Skyrmion Hall Effect Research Articles

A magnetic skyrmion diode based on potential well inducting effect

Magnetic skyrmions have great potential in the application of spintronic devices due to their stable topologically protected spin configuration. To meet the needs of spintronic device design, it is necessary to manipulate the movement of the magnetic skyrmions. Here we propose a skyrmion diode based on potential well induced skyrmion motion through theoretical calculations. The potential well is generated by the voltage-controlled magnetic anisotropy (VCMA) gradient. By utilizing the induction of the potential well as well as the skyrmion Hall effect (SkHE), the velocity and trajectory of the skyrmions can be controlled and the forward pass and reverse cutoff functions of diode-like devices have been realized. Furthermore, we report the dynamics of current-driven skyrmions in a racetrack with locally applied VCMA. Under the influence of the SkHE, the difference in dynamic behavior between forward and reverse motion of the skyrmions is obvious, and the potential well can produce different pinning, depinning and annihilating effects on forward and reverse moving skyrmions. Our results can be beneficial for the design and development of magnetic skyrmion diodes.

Harnessing Skyrmion Hall Effect by Thickness Gradients in Wedge-Shaped Samples of Cubic Helimagnets.

The skyrmion Hall effect, which is regarded as a significant hurdle for skyrmion implementation in thin-film racetrack devices, is theoretically shown to be suppressed in wedge-shaped nanostructures of cubic helimagnets. Under an applied electric current, ordinary isolated skyrmions with the topological charge 1 were found to move along the straight trajectories parallel to the wedge boundaries. Depending on the current density, such skyrmion tracks are located at different thicknesses uphill along the wedge. Numerical simulations show that such an equilibrium is achieved due to the balance between the Magnus force, which instigates skyrmion shift towards the wedge elevation, and the force, which restores the skyrmion position near the sharp wedge boundary due to the minimum of the edge-skyrmion interaction potential. Current-driven dynamics is found to be highly non-linear and to rest on the internal properties of isolated skyrmions in wedge geometries; both the skyrmion size and the helicity are modified in a non-trivial way with an increasing sample thickness. In addition, we supplement the well-known theoretical phase diagram of states in thin layers of chiral magnets with new characteristic lines; in particular, we demonstrate the second-order phase transition between the helical and conical phases with mutually perpendicular wave vectors. Our results are useful from both the fundamental point of view, since they systematize the internal properties of isolated skyrmions, and from the point of view of applications, since they point to the parameter region, where the skyrmion dynamics could be utilized.

Encoding and Multiplexing Information Signals in Magnetic Multilayers with Fractional Skyrmion Tubes.

Tailored magnetic multilayers (MMLs) provide skyrmions with enhanced thermal stability, leading to the possibility of skyrmion-based devices for room-temperature applications. At the same time, the search for additional stable topological spin textures has been under intense research focus. Besides their fundamental importance, such textures may expand the information encoding capability of spintronic devices. However, fractional spin texture states within MMLs in the vertical dimension are yet to be investigated. In this work, we demonstrate numerically fractional skyrmion tubes (FSTs) in a tailored MML system. We subsequently propose to encode sequences of information signals with FSTs as information bits in a tailored MML device. Micromagnetic simulations and theoretical calculations are used to verify the feasibility of hosting distinct FST states within a single device, and their thermal stability is investigated. A multilayer multiplexing device is proposed, where multiple sequences of the information signals can be encoded and transmitted based on the nucleation and propagation of packets of FSTs. Finally, pipelined information transmission and automatic demultiplexing are demonstrated by exploiting the skyrmion Hall effect and introducing voltage-controlled synchronizers and width-based track selectors. The findings indicate that FSTs can be potential candidates as information carriers for future spintronic applications.

Realizing high-velocity skyrmions via anisotropy engineering

Skyrmion-based racetrack memories are expected to be operated by the motion of skyrmions through magnetic nano-wires made of metallic multi-layers with high spin–orbit coupling and Dzyaloshinskii–Moriya interaction. The current-driven skyrmions in a ferromagnetic system had limitations due to their higher Hall angles and lower velocity. We addressed this by interfacial anisotropy engineering, which helped us to stabilize skyrmions at a thickness of x = 0.65 nm of Cu in the HM–FM interface of perpendicularly magnetized Ta3nmPt3nmCuxCo0.5nmPt1nm. At x = 0.60 nm Cu, the system showed worm like structures, while at 0.70 nm of Cu, the system showed in-plane magnetization. This system with optimum magnetic anisotropy enabled one to achieve skyrmions with a velocity of 260 m/s and low skyrmion Hall effect at room temperature with driving current <3×1011A/m2.

Reversible conversion between skyrmions and skyrmioniums

Skyrmions and skyrmioniums are topologically non-trivial spin textures found in chiral magnetic systems. Understanding the dynamics of these particle-like excitations is crucial for leveraging their diverse functionalities in spintronic devices. This study investigates the dynamics and evolution of chiral spin textures in [Pt/Co]3/Ru/[Co/Pt]3 multilayers with ferromagnetic interlayer exchange coupling. By precisely controlling the excitation and relaxation processes through combined magnetic field and electric current manipulation, reversible conversion between skyrmions and skyrmioniums is achieved. Additionally, we observe the topological conversion from a skyrmionium to a skyrmion, characterized by the sudden emergence of the skyrmion Hall effect. The experimental realization of reversible conversion between distinct magnetic topological spin textures represents a significant development that promises to expedite the advancement of the next generation of spintronic devices.

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.

Skyrmion size-tuning in two-dimensional antiferromagnetic monolayers by applying local spin-polarized current-induced spin-transfer torque

Antiferromagnetic (AFM) skyrmions exhibit a variety of outstanding features, including stability, non-volatility, processability, and resistance to the skyrmion Hall effect (SkHE). However, AFM skyrmions are insensitive to an external magnetic field, posing a major challenge for controlling their size. Tuning the key magnetic properties in AFM thin films is a feasible method for controlling skyrmion size, but it may also adversely affect other magnetic characteristics, such as the velocity and stability of the skyrmion, especially for small skyrmion sizes. In this study, we have investigated the size controllability of AFM skyrmions in the presence of the Dzyaloshinskii–Moriya interaction (DMI), applying a pure spin current in a bilayer structure consisting of a 2D AFM nanodisk placed over a thin coating of heavy metal (HM). The method relies on destabilizing the AFM lattice by targeting the 2D AFM nanodisk in a specific area defined by the diameter (dtr) using spin-polarized current-perpendicular-to-plane (CPP), causing a localized magnetization precession induced by spin-transfer torque (STT). As a result, a series of AFM skyrmions of different radii was stabilized depending on the diameter used without resorting to re-tuning the magnetic characteristics of the material. Moreover, we have found that for strong DMI, robust AFM skyrmions of small sizes can also be generated by adopting small diameters. Besides, the impact of spin current and nucleation time has been examined, and it was found that adjusting these parameters does not help to fine-tune the skyrmion size as much as it affects the nucleation process. Finally, we demonstrate how this method may be used to adjust both the radius and site of the skyrmion in the 2D AFM monolayer by simultaneously targeting different locations using pure spin currents. This method allows us to tune the AFM skyrmion size and to directly address the target skyrmion without disturbing the surrounding magnetic environment. Therefore, our results may pave the way for high-functional spintronics applications based on AFM skyrmions.

Current-induced dynamics of isolated antiferromagnetic antiskyrmion and antiskyrmionium

Topologically stable spin structures known as magnetic antiskyrmions spontaneously emerge in magnets with broken in-plane rotation symmetry when current is injected. While many studies have focused on their behaviors in ferromagnetic (FM) materials, limited attention has been paid to antiskyrmions in their antiferromagnetic (AFM) counterparts. In spintronic applications, the Magnus force of an AFM antiskyrmion cancels out completely due to its comparable but opposite sign spin pattern on the A and B sublattices in the AFM bipartite system, while an FM antiskyrmion exhibits transverse motion when driven by the currents, causing limitations to antiskyrmion motion velocity and information loss when the antiskyrmion is annihilated at the edges of racetracks. Here, we report the nucleation and dynamics of an isolated AFM antiskyrmion and antiskyrmionium induced by current analytically and numerically. We demonstrate how AFM antiskyrmions and antiskyrmioniums are stabilized and manipulated with the same velocity by spin transfer torques and with different velocities by spin-orbit torques. Under suitable conditions, the AFM antiskyrmion and antiskyrmionium can be driven at velocities as high as 6 km/s without the skyrmion Hall effect, far greater than their ferromagnetic counterparts. Furthermore, the critical driving current density of the AFM antiskyrmion (antiskyrmionium) is much larger than that of the FM antiskyrmion (antiskyrmionium). Our results contribute to the development of antiferromagnetic antiskyrmions and antiskyrmioniums by shedding light on their stabilization and dynamics.

Dynamics of hybrid magnetic skyrmion driven by spin–orbit torque in ferrimagnets

Precise control of skyrmion dynamics is essential for the future spintronic device design based on the magnetic skyrmions. In this work, we propose a scheme to implement hybrid magnetic skyrmions (HMS) in ferrimagnets and we study the dynamics of the HMS driven by spin–orbit torque. It is revealed that the skyrmion Hall effect depends on the skyrmion helicity and the net angular momentum (δs), allowing the effective modulation of the HMS motion through tuning Dzyaloshinskii–Moriya interaction and δs. Moreover, the Magnus force for finite δs suppresses the transverse motion and enhances the longitudinal propagation, resulting in the decrease in Hall angle accompanying faster dynamics than that in antiferromagnets. Thus, the Hall effect can be suppressed through selecting suitable materials to better control the HMS motion. Finally, we propose a convenient skyrmion diversion scheme through modulating the helicity and Hall angle of the HMS, benefiting the future spintronic device design.

Gyromotion of skyrmion along the nanofilm edge driven by spin waves

The dynamic behaviors of skyrmion in a nanofilm driven by spin waves have been numerically investigated by means of micromagnetic simulation. The results show that (i) the skyrmion shows a backward motion (towards the spin wave source) in the nanofilm with skyrmion Hall effect due to the spin wave scattering from the skyrmion; (ii) a fast (>100m/s) and periodic skyrmion motion can be achieved by introducing two spin wave sources to force the skyrmion move along the film edges; (iii) the velocity of the skyrmion motion depends on the amplitude and frequency of the driving magnetic fields as well as the nanofilm geometry, and the rotation sense of the skyrmion motion along the film edge depends on the topological number (Q=±1). The results might be a guidance for the design and development of future skyrmion-based devices in which skyrmions are used as information carriers.

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.

Mirroring Skyrmions in Synthetic Antiferromagnets via Modular Design.

Skyrmions are promising for the next generation of spintronic devices, which involves the production and transfer of skyrmions. The creation of skyrmions can be realized by a magnetic field, electric field, or electric current while the controllable transfer of skyrmions is hindered by the skyrmion Hall effect. Here, we propose utilizing the interlayer exchange coupling induced by the Ruderman-Kittel-Kasuya-Yoshida interactions to create skyrmions through hybrid ferromagnet/synthetic antiferromagnet structures. An initial skyrmion in ferromagnetic regions could create a mirroring skyrmion with an opposite topological charge in antiferromagnetic regions driven by the current. Furthermore, the created skyrmions could be transferred in synthetic antiferromagnets without deviations away from the main trajectories due to the suppression of the skyrmion Hall effect in comparison to the transfer of the skyrmion in ferromagnets. The interlayer exchange coupling can be tuned, and the mirrored skyrmions can be separated when they reach the desired locations. Using this approach, the antiferromagnetic coupled skyrmions can be repeatedly created in hybrid ferromagnet/synthetic antiferromagnet structures. Our work not only supplies a highly efficient approach to create isolated skyrmions and correct the errors in the process of skyrmion transport, but also paves the way to a vital information writing technique based on the motion of skyrmions for skyrmion-based data storage and logic devices.

Temperature dependence of current-driven and Brownian skyrmion dynamics in ferrimagnets with compensation point

Magnetic skyrmions are topological spin textures and promising candidates for novel spintronic applications. Recent studies on the current-driven dynamics of ferromagnetic (FM) skyrmions revealed that they exhibit an undesirable transverse motion, the skyrmion Hall effect. For antiferromagnetic (AFM) skyrmions, a vanishing skyrmion Hall effect was predicted, along with faster dynamics. However, their zero net magnetization obstructs efficient detection. Ferrimagnetic (FI) materials promise to combine both advantages: fast, AFM-like dynamics and easy read-out via stray fields. Here, we investigate the current-driven and Brownian dynamics of skyrmions in a FI with a compensation point. We perform atomistic spin dynamics simulations based on a model Hamiltonian and the stochastic Landau-Lifshitz-Gilbert equation supplemented with spin-orbit torques, accompanied by analytical calculations based on a collective coordinate approach. Our results unveil a nonmonotonic temperature dependence of the velocities and the diffusion coefficient with a strong enhancement at the angular momentum compensation temperature, due to scaling from FM- to AFM-like dynamics. These findings open up a new pathway for the efficient manipulation of skyrmion dynamics via temperature.

Bilayer-Skyrmion-Based Design of Neuron and Synapse for Spiking Neural Network

Magnetic skyrmion technology is promising for the next-generation spintronics-based memory and neuromorphic computing due to their small size, nonvolatility and low depinning current density. However, the Magnus force originating from the skyrmion Hall effect causes the skyrmion to move along a curved trajectory, which may lead to the annihilation of the skyrmion in a nanotrack during current-induced skyrmion motion. Consequently, circuits utilizing skyrmionic motion need to be designed to limit the impact of the skyrmion Hall effect. In this work we propose a design of an artificial neuron, and a synapse using the bilayer device consisting of two antiferromagnetically exchange coupled ferromagnetic layers, which achieves robustness against the skyrmion Hall effect by nullifying the Magnus force. Using micromagnetic simulations, we show that the bilayer device can work as an artificial neuron and also as a synapse by modifying its uniaxial anisotropy. We also demonstrate that our proposed skyrmionic synapse has an intrinsic property of a perfectly linear and symmetric weight update, which is highly desirable for the synapse operation. We simulate a spiking neural network implemented using our proposed synapse and neuron and achieve a 96.23% accuracy in performing classification on the modified National Institute of Standards and Technology handwritten digit dataset.

Antiferromagnetic topological magnetism in synthetic van der Waals antiferromagnets

Antiferromagnetic (AFM) skyrmions are now becoming an intensively studied topic because they can overcome limitations of the skyrmion Hall effect and dipolar field-induced large size of skyrmions. However, most studies of the AFM skyrmions are focusing on the synthetic antiferromagnets consisting of metallic multilayers, but the investigation of AFM topological magnetism in synthetic vdW antiferromagnets is still rare as far as we know. Here, we propose and demonstrate from first-principles calculations and atomic spin model simulations that a variety of AFM topological spin textures, including skyrmion, chiral domain wall, and meron, can be induced in van der Waals (vdW) synthetic antiferromagnets, i.e., $\mathrm{Mn}{\mathrm{Bi}}_{2}\mathrm{Se}{(\mathrm{S})}_{2}{\mathrm{Te}}_{2}$ bilayer and trilayer. We further show that these noncollinear spin textures are closely hinged with stacking properties and possess unique spin dynamics. Our findings provide not only specific material candidates but also a general approach for achieving and controlling AFM topological magnetism in vdW magnets.

Gate-voltage control of alternating-current-driven skyrmion propagation in ferromagnetic nanotrack devices

Magnetic skyrmions, with topologically protected particle-like magnetization configurations, are promising information carriers for future spintronics devices with ultralow energy consumption. Generally, during motion, skyrmions suffer from the skyrmion Hall effect (SkHE) wherein the skyrmions deflect away from the intended path of the driving force. Numerous methods have been proposed to avoid this detrimental effect. In this study, we propose controllable alternating current (AC)-driven skyrmion propagation in a ferromagnetic nanowire based on combination of gate-voltage-controlled magnetic anisotropy (VCMA) and SkHE. Micromagnetic simulations show that a skyrmion oscillatory closed-loop-like in situ motion driven by AC can be transformed into directional ratchet-like propagation along the nanotrack by creating a VCMA-gate barrier. Additionally, we show that the skyrmion propagation conditions depend on the gate barrier potential and driving AC parameters, and they can be used for the optimal design of nanotrack devices. Moreover, this mechanism could be used to control skyrmion macroscopic propagation directions by dynamically alternating the voltage of another series of gates. We further show the dynamic control of the long-distance propagation of skyrmions along with the pinning state. The study results provide a promising route for designing future skyrmion-based spintronics logical and memory devices.

Enhancement of skyrmion density via interface engineering

Magnetic skyrmions are promising candidates for computing and memory applications. The static and dynamic behaviors of skyrmions are tunable by altering the interfacial magnetic properties. These interfacial magnetic properties are alterable by modifying the interface structure of thin films. However, the relationship between the structural properties of the interface and the skyrmions properties is not straightforward, and a comprehensive insight is required to facilitate better controllability of the skyrmions’ behaviors. Here, we comprehensively understand the relationship between atomic displacements at the interface and skyrmions’ static behavior. In this study, we used ion irradiation to achieve inter-atomic displacements. We observed that the inter-atomic displacements could tailor the physical properties of skyrmions. We noticed a peculiar increase in the magnetization, Dzyaloshinskii–Moriya interaction, and exchange stiffness. The modifications in magnetic properties reduced the domain wall energy, which enhanced the skyrmion density (by six-folds) and reduced the average skyrmion diameter (by 50%). Furthermore, we compared the observed results of ion irradiation with those from the annealing process (a well-studied method for modifying magnetic properties) to better understand the effect of atomic displacements. Our study provides a route to achieve a highly-dense skyrmion state, and it can be explored further to suppress the skyrmion Hall effect for skyrmion-based applications.

Skyrmion and meron ordering in quasi-two-dimensional chiral magnets

We revisit the well-known theoretical phase diagram for a two-dimensional chiral magnet with an easy-axis uniaxial anisotropy and an applied magnetic field. A particular emphasis is given to merons---quanta of the phase transition between the cycloid and the hexagonal skyrmion lattice, which possess fractional topological charges $\ifmmode\pm\else\textpm\fi{}1/2$. A localized state of two coupled merons with opposite topological charges exhibits the nonreciprocal current-driven dynamics: it experiences no skyrmion Hall effect, but due to the asymmetry of the attracting intermeron potential gives rise to asymmetric current-velocity characteristics. We also address the problem of skyrmion ordering into hexagonal and square skyrmion crystals. In an entire field range, the square lattice turns out a saddle point state between differently oriented hexagonal lattices. Merons separating elongated skyrmions were also shown to form a local energy minimum by forming a hexagonal lattice shadowing the ordinary lattice of skyrmions. In addition, we focus on the anisotropy-driven transformations of modulated phases and their isolated counterparts, which exist as detached branches of solutions on both sides from the critical anisotropy value. Moreover, a family of isolated skyrmions with both rotational senses can be found near this anisotropy value. Our results are useful from both the fundamental point of view, since they complement previous findings, and from the point of view of applications, since they provide guidelines for developing meron-based spintronic devices.

A skyrmion helicity-based multistate memory in synthetic antiferromagnets

Skyrmions in synthetic antiferromagnets (SAFs) are famous for being immune to the skyrmion Hall effect and hold the advantages of significantly higher speed for motion and smaller size than ferromagnetic systems. Therefore, skyrmions in SAFs are promising in spintronic devices. Here, we investigated the formation and in-plane-current-driven motion of bilayer skyrmions in the absence of Dzyaloshinskii–Moriya interaction by using micromagnetic simulations. Then, we studied the spacing variation between consecutive skyrmionic bits on the antiferromagnetic coupled nanotrack; it is found that there is an equilibrium distance between two Bloch skyrmions with opposite helicities. We also propose a reasonable method to distinguish skyrmions with opposite helicities. Finally, we displayed that the SAF skyrmion could pass through impurities due to topological protection. Based on these results, we designed the skyrmion helicity-based multistate memory devices in the SAF system, which have the advantages of high density and energy efficiency.