Skyrmion Hall Angle Research Articles

Steady motion of 80-nm-size skyrmions in a 100-nm-wide track

The current-driven movement of magnetic skyrmions along a nanostripe is essential for the advancement and functionality of a new category of spintronic devices resembling racetracks. Despite extensive research into skyrmion dynamics, experimental verification of current-induced motion of ultra-small skyrmions within an ultrathin nanostripe is still pending. Here, we unveil the motion of individual 80 nm-size skyrmions in an FeGe track with an ultrathin width of 100 nm. The skyrmions can move steadily along the track over a broad range of current densities by using controlled pulse durations of as low as 2 ns. The potential landscape, arising from the magnetic edge twists in such a geometrically confined system, introduces skyrmion inertia and ensures efficient motion with a vanishing skyrmion Hall angle. Our results showcase the steady motion of skyrmions in an ultrathin track, offering a practical pathway for implementing skyrmion-based spintronic devices.

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.

Dynamics of magnetic skyrmionium driven by voltage-controlled strain gradients

A magnetic skyrmionium with zero topological number has no skyrmion Hall effect during motion; hence, it has excellent application prospects in racetrack memory. Here, we investigate dynamics of magnetic skyrmionium driven by voltage-controlled in-plane strain gradients via both electromechanical and micromagnetic simulations. It is found that the skyrmionium can be efficiently driven along the direction of the in-plane strain gradients without deflection, that is, the skyrmion Hall angle is zero, and the velocity of skyrmionium can be effectively increased by reducing the magnetic damping constant and increasing the intensity of the strain gradient. Moreover, the driving force and velocity of the skyrmionium increase correspondingly with the increase in size. Most importantly, we demonstrate that the skyrmionium can be efficiently driven by strain gradients under realistic conditions with thermal noise and material inhomogeneity in the ferromagnetic film. The results presented in this study are promising for applications in skyrmionium-based information memory devices.

Generalizing Thiele equation

We generalize the Thiele equation with a transverse velocity to the skyrmion motion described by the collective coordinate of magnetization vector. It is applied to investigate a significant disparity in the existing data sets of skyrmion and antiskyrmion Hall angles. Our analysis further reveals interesting differences of these Hall angles near the angular momentum compensation point. We identify a possible physical quantity that is responsible for the disparity.

Suppression of skyrmion Hall effect via standing surface acoustic waves in hybrid ferroelectric/ferromagnetic heterostructures

Magnetic skyrmion is a promising information carrier for its low critical driven current density, topological stability, and small size, which has been proposed for various devices such as racetrack memory and logic gates. However, the skyrmion Hall effect originating from Magnus force leads to transverse motion, which hinders the development of skyrmionic device applications. Here, we propose artificial tracks built by standing surface acoustic waves (SSAWs) to suppress the skyrmion Hall effect through micromagnetic simulations. We systematically study the dynamics of an isolated skyrmion under SSAWs and driven currents in a prototype of the ferromagnetic skyrmion system. The skyrmion Hall angle changes from 80° to 0°, where the skyrmion motion is along the driven current. An analytical model considering magnetoelastic energy induced by SSAWs is developed, and a linear relation between the current density and the critical SSAW amplitude to eliminate the skyrmion Hall effect is achieved. Furthermore, a reconfigurable multichannel skyrmion racetrack is constructed through the change of SSAW wavelengths. Our work opens a feasible route for the suppression of skyrmion Hall effect via SSAWs.

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.

Skyrmion based majority logic gate by voltage controlled magnetic anisotropy in a nanomagnetic device

Magnetic skyrmions are topologically protected spin textures and they are suitable for future logic-in-memory applications for energy-efficient, high-speed information processing and computing technologies. In this work, we have demonstrated skyrmion-based 3 bit majority logic gate using micromagnetic simulations. The skyrmion motion is controlled by introducing a gate that works on voltage controlled magnetic anisotropy. Here, the inhomogeneous magnetic anisotropy behaves as a tunable potential barrier/well that modulates the skyrmion trajectory in the structure for the successful implementation of the majority logic gate. In addition, several other effects such as skyrmion–skyrmion topological repulsion, skyrmion-edge repulsion, spin–orbit torque and skyrmion Hall effect have been shown to govern the logic functionalities. We have systematically presented the robust logic operations by varying the current density, magnetic anisotropy, voltage-controlled gate dimension and geometrical parameters of the logic device. The skyrmion Hall angle is monitored to understand the trajectory and stability of the skyrmion as a function of time in the logic device. The results demonstrate a novel method to achieve majority logic by using voltage controlled magnetic anisotropy which further opens up a new route for skyrmion-based low-power and high-speed computing devices.

Experimental verification of the Thiele equation for skyrmion Hall angle

Magnetic skyrmions are a topologically stable spin configurations that are currently extensively studied as promising information carriers in spintronic devices. When an electric current is injected, the skyrmions exhibit the skyrmion Hall effect. This skyrmion Hall effect can be described by the Thiele equation. Here, we experimentally examined the validity of the Thiele equation. For this study, a series of Pt/Co/W films with a wide range of Co layer thicknesses were examined. The results verified the Thiele equation of the skyrmion Hall angle as a function of the magnetic anisotropy and Gilbert damping constants.

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.

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.

Temperature-Gradient-Driven Magnetic Skyrmion Motion

The static and dynamic properties of skyrmions have recently received increased attention due to the potential application of skyrmions as information carriers and for unconventional computing. While the current-driven dynamics has been explored deeply, both theoretically and experimentally, the theory of temperature gradient-induced dynamics---skyrmion caloritronics---is still at its early stages of development. Here, we move the topic forward by identifying the role of entropic torques due to the temperature dependence of magnetic parameters. Our results show that skyrmions move towards higher temperatures in single-layer ferromagnets with interfacial Dzyaloshinski-Moriya interactions, whereas, in multilayers, they move to lower temperatures. We analytically and numerically demonstrate that the opposite behaviors are due to different scaling relations of the material parameters as well as a non-negligible magnetostatic field gradient in multilayers. We also find a spatially dependent skyrmion Hall angle in multilayers hosting hybrid skyrmions due to variations of the thickness-dependent chirality as the skyrmion moves along the temperature gradient.

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.

Current-driven dynamics of skyrmions in the presence of pinning at finite temperatures

Magnetic skyrmions are topological solitons in magnetic materials with broken spatial inversion symmetry. They offer potential as an information carrier for future low-power memory and computing systems owing to the small size and relatively low driving current compared to traditional devices. To develop applications such as racetrack memory at ambient temperature, the interaction of current-driven motion, pinning and thermal fluctuations must be investigated. The skyrmion dynamics at finite temperatures are shown using the expanded Thiele equation, and the relationship between critical depinning current and temperature is established with regard to different damping constants. Furthermore, we found that the Thiele equation still is insufficient to describe the dynamics of skyrmion precisely at low temperatures with the presence of pinning. Moreover, we have shown that the skyrmion Hall angle is dependent on the driving current in the presence of the pinning effect at various finite temperatures.

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.

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.

Soliton motion in skyrmion chains: Stabilization and guidance by nanoengineered pinning

Using a particle-based model we examine the depinning motion of solitons in skyrmion chains in quasi-one-dimensional (1D) and two-dimensional (2D) systems containing embedded 1D interfaces. The solitons take the form of a particle or hole in a commensurate chain of skyrmions. Under an applied drive, just above a critical depinning threshold, the soliton moves with a skyrmion Hall angle of zero. For higher drives, the entire chain depins, and in a 2D system we observe that both the solitons and chain move at zero skyrmion Hall angle and then transition to a finite skyrmion Hall angle as the drive increases. In a 2D system with a 1D interface that is at an angle to the driving direction, there can be a reversal of the sign of the skyrmion Hall angle from positive to negative. Our results suggest that solitons in skyrmion systems could be used as information carriers in racetrack geometries that would avoid the drawbacks of finite skyrmion Hall angles. The soliton states become mobile at significantly lower drives than the depinning transition of the skyrmion chains themselves.

Nonzero Skyrmion Hall Effect in Topologically Trivial Structures

It is widely believed that the skyrmion Hall effect, often disruptive for device applications, vanishes for overall topologically neutral structures such as (synthetic) antiferromagnetic skyrmions and skyrmioniums due to a compensation of Magnus forces. In this paper, however, we report that in contrast to the case of spin-transfer-torque-driven skyrmion motion, this notion is generally false for spin-orbit-torque-driven objects. We show that the skyrmion Hall angle is directly related to their helicity and imposes an unexpected roadblock for developing faster and lower input racetrack memories based on spin-orbit torques.

Magnetic skyrmion manipulation in CrTe2/WTe2 2D van der Waals heterostructure

Magnetic skyrmions in two-dimensional van der Waals materials provide an ideal platform to push skyrmion technology to the ultimate atomically thin limit. In this work, we theoretically demonstrate the Dzyaloshinskii–Moriya interaction and the formation of a Néel-type skyrmion lattice at the CrTe2/WTe2 bilayer van der Waals heterostructure. Our calculations suggest a field-controlled Néel-type skyrmion lattice—a ferromagnet transition cycle. In addition, a spin-torque induced by spin-polarized current injection was simulated in order to study the motion of a skyrmion on a racetrack, where an increase in the skyrmion Hall angle is observed at high temperatures. Consequently, this study suggests that generation and annihilation of skyrmions can be achieved with temperature or field control and also manipulate the velocity and the direction of the Néel-type skyrmions through ultra-low current densities and temperature, thus shedding light on the general picture of magnetic skyrmion control and design of two-dimensional van der Waals heterostructures.

Spin–orbit torque driven skyrmion motion under unconventional spin Hall effect

The effective control of skyrmion motion is a critical aspect for realizing skyrmion-based devices. Among the potential directions, the use of current induced spin–orbit torque (SOT) is energetically efficient. However, the conventional heavy metals with high crystal symmetry limit the charge-to-spin conversion to the orthogonal configuration, which causes the skyrmions to deflect from the electrical current direction with a finite skyrmion Hall angle. Here, we investigate the SOT driven skyrmion motion under unconventional spin Hall effect. We systematically study the effect of a noncollinear low-symmetry spin source layer with spin moments mixed by Rashba-like S y , Dresselhaus-like S x and out-of-plane like S z on skyrmion features (velocity, diameter and Hall angle) stabilized in a ferromagnet/WTe2 heterostructure. Our results may provide a new degree of freedom for controlling the skyrmion Hall angle, and can open the way for the discovery of new ferromagnetic multilayer where the skyrmion Hall angle is suppressed by the proper design of different SOT driven forces.