Skyrmion Velocity Research Articles

Skyrmion dynamics in attractive and repulsive local magnetic fields

The study of the behavior of magnetic skyrmions in local magnetic fields’ nanometric length-scale has gained increasing interest in recent years due to the theoretical proposal of magnetic skyrmion–superconducting vortex pairs as potential hosts for topologically protected bound states, which hold high promise for applications in quantum computing. From a magnetic interaction point-of-view, the key interest lies in understanding the skyrmion dynamics triggered by the magnetic energy landscape generated by the superconducting vortex. Here, we present a micromagnetic study of the dynamics of nanometric skyrmions inside a Gaussian magnetic field profile, which is used as a simplified version of the vortex magnetic flux. On the one hand, our calculations show that local non-linear magnetic fields can be very effective in controlling the dynamics of magnetic skyrmions; in particular, they offer the appealing possibility to manipulate skyrmions in a two dimensional space. On the other hand, they also show that the dynamics of a skyrmion in a local magnetic field can be manipulated via a uniform external magnetic field without any change in the magnetic field gradient. An analytical expression for the skyrmion velocity is given, and the corresponding microscopic dynamics are confirmed by the micromagnetic simulations. This work is expected to motivate more theoretical and experimental studies of the behavior of magnetic skyrmions in proximity to superconducting vortices.

Dynamic transition and Galilean relativity of current-driven skyrmions.

The coupling of conduction electrons and magnetic textures leads to quantum transport phenomena described by the language of emergent electromagnetic fields1-3. For magnetic skyrmions, spin-swirling particle-like objects, an emergent magnetic field is produced by their topological winding4-6, resulting in the conduction electrons exhibiting the topological Hall effect (THE)7. When the skyrmion lattice (SkL) acquires a drift velocity under conduction electron flow, an emergent electric field is also generated8,9. The resulting emergent electrodynamics dictate the magnitude of the THE by the relative motion of SkL and conduction electrons. Here we report the emergent electrodynamics induced by SkL motion in Gd2PdSi3, facilitated by its giant THE10,11. With increasing current excitation, we observe the dynamic transition of the SkL motion from the pinned to creep regime and finally to the flow regime, in which the THE is totally suppressed. We argue that the Galilean relativity required for the total cancellation of the THE may be generically recovered in the flow regime, even in complex multiband systems such as the present compound. Moreover, the observed THE voltages are large enough to enable real-time measurement of the SkL velocity-current profile, which shows the inertial-like motion of the SkL in the creep regime, appearing as the current hysteresis of the skyrmion velocity.

Antiferromagnetic interlayer exchange coupled Co68B32/Ir/Pt multilayers

Synthetic antiferromagnetic structures can exhibit the advantages of high velocity similarly to antiferromagnets with the additional benefit of being imaged and read-out through techniques applied to ferromagnets. Here, we explore the potential and limits of synthetic antiferromagnets to uncover ways to harness their valuable properties for applications. Two synthetic antiferromagnetic systems have been engineered and systematically investigated to provide an informed basis for creating devices with maximum potential for data storage, logic devices, and skyrmion racetrack memories. The two systems considered are (system 1) CoB/Ir/Pt of N repetitions with Ir inducing the negative coupling between the ferromagnetic layers and (system 2) two ferromagnetically coupled multilayers of CoB/Ir/Pt, coupled together antiferromagnetically with an Ir layer. From the hysteresis, it is found that system 1 shows stable antiferromagnetic interlayer exchange coupling between each magnetic layer up to N = 7. Using Kerr imaging, the two ferromagnetic multilayers in system 2 are shown to undergo separate maze-like switches during hysteresis. Both systems are also studied as a function of temperature and show different behaviors. Micromagnetic simulations predict that in both systems the skyrmion Hall angle is suppressed with the skyrmion velocity five times higher in system 1 than system 2.

Collective variable model for the dynamics of liquid crystal skyrmions

Liquid crystal skyrmions are topologically protected spatially-localized distortions of the director field which exhibit particle-like properties including translational motion in oscillating electric fields. Here, we develop a collective variable model of the skyrmion dynamics, extending the approach of Long and Selinger proposed earlier for one dimensional systems. The model relates the skyrmion motion to a complex dynamics of the width of the twist wall around the skyrmion core. The width evolves in a non-reciprocal way, quantifying squirming deformations of the high twist region within on and off states of the field. We analyze in details the average skyrmion velocity as a function of the frequency and strength of the field as well as its duty cycle. The model predictions agrees qualitatively with experiments and results of numerical minimization of the Frank-Oseen model. Our results provide insights into the conditions necessary to observe velocity reversal as a function of the field parameters.

Soliton motion induced along ferromagnetic skyrmion chains in chiral thin nanotracks

Using atomistic magnetic simulations we investigate the soliton motion along a pinned skyrmion chain containing an interstitial skyrmion. We find that the soliton can exhibit stable motion along the chain without a skyrmion Hall effect for an extended range of drives. Under a constant drive the solitons have a constant velocity. We also measure the skyrmion velocity–current curves and identify the signatures of different phases including a pinned phase, stable soliton motion, and quasi-free motion at higher drives where all of the skyrmions depin from the pinning centers and move along the rigid wall. In the quasi-free motion regime, the velocity is oscillatory due to the motion of the skyrmions over the pinning sites. For increasing pinning strength, the onset of soliton motion shifts to higher values of current density. We also find that for stronger pinning, the characteristic velocity–current shape is affected by the annihilation of single or multiple skyrmions in the drive interval over which the soliton motion occurs. Our results indicate that stable skyrmion soliton motion is possible and that the solitons could be used as information carriers instead of the skyrmions themselves for technological applications.

Manipulating Skyrmion Motion on a Nanotrack with Varied Material Parameters and Tilted Spin Currents

Magnetic skyrmions are topological quasiparticles with nanoscale size and high mobility, which have potential applications in information storage and spintronic devices. The manipulation of skyrmion’s dynamics in the track is an important topic due to the skyrmion Hall effect, which can deviate the skyrmions from the preferred direction. We propose a new model based on the ferromagnetic skyrmion, where the skyrmion velocity can be well controlled by adjusting the direction of the current. Using this design, we can avoid the annihilation of the skyrmion induced by the skyrmion Hall effect, which is confirmed by our micromagnetic simulation based on Mumax3. In the meantime, we increase the average velocity of the skyrmion by varying the intrinsic material parameters in the track, where the simulations agree well with our analytical results based on the Thiele equation. Finally, we give a phase diagram of the output of the skyrmion in the T-type track, which provides some practical ways for design of logic gates by manipulating crystalline anisotropy through the electrical control.

Giant tunability of microwave responses for current-driven skyrmions in a tapered nanostructure with notches

The investigation of the gigahertz dynamics of a skyrmion—a topologically protected chiral spin texture, offers several applications in high-frequency magnonic devices. In this work, we have investigated the motion and microwave resonant dynamics of skyrmions in an engineered nanostructure using micromagnetic simulations. The structure is a tapered ferromagnetic/heavy metal bilayer with notches to stabilize the skyrmion for dynamic studies. The skyrmion is moved along the nanostructure via current-induced spin–orbit torques. Multiple stable skyrmion states were demonstrated in the structure, where a remarkable tunability of 6 GHz is observed between the initial and the final state. This large shift in the resonant frequency has been attributed to the variation in the size of the skyrmion at various locations in the engineered nanostructure. The dependency of the skyrmion velocity and their microwave responses on the DzyalosnDzyaloshinskii–Moriya interaction strength and the perpendicular magnetic anisotropy is described. The calculation of the skyrmion Hall angle shed light on the motion and stability of the skyrmion in the structure.

Control of Skyrmion Chirality in Ta/Fe−Co−B/TaOx Trilayers by TaOx Oxidation and Fe−Co−B Thickness

Skyrmions are magnetic bubbles with nontrivial topology envisioned as data bits for ultrafast and power-efficient spintronic memory and logic devices. They may be stabilized in heavy-metal/ferromagnetic/oxide trilayer systems. The skyrmion chirality is then determined by the sign of the interfacial Dzyaloshinskii-Moriya interaction (DMI). Nevertheless, for apparently identical systems, there is some controversy about the DMI sign. Here, we show that the degree of oxidation of the top interface and the thickness of the ferromagnetic layer play a major role. Using Brillouin light-scattering measurements in $\mathrm{Ta}/\mathrm{Fe}$-$\mathrm{Co}$-$\mathrm{B}/{\mathrm{Ta}\mathrm{O}}_{x}$ trilayers, we demonstrate a sign change of the DMI with the degree of oxidation of the $\mathrm{Fe}$-$\mathrm{Co}$-$\mathrm{B}/{\mathrm{Ta}\mathrm{O}}_{x}$ interface. Using polar magneto-optical Kerr effect microscopy, we consistently observe a reversal of the direction of current-induced motion of skyrmions with the oxidation level of ${\mathrm{Ta}\mathrm{O}}_{x}$; this is attributed to their chirality reversal. In addition, a second chirality reversal is observed when changing the $\mathrm{Fe}$-$\mathrm{Co}$-$\mathrm{B}$ thickness, probably due to the proximity of the two $\mathrm{Fe}$-$\mathrm{Co}$-$\mathrm{B}$ interfaces in the ultrathin case. By properly tuning the chirality of the skyrmion, spin-transfer and spin-orbit torques combine constructively to enhance the skyrmion velocity. These observations thus allow us to envision an optimization of the material parameters to produce highly mobile skyrmions. Moreover, this chirality control enables a versatile manipulation of skyrmions and paves the way towards multidirectional devices.

Driving skyrmions with low threshold current density in Pt/CoFeB thin film

Magnetic skyrmions are topologically stable spin swirling particle like entities which are appealing for next generation spintronic devices. The expected low critical current density for the motion of skyrmions makes them potential candidates for future energy efficient electronic devices. Several heavy metal/ferromagnetic (HM/FM) systems have been explored in the past decade to achieve faster skyrmion velocity at low current densities. In this context, we have studied Pt/CoFeB/MgO heterostructures in which skyrmions have been stabilized at room temperature (RT). It has been observed that the shape of the skyrmions are perturbed even by the small stray field arising from low moment magnetic tips while performing the magnetic force microscopy (MFM), indicating presence of low pinning landscape in the samples. This hypothesis is indeed confirmed by the low threshold current density to drive the skyrmions in our sample, at velocities of few ∼10 m s−1.

Magnus induced diode effect for skyrmions in channels with periodic potentials

Using a particle based model, we investigate the skyrmion dynamical behavior in a channel where the upper wall contains divots of one depth and the lower wall contains divots of a different depth. Under an applied driving force, skyrmions in the channels move with a finite skyrmion Hall angle that deflects them toward the upper wall for −x direction driving and the lower wall for +x direction driving. When the upper divots have zero height, the skyrmions are deflected against the flat upper wall for −x direction driving and the skyrmion velocity depends linearly on the drive. For +x direction driving, the skyrmions are pushed against the lower divots and become trapped, giving reduced velocities and a nonlinear velocity-force response. When there are shallow divots on the upper wall and deep divots on the lower wall, skyrmions get trapped for both driving directions; however, due to the divot depth difference, skyrmions move more easily under −x direction driving, and become strongly trapped for +x direction driving. The preferred −x direction motion produces what we call a Magnus diode effect since it vanishes in the limit of zero Magnus force, unlike the diode effects observed for asymmetric sawtooth potentials. We show that the transport curves can exhibit a series of jumps or dips, negative differential conductivity, and reentrant pinning due to collective trapping events. We also discuss how our results relate to recent continuum modeling on a similar skyrmion diode system.

Clogging, diode and collective effects of skyrmions in funnel geometries

Using a particle-based model, we examine the collective dynamics of skyrmions interacting with a funnel potential under dc driving as the skyrmion density and relative strength of the Magnus and damping terms are varied. For driving in the easy direction, we find that increasing the skyrmion density reduces the average skyrmion velocity due to jamming of skyrmions near the funnel opening, while the Magnus force causes skyrmions to accumulate on one side of the funnel array. For driving in the hard direction, there is a critical skyrmion density below which the skyrmions become trapped. Above this critical value, a clogging effect appears with multiple depinning and repinning states where the skyrmions can rearrange into different clogged configurations, while at higher drives, the velocity-force curves become continuous. When skyrmions pile up near the funnel opening, the effective size of the opening is reduced and the passage of other skyrmions is blocked by the repulsive skyrmion–skyrmion interactions. We observe a strong diode effect in which the critical depinning force is higher and the velocity response is smaller for hard direction driving. As the ratio of Magnus force to dissipative term is varied, the skyrmion velocity varies in a non-linear and non-monotonic way due to the pile up of skyrmions on one side of the funnels. At high Magnus forces, the clogging effect for hard direction driving is diminished.

Skyrmion transport driven by pure voltage generated strain gradient

The magnetic skyrmion transport driven by pure voltage-induced strain gradient is proposed and studied via micromagnetic simulation. Through combining the skyrmion with multiferroic heterojunction, a voltage-induced uniaxial strain gradient is adjusted to move skyrmions. In the system, a pair of short-circuited trapezoidal top electrodes can generate the symmetric strain. Due to the symmetry of strain, the magnetic skyrmion can be driven with a linear motion in the middle of the nanostrip without deviation. We calculate the strain distribution generated by the trapezoidal top electrodes pair, and further investigate the influence of the strain intensity as well as the strain gradient on the skyrmion velocity. Our findings provide a stable and low-energy regulation method for skyrmion transport.

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.

Reconfigurable Logic Operations via Gate Controlled Skyrmion Motion in a Nanomagnetic Device

Owing to the topological protection and the ease of efficient manipulation, skyrmions have emerged as potential candidates for carrying information in future memory and logic devices. Here, we have proposed a reconfigurable skyrmion based two-input logic device architecture. Using micromagnetic simulations, we have demonstrated that the device is capable of performing both OR and AND logic gate functionalities in a reconfigurable manner. Different logic functionality of the device is selected by using a current through a nonmagnetic metallic gate, and the resultant Oersted field controls the trajectory of the skyrmion, which in turn determines the logic states. The logic functions are implemented on a ferromagnet/heavy metal bilayer device structure by virtue of several physical effects, such as the spin–orbit torque, skyrmion–edge repulsion, skyrmion–skyrmion topological repulsion, and skyrmion Hall effect. The skyrmion trajectory has been characterized by estimating the skyrmion Hall angle. A wide range of operations by varying the current density, skyrmion velocity, Dzyaloshinskii–Moriya interaction, magnetic anisotropy, and geometrical parameters have been presented in detail. We believe that our spin orbit torque driven logic design will have potential implications for a high-speed and low-power skyrmion based computing architecture.

Skyrmion velocities in FIB irradiated W/CoFeB/MgO thin films

In recent years magnetic skyrmions attracted great attention for the possibility to move them with low current density, their intrinsic stability and their robustness against defects and edge roughness compared to other magnetic textures. For applications, it is very important to be able to influence the behaviour of skyrmions locally. In this article, we present an evaluation on the effects of FIB Ga+ irradiation on skyrmion motion in W/CoFeB/MgO thin films. The influence of FIB irradiation is evaluated both, in terms of modification of the skyrmion Hall angle and the skyrmion velocity. An overview of the effects of the pulsing parameters on the skyrmion motion, shows low influence of the pulses rise-time and an external magnetic field. In addition the analysis after the irradiation shows that it influences notably the dynamics of skyrmions. In the irradiated zone the speed and angle of motion of these magnetic textures are strongly reduced.

Velocity increase of skyrmion motion by constructing wedge nanotracks

Spin waves (SWs) have been proved to be promising candidates for driving skyrmion motion, while the small velocity limits its further applications. Herein, we demonstrated theoretically the regulation of SW-driven skyrmion dynamics on wedge nanotracks. It is found that the edge potential barrier acts as an extra driving force and increases the skyrmion velocity by nearly 60%. By analyzing Thiele equation and velocity fitting function, we determined the optimal inclined angle and gave the quantitative expression of the increased velocity with respect to material and geometric parameters. Our results are useful for understanding the dynamic behaviors of SW-driven skyrmion and may provide guidelines for designing skyrmionic racetrack memory.

Dynamic transition of current-driven single-skyrmion motion in a room-temperature chiral-lattice magnet

Driving and controlling single-skyrmion motion promises skyrmion-based spintronic applications. Recently progress has been made in moving skyrmionic bubbles in thin-film heterostructures and low-temperature chiral skyrmions in the FeGe helimagnet by electric current. Here, we report the motion tracking and control of a single skyrmion at room temperature in the chiral-lattice magnet Co9Zn9Mn2 using nanosecond current pulses. We have directly observed that the skyrmion Hall motion reverses its direction upon the reversal of skyrmion topological number using Lorentz transmission electron microscopy. Systematic measurements of the single-skyrmion trace as a function of electric current reveal a dynamic transition from the static pinned state to the linear flow motion via a creep event, in agreement with the theoretical prediction. We have clarified the role of skyrmion pinning and evaluated the intrinsic skyrmion Hall angle and the skyrmion velocity in the course of the dynamic transition. Our results pave a way to skyrmion applications in spintronic devices.

Real-space observations of 60-nm skyrmion dynamics in an insulating magnet under low heat flow

Thermal-current induced electron and spin dynamics in solids –dubbed “caloritronics”– have generated widespread interest in both fundamental physics and spintronics applications. Here, we examine the dynamics of nanometric topological spin textures, skyrmions driven by a temperature gradient ∇T or heat flow, that are evaluated through in-situ real-space observations in an insulating helimagnet Cu2OSeO3. We observe increases of the skyrmion velocity and the Hall angle with increasing ∇T above a critical value of ~ 13 mK/mm, which is two orders of magnitude lower than the ∇T required to drive ferromagnetic domain walls. A comparable magnitude of ∇T is also observed to move the domain walls between a skyrmion domain and the non-topological conical-spin domain from cold to hot regions. Our results demonstrate the efficient manipulation of skyrmions by temperature gradients, a promising step towards energy-efficient “green” spintronics.

Motion-induced inertial effects and topological phase transitions in skyrmion transport

When the skyrmion dynamics beyond the particle-like description is considered, this topological structure can deform due to a self-induced field. In this work, we perform Monte Carlo simulations to characterize the skyrmion deformation during its steady movement. In the low-velocity regime, the deformation in the skyrmion shape is quantified by an effective inertial mass, which is related to the dissipative force. When skyrmions move faster, the large self-induced deformation triggers topological transitions. These transitions are characterized by the proliferation of skyrmions and a different total topological charge, which is obtained as a function of the skyrmion velocity. Our findings provide an alternative way to describe the dynamics of a skyrmion that accounts for the deformations of its structure. Furthermore, such motion-induced topological phase transitions make it possible to control the number of ferromagnetic skyrmions through velocity effects.

Skyrmion logic clocked via voltage-controlled magnetic anisotropy

Magnetic skyrmions are exciting candidates for energy-efficient computing due to their nonvolatility, detectability, and mobility. A recent proposal within the paradigm of reversible computing enables large-scale circuits composed of directly cascaded skyrmion logic gates, but it is limited by the manufacturing difficulty and energy costs associated with the use of notches for skyrmion synchronization. To overcome these challenges, we, therefore, propose a skyrmion logic synchronized via modulation of voltage-controlled magnetic anisotropy (VCMA). In addition to demonstrating the principle of VCMA synchronization through micromagnetic simulations, we also quantify the impacts of current density, skyrmion velocity, and anisotropy barrier height on skyrmion motion. Further micromagnetic results demonstrate the feasibility of cascaded logic circuits in which VCMA synchronizers enable clocking and pipelining, illustrating a feasible pathway toward energy-efficient large-scale computing systems based on magnetic skyrmions.