Skyrmion Motion Research Articles

Chiral edge currents for ac-driven skyrmions in confined pinning geometries

We show that ac driven skyrmion lattices in a weak pinning channel confined by regions of strong pinning exhibit edge transport carried by skipping orbits while skyrmions in the bulk of the channel undergo localized orbits with no net transport. The magnitude of the edge currents can be controlled by varying the amplitude and frequency of the ac drive or by changing the ratio of the Magnus force to the damping term. We identify a localized phase in which the orbits are small and edge transport is absent, an edge transport regime, and a fluctuating regime that appears when the ac drive is strong enough to dynamically disorder the skyrmion lattice. We also find that in some cases, multiple rows of skyrmions participate in the transport due to a drag effect from the skyrmion-skyrmion interactions. The edge currents are robust for finite disorder and should be a general feature of skyrmions interacting with confined geometries or inhomogeneous disorder under an ac drive. We show that similar effects can occur for skyrmion lattices at interfaces or along domain boundaries for multiple coexisting skyrmion species. The edge current effect provides a new method to control skyrmion motion, and we discuss the connection of these results with recent studies on the emergence of edge currents in chiral active matter systems and gyroscopic metamaterials.

Dynamics of an antiferromagnetic skyrmion in a racetrack with a defect

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.

A ferromagnetic skyrmion-based nano-oscillator with modified profile of Dzyaloshinskii-Moriya interaction

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.

Dynamics of antiskyrmions induced by the voltage-controlled magnetic anisotropy gradient

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 motion induced by voltage-controlled in-plane strain gradients

Micromagnetic simulations are used to investigate the motion of magnetic skyrmions in an in-plane strain gradient. The skyrmion diameter and energy are found to depend on the strain, which leads to a force that moves the skyrmion toward regions with higher strain. An analytical expression for the skyrmion velocity as a function of the strain gradient is derived assuming a rigid profile for the skyrmion, and good agreement with simulations is obtained. Furthermore, electromechanical simulations of a hybrid ferromagnetic/piezoelectric device show that the in-plane strain gradients needed to move skyrmions can be achieved by applying moderate voltages in the piezoelectric substrate, which offers an original way to control skyrmion motion efficiently.

Stabilization of the skyrmion crystal phase and transport in thin-film antiferromagnets

We investigate the formation and stability of the skyrmion crystal phase in antiferromagnetic thin films subjected to fieldlike torques such as, e.g., those induced by an electric current in CuMnAs and Mn$_{2}$Au via the inverse spin-galvanic effect. We show that the skyrmion lattice represents the ground state of the antiferromagnet in a substantial area of the phase diagram, parametrized by the staggered field and the (effective) uniaxial anisotropy constant. Skyrmion motion can be driven in the crystal phase by the spin transfer effect. In the metallic scenario, itinerant electrons experience an emergent SU$(2)$-electromagnetic field associated with the (N\'{e}el) skyrmion background, leading to a topological spin-Hall response. Experimental signatures of the skyrmion crystal phase and readout schemes based on topological transport are discussed.

Manipulating skyrmions in synthetic antiferromagnetic nanowires by magnetic field gradients

The effective manipulation of skyrmion motion by magnetic field gradients introduces the technological possibility with skyrmion as information carriers for spintronic applications. Recent studies indicate that the skyrmion Hall effect can be suppressed in a synthetic antiferromagnetic (SAF) multilayer structure driven by a spin polarized current. In this paper, an analytical model based on Thiele equation is developed to describe the properties of a skyrmion pair in a SAF structure driven by a magnetic field gradient. Combining the analytical solutions with the micromagnetic simulation results, we demonstrate the essential dynamic features of the skyrmion pair as a function of AF coupling and magnetic field gradients, revealing that the skyrmion pair motion could be suppressed by increasing the interlayer antiferromagnetic coupling.

Skyrmion latch and flip-flop in magnetic nanotracks with gradient anisotropy

Skyrmion sequential elements are proposed and demonstrated. A skyrmion latch is implemented in a single device where skyrmion motion is controlled by spin-orbit torque and voltage-controlled magnetic anisotropy in a magnetic nanotrack with gradient anisotropy. Micromagnetic simulations have been carried out to verify the feasibility of the latch function and to study device performance. The results indicate that the proposed skyrmion latch have potential advantages, including a small device footprint, a tunable switching speed, and low power consumption. Furthermore, a master-slave skyrmion flip-flop can be simply implemented by cascading two skyrmion latches to be further used for constructing a skyrmion register. This work provides a guideline to design spintronics for sequential logic circuits.

Magnetic skyrmion field-effect transistors

Magnetic skyrmions are of considerable interest for low-power memory and logic devices because of high speed at low current and high stability due to topological protection. We propose a skyrmion field-effect transistor based on a gate-controlled Dzyaloshinskii-Moriya interaction. A key working principle of the proposed skyrmion field-effect transistor is a large transverse motion of skyrmions, caused by an effective equilibrium dampinglike spin–orbit torque due to spatially inhomogeneous Dzyaloshinskii-Moriya interaction. This large transverse motion can be categorized as the skyrmion Hall effect but has been unrecognized previously. The proposed device is capable of performing multibit operation and Boolean functions and thus is expected to serve as a low-power logic device based on magnetic solitons.

Manipulating movement of skyrmion by strain gradient in a nanotrack

Abstract Magnetic skyrmions are swirling nanometric spin textures, which have attracted extensive attention by virtue of their potential applications as information carriers for future memory technology and spintronic devices. Here, we investigate the effect of strain gradient on the in-plane current-driven motion of magnetic skyrmion in a nanotrack. It is found that a longitudinal strain gradient will induce a transverse velocity with its value linearly proportional to the strain gradient. As well, we find that skyrmions can be accelerated or decelerated by the boundary of nanotrack. This behavior depends on the repulsive force induced by boundary and the topological number of skyrmion. Our results not only explain the effect of strain gradient, but also show the influence of the boundary on the skyrmion motion. This work may provide a guide for designing and developing the racetrack memory based on magnetic skyrmions.

A skyrmion-based spin-torque nano-oscillator with enhanced edge

Abstract The oscillation frequency of the circular skyrmion motion in a nanodisk increases with the driving current density. However, the skyrmion may be destroyed at the nanodisk edge when the driving current density is larger than a threshold, which leads to a maximum oscillation frequency that may not be enough for ultrahigh frequency applications based on skyrmions. In this work, a modified nanodisk structure, in which a skyrmion can be driven by a large current density, is proposed. Numerical simulations demonstrate that when the edge of a ferromagnetic nanodisk has enhanced perpendicular magnetic anisotropy, the upper threshold of the skyrmion oscillation frequency can be increased by 75% compared to the original structure without enhanced edge. Our results may be useful for overcoming the frequency limit of the skyrmion-based spin-torque oscillator, which utilizes the current-induced oscillation of a skyrmion as the source of microwave power.

Skyrmion-generated spinmotive forces in inversion broken ferromagnets

We present an analytical study on the spinmotive force (SMF) generated by translational motion of magnetic skyrmion. A SMF refers to an electrical voltage induced by dynamical magnetic textures, which reflects the spatiotemporal variation of the magnetization. The dynamics of a skyrmion thus can be detected by a SMF measurement, which may play an important role in future skyrmion-based technologies. We find the dependence of the SMF on skyrmion structure (e.g., skyrmion or anti-skyrmion, N\'{e}el or Bloch type, and the polarity of the skyrmion core) and Rashba and Dresselhaus spin-orbit couplings (SOCs). To this end, we derive explicit formulae for the spin-dependent electric fields originating from the two SOCs. Our findings offer a comprehensive understanding of the phenomenon and an estimation of the electrical voltage signal associated with a moving skyrmion for a given experiment.

Effect of inter-layer spin diffusion on skyrmion motion in magnetic multilayers

It is well known that skyrmions can be driven using spin-orbit torques due to the spin-Hall effect. Here we show an additional contribution in multilayered stacks arises from vertical spin currents due to inter-layer diffusion of a spin accumulation generated at a skyrmion. This additional interfacial spin torque is similar in form to the in-plane spin transfer torque, but is significantly enhanced in ultra-thin films and acts in the opposite direction to the electron flow. The combination of this diffusive spin torque and the spin-orbit torque results in skyrmion motion which helps to explain the observation of small skyrmion Hall angles even with moderate magnetisation damping values. Further, the effect of material imperfections on threshold currents and skyrmion Hall angle is also investigated. Topographical surface roughness, as small as a single monolayer variation, is shown to be an important contributing factor in ultra-thin films, resulting in good agreement with experimental observations.

Current-Driven Skyrmion Dynamics Along Curved Tracks

The current-driven skyrmion (Sk) motion along two exchange-coupled ferromagnetic (FM) layers with perpendicular magnetic anisotropy is studied by means of micromagnetic simulations and compared to the conventional case of a single FM layer. Our results indicate that the two coupled Sks can be synchronously driven along each FM layer in the presence of a strong interlayer exchange coupling and that the velocity is significantly enhanced due to the antiferromagnetic (AF) exchange coupling as compared with the single-FM-layer case. The interfacial Dzyaloshinskii–Moriya interaction gives the required chirality to the magnetization textures, while the interlayer exchange coupling favors the synchronous movement of the coupled Sks by a dragging mechanism, without depicting the unwanted Sk Hall effect. This observation is particularly relevant to drive Sks along curved strips, which are also evaluated here. Sks move with different velocities along single FM stacks with curved parts. On the contrary, the AF coupling between the FM layers mitigates the Sk Hall effect, which suggests these systems to achieve efficient and highly packed displacement of trains of Sks for spintronics devices. A study taking into account defects and thermal fluctuations analyzes the validity range of these claims.

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.

Topological spin Hall effects and tunable skyrmion Hall effects in uniaxial antiferromagnetic insulators

Recent advances in the physics of current-driven antiferromagnetic skyrmions have observed the absence of a Magnus force. We outline the symmetry reasons for this phenomenon, and show that this cancellation will fail in the case of spin polarized currents. Pairing micromagnetic simulations with semiclassical spin wave transport theory, we demonstrate that skyrmions produce a spin-polarized transverse magnon current, and that spin-polarized magnon currents can in turn produce transverse motion of antiferromagnetic skyrmions. We examine qualitative differences in the frequency dependence of the skyrmion Hall angle between ferromagnetic and antiferromagnetic cases, and close by proposing a simple skyrmion-based magnonic device for demultiplexing of spin channels.

Orientation-dependent current-induced motion of skyrmions with various topologies

We study the current-driven motion of metastable localized spin structures with various topological charges in a (Pt$_{1-x}$Ir$_{x}$)/Fe bilayer on a Pd(111) surface by combining atomistic spin model simulations with an approach based on the generalized Thiele equation. We demonstrate that besides a distinct dependence on the topological charge itself the dynamic response of skyrmionic structures with topological charges $\mathrm{Q} = -1$ and $\mathrm{Q}= 3$ to a spin-polarized current exhibits an orientation dependence. We further show that such an orientation dependence can be induced by applying an in-plane external field, possibly opening up a new pathway to the manipulation of skyrmion dynamics.

Dynamics of bimeron skyrmions in easy-plane magnets induced by a spin supercurrent

We theoretically study the interaction of an isolated bimeron skyrmion in quasi-two-dimensional easy-plane magnets with a surrounding spin superfluid associated with spontaneously broken U(1) spin-rotational symmetry, revealing that skyrmion energy depends on the local spin current flowing in its background. The finding leads us to propose to manipulate a skyrmion energy landscape via a spin supercurrent, which can be controlled nonlocally by varying the magnitudes of spin-current injection and ejection through the boundaries. Two exemplary cases are discussed: a steady-state motion of a skyrmion induced by a uniform force and a skyrmion motion localized along a one-dimensional racetrack. We envision that a skyrmion interacting with a spin superfluid can serve as a robust pointlike information carrier that can be operated with minimal dissipation.

Effect of Dzyaloshinskii–Moriya Interaction Energy Confinement on Current‐Driven Dynamics of Skyrmions

Magnetic skyrmions, which are topological spin configuration, have gained interest in the past few years. However, skyrmions suffer from the skyrmion Hall effect, a phenomenon where skyrmions deflect from the path of the electron flow and annihilate at the edge of the track. There are attempts to overcome this effect using synthetic antiferromagnetic layer structures and ferrimagnetic layer structures. Herein, a new approach based on introducing Dzyaloshinskii–Moriya interaction (DMI) energy wells is reported to direct the motion of skyrmions in a nanowire. It is shown through simulations that by creating DMI energy wells with a critical DMI value, a skyrmion moves within the boundaries set by the energy wells. It is also shown that the diameter of a skyrmion can be reduced by decreasing the space between the DMI energy wells. The proposed DMI energy well enables packing of skyrmion tracks at a high density. In this view, the effect of magnetostatic interactions between multiple skyrmions on their motion in parallel tracks is also investigated. Furthermore, the effect of changing the distance between skyrmions on magnetostatic interactions is studied. These results offer a new path toward maneuvering the skyrmion motion for racetrack memory or logic devices.

Current-induced motion of twisted skyrmions

Twisted skyrmions, whose helicity angles are different from those of Bloch and Néel skyrmions, have recently been demonstrated in experiments. In this work, we first discuss the origin and the topological properties of twisted skyrmions. Following that, we investigate the current-induced motion of twisted skyrmions by using micromagnetic simulations. It is found that the skyrmion Hall angle of twisted skyrmions driven by the spin Hall effect (SHE) varies continuously with the helicity, which means that the skyrmion Hall angle depends significantly upon the helicity in addition to the dissipative force tensor and the Gilbert damping. More importantly, we demonstrate that the trajectory of the twisted skyrmion can be controlled in a two-dimensional plane with a Gilbert damping gradient, which makes it possible to achieve the SHE-induced motion of twisted skyrmions with zero skyrmion Hall angle. At last, the simulation results demonstrate that the dynamics of twisted skyrmions driven by the spin transfer torque can be described by Thiele's equation, and they are essentially identical to the dynamics of Bloch and Néel skyrmions. Our results provide an understanding of the current-induced motion of twisted skyrmions, which may contribute to the applications of skyrmion-based racetrack memories.