here, we employ a phase-field model to simulate the effect of mechanical strain on skyrmion motion in a temperature gradient, and demonstrate that the strain-induced anisotropic deformation of skyrmions increases the driving force and accelerates their motion. To model the mechanical effect, we propose a kinematic equation for describing the relationship between skyrmion velocity and multiphysics field variables. Lastly, the potential application of the mechanically controlled skyrmion thermal motion is demonstrated via tip indentation simulations. This work provides the thermodynamic mechanism and kinematic equation for mechanically accelerated skyrmion thermal motions, which is expected to be a guidance for future research on skyrmion dynamics and application of functional devices.

Dynamics of magnetic skyrmions driven by a temperature gradient in a chiral magnet FeGe

We experimentally demonstrate the reversible motion of skyrmions driven by the controlled thermal fluctuations in a chiral magnet FeGe. A temperature gradient applied to the chiral magnet not only induces a flow of electrons but also excites a flow of magnons. Consequently, it is found that the skyrmion shows directional thermal diffusion toward two opposite directions along the gradient of temperature. We show that the skyrmions driven by the temperature gradient move from the cold terminal to the hot terminal due to the effect of magnon current induced by the temperature gradient. An obvious transverse shift of skyrmions is observed, which indicates the thermal-induced skyrmion Hall effect. Moreover, the thermal diffusion of skyrmions from the hot terminal to the cold terminal with a Hall motion as a result of competition of the magnon current, entropic force, and the spin-transfer torques induced by the thermally excited electron flow is also observed when the temperature at the hot terminal is high enough. Our results demonstrate an efficient manipulation of skyrmion dynamics by a controllable temperature gradient, which may provide a promising way for the realization of caloritronic applications based on topological spin textures.

Simulation and Modeling of Racetrack Memories With VCMA Synchronization

The control of the motion of magnetic domains is of crucial interest for the development of several spintronic applications, such as high-density racetrack memories and domain wall logic. In these devices, domain wall manipulation can be achieved via pulsed currents or applying external fields. However, real-world applications require accurate signal synchronization systems, keeping limited the power budget. Up to now, geometrical restrictions in the magnetic wire, known as notches, were used to confine domain walls at the expense of high resolution of the fabrication process. The solution based on the Voltage-Controlled Magnetic Anisotropy (VCMA) effect appears more promising—it is successful for controlling the skyrmion motion—avoids the need for strong depinning currents, simplifies the fabrication process, and gives more freedom in the control logic. The anisotropy variation induced by the VCMA can create barriers or wells that can be used to limit the movement of domain walls and obtain an effective synchronization. In this article, we propose a system-level evaluation of the effectiveness of the proposed VCMA synchronization method. Starting from a two-coordinates model, the motion of domain walls, the performance, and the efficiency of the approach are evaluated. We modeled the delay using SPICE. The VCMA showed clear advantages in the realization of the confinement structure at the system level with respect to the notch solution.

Commensuration effects on skyrmion Hall angle and drag for manipulation of skyrmions on two-dimensional periodic substrates

We examine the dynamics of an individually driven skyrmion moving through a background lattice of skyrmions coupled to a 2D periodic substrate as we vary the ratio of the number of skyrmions to the number of pinning sites across commensurate and incommensurate conditions. As the skyrmion density increases, the skyrmion Hall angle is nonmonotonic, dropping to low or zero values in commensurate states and rising to an enhanced value in incommensurate states. Under commensuration, the driven skyrmion is channeled by a symmetry direction of the pinning array and exhibits an increased velocity. At fillings for which the skyrmion Hall angle is zero, the velocity has a narrow band noise signature, while for incommensurate fillings, the skyrmion motion is disordered and the velocity noise is broad band. Under commensurate conditions, multi-step depinning transitions appear and the skyrmion Hall angle is zero at low drives but becomes finite at higher drives, while at incommensurate fillings there is only a single depinning transition. As the gyrotropic component of the skyrmion dynamics, called the Magnus force, increases, peaks in the velocity that appear in commensurate regimes cross over to dips, and new types of directional locking effects can arise in which the skyrmion travels along other symmetry directions of the background lattice. At large Magnus forces, and particularly at commensurate fillings, the driven skyrmion can experience a velocity boost in which the skyrmion moves faster than the applied drive due to the alignment of the Magnus-induced velocity with the driving direction. In some cases, an increase of the Magnus force can produce regimes of enhanced pinning when the skyrmion is forced to move along a nonsymmetry direction of the periodic pinning array. This is in contrast to systems with random pinning, where increasing the Magnus force generally reduces the pinning effect. We demonstrate these dynamics for both square and triangular substrates and map out the different regimes as a function of filling fraction, pinning force, and the strength of the Magnus force in a series of dynamic phase diagrams.

Collective skyrmion motion under the influence of an additional interfacial spin-transfer torque

Here we study the effect of an additional interfacial spin-transfer torque, as well as the well-established spin–orbit torque and bulk spin-transfer torque, on skyrmion collections—group of skyrmions dense enough that they are not isolated from one another—in ultrathin heavy metal/ferromagnetic multilayers, by comparing modelling with experimental results. Using a skyrmion collection with a range of skyrmion diameters and landscape disorder, we study the dependence of the skyrmion Hall angle on diameter and velocity, as well as the velocity as a function of diameter. We show that inclusion of the interfacial spin-transfer torque results in reduced skyrmion Hall angles, with values close to experimental results. We also show that for skyrmion collections the velocity is approximately independent of diameter, in marked contrast to the motion of isolated skyrmions, as the group of skyrmions move together at an average group velocity. Moreover, the calculated skyrmion velocities are comparable to those obtained in experiments when the interfacial spin-transfer torque is included. Our results thus show the significance of the interfacial spin-transfer torque in ultrathin magnetic multilayers, which helps to explain the low skyrmion Hall angles and velocities observed in experiment. We conclude that the interfacial spin-transfer torque should be considered in numerical modelling for reproduction of experimental results.

Stabilizing magnetic skyrmions in constricted nanowires

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

Non-Hermitian adiabatic perturbation theory of topological quantization of the average velocity of a magnetic skyrmion under thermal fluctuations

We study the two-dimensional motion of a magnetic skyrmion driven by a ratchetlike polarized electric current that is periodic in both space and time. Some general cases are considered in each of which in the low-temperature and adiabatic limit, regardless of the details of the driving current, the time and statistical average velocity along any direction is topologically quantized as a Chern number multiplied by a basic unit. We make two approaches, one based on identifying the drift direction and the other based on the non-Hermitian adiabatic perturbation theory developed for the Fokker-Planck operator. Both approach apply in the case of periodicity along the direction of the driving current and homogeneity in the transverse direction for which the analytical result is confirmed by our numerical simulation on the constituent spins, and a convenient experiment is proposed.

Spin polarized STM imaging of nanoscale Néel skyrmions in an SrIrO3/SrRuO3 perovskite bilayer

Oxide heterostructures are an emerging materials platform for engineering the size, stability and motion of magnetic skyrmions in next-generation devices. Here we use off-axis sputtering to grow epitaxial thin films, comprising just two unit cells of SrIrO3 on ten unit cells of the oxide ferromagnet, SrRuO3. Spin polarized scanning tunneling microscopy reveals isolated skyrmions and directly establishes their Néel character, attributed to non-collinear exchange interactions at the interface. Statistical analysis reveals a distribution of sizes and shapes, with an average diameter of 3 nm that is among the smallest reported to date in any system. Skyrmions were only observed in SrIrO3-covered regions of the film, but were otherwise independent of SrIrO3 grain area and thickness. To help explain these observations, we performed density functional theory calculations, which suggest SrIrO3 acquires an induced magnetic moment in proximity to SrRuO3 and thus may host columnar spin textures stabilized by the interface.