Skyrmion Trajectories Research Articles

Gesture recognition with Brownian reservoir computing using geometrically confined skyrmion dynamics

Physical reservoir computing leverages the dynamical properties of complex physical systems to process information efficiently, significantly reducing training efforts and energy consumption. Magnetic skyrmions, topological spin textures, are promising candidates for reservoir computing systems due to their enhanced stability, non-linear interactions and low-power manipulation. Traditional spin-based reservoir computing has been limited to quasi-static detection or real-world data must be rescaled to the intrinsic timescale of the reservoir. We address this challenge by time-multiplexed skyrmion reservoir computing, that allows for aligning the reservoir’s intrinsic timescales to real-world temporal patterns. Using millisecond-scale hand gestures recorded with Range-Doppler radar, we feed voltage excitations directly into our device and detect the skyrmion trajectory evolution. This method scales down to the nanometer level and demonstrates competitive or superior performance compared to energy-intensive software-based neural networks. Our hardware approach’s key advantage is its ability to integrate sensor data in real-time without temporal rescaling, enabling numerous applications.

Annihilation mechanisms for interacting skyrmions in magnetic nanowire

Abstract Magnetic skyrmions are considered potential candidates for spintronics-based memory and logic devices. For achieving high-density and high-speed devices, it is essential to study their interactions. In this paper, the interaction, dynamics, and annihilation mechanisms of Néel skyrmions in nanowire confinement under the influence of spin-transfer torque (STT) and edge forces have been studied. Initially isolated, two Néel skyrmions are brought into proximity, leading to distinct interaction scenarios characterized by varying current densities. We explore the impact of these interactions on skyrmion trajectories, size evolution, and annihilation phenomena. Our findings reveal the interplay of skyrmion-skyrmion repulsive forces, edge effects, and the influence of STT, shedding light on the rich dynamics of these topological magnetic textures. Furthermore, we unveil the distinct annihilation mechanisms of the leading and trailing skyrmions under different forces, providing valuable insights into the fundamental physics of skyrmion behavior in confined geometries.

Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures

Introduction: Magnetic skyrmions hold great promise for realizing compact and stable memory devices that can be manipulated at very low energy costs via electronic current densities.Methods: In this work, we extend a recently introduced method to describe classical skyrmion textures coupled to dynamical itinerant electrons. In this scheme, the electron dynamics is described via nonequilibrium Green’s function (NEGF) within the generalized Kadanoff–Baym ansatz, and the classical spins are treated via the Landau–Lifshitz–Gilbert equation. Here, the framework is extended to open systems by the introduction of a non-interacting approximation to the collision integral of NEGFs. This, in turn, allows us to perform computations of the real-time response of skyrmions to electronic currents in large quantum systems coupled to electronic reservoirs, which exhibit linear scaling in the number of time steps. We use this approach to investigate how electronic spin currents and dilute spin disorder affect skyrmion transport and the skyrmion Hall drift.Results: Our results show that the skyrmion dynamics is sensitive to a specific form of the spin disorder, such that different disorder configurations lead to qualitatively different skyrmion trajectories for the same applied bias.Discussion: This sensitivity arises from the local spin dynamics around the magnetic impurities, a feature that is expected not to be well-captured by phenomenological or spin-only descriptions. At the same time, our findings illustrate the potential of engineering microscopic impurity patterns to steer skyrmion trajectories.

Particle-based model of liquid crystal skyrmion dynamics.

Motivated by recent experimental results that reveal rich collective dynamics of thousands-to-millions of active liquid crystal skyrmions, we have developed a coarse-grained, particle-based model of the dynamics of skyrmions in a dilute regime. The basic physical mechanism of skyrmion motion is related to squirming undulations of domains with high director twist within the skyrmion cores when the electric field is turned on and off. The motion is not related to mass flow and is caused only by the reorientation dynamics of the director field. Based on the results of the "fine-grained" Frank-Oseen continuum model, we have mapped these squirming director distortions onto an effective force that acts asymmetrically upon switching the electrical field on or off. The resulting model correctly reproduces the skyrmion dynamics, including velocity reversal as a function of the frequency of a pulse width modulated driving voltage. We have also obtained approximate analytical expressions for the phenomenological model parameters encoding their dependence upon the cholesteric pitch and the strength of the electric field. This has been achieved by fitting coarse-grained skyrmion trajectories to those determined in the framework of the Frank-Oseen model.

Reversal of the skyrmion topological deflection across ferrimagnetic angular momentum compensation

Due to their non-trivial topology, skyrmions describe deflected trajectories, which hinders their straight propagation in nanotracks and can lead to their annihilation at the track edges. This deflection is caused by a gyrotropic force proportional to the topological charge and the angular momentum density of the host film. In this article, we present clear evidence of the reversal of the topological deflection angle of skyrmions with the sign of angular momentum density. We measured the skyrmion trajectories across the angular momentum compensation temperature (TAC) in GdCo thin films, a rare earth/transition metal ferrimagnetic alloy. The sample composition was used to engineer the skyrmion stability below and above the TAC. A refined comparison of their dynamical properties evidenced a reversal of the skyrmions deflection angle with the total angular momentum density. This reversal is a clear demonstration of the possibility of tuning the skyrmion deflection angle in ferrimagnetic materials and paves the way for deflection-free skyrmion devices.

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.

Analysis of Skyrmion Shuffling Chamber Stochasticity for Neuromorphic Computing Applications

In this study, micromagnetic simulations of a magnetic skyrmion reshuffling chamber for probabilistic computing applications are performed. The skyrmion shuffling chamber is modeled with a custom current density masking technique to capture current density variation, grain boundary variations, and anisotropy changes. The results show that the skyrmion oscillatory dynamics contribute to the system's stochasticity, allowing uncorrelated signals to be achieved with a single chamber. Our findings indicate that uncorrelated signals are generally achieved at all temperatures simulated, with the skyrmion diameter playing a role in the resulting stochasticity. Furthermore, we find that local temperature control has the benefit of not affecting the overall skyrmion diameter, while still perturbing the skyrmion trajectory. The results from varying chamber size, global temperature, and local temperature are analyzed using Pearson correlation coefficient (PCC) and p-value. This research contributes to the development of tunable probabilistic computing devices and artificial synapses using magnetic skyrmions.

SSRL: Single Skyrmion Reconfigurable Logic Utilizing 2-D Magnus Force on Magnetic Racetracks

Magnetic racetrack memory has frequently been complicated by the pinning of domain wall bits on the one hand and the need to engineer precise synchronization and inter-track repulsion between skyrmionic bits on the other. Such proposals, however, do not capitalize on the complex two-dimensional motion of skyrmions, such as transverse Magnus force that tends to deviate the skyrmion trajectory from rectilinear motion along the current drive. The transverse deviation associated with such a skyrmion Hall effect is normally considered a liability for skyrmions, and efforts have focused on eliminating rather than utilizing it for proposed device applications. We propose a simple single skyrmion-based circuit macro with elementary and higher-order logic gates that utilize Magnus force and propose reconfigurable logic built on these gates. We demonstrate the reliability of the proposed approach with micromagnetics simulation. The energy consumption in this circuit lies mainly in the overhead, with the racetrack consuming a small fraction. The energy-delay-product (EDP) is correspondingly low and can be improved by boosting the skyrmion speed.

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.

Electric Field Control of the Skyrmion Hall Effect in Piezoelectric-Magnetic Devices

Relying on both electromechanical and micromagnetic simulations, we propose a method to control the trajectory of current-driven skyrmions using an electric field in hybrid piezoelectric-magnetic systems. By applying a voltage between two lateral electrodes, a transverse strain gradient is created, as a result of the nonuniform electric field profile in the piezoelectric material. Due to magnetoelastic coupling, this transverse gradient leads to a lateral force on the skyrmions that can be used to suppress the skyrmion Hall angle for any given current density, if a proper voltage is applied. We show that this method works under realistic conditions, such as the presence of disorder in the ferromagnet, and that skyrmion trajectories can be controlled with moderate voltages. Moreover, our method allows the maximum current density that can be injected before the skyrmion is annihilated at the nanostrip edge to be increased, which leads to an increase in the maximum achievable velocities.

Control of the Half‐Skyrmion Hall Effect and Its Application to Adder–Subtractor

AbstractSkyrmions have attracted a great attention in spintronics because of their potential use as robust information carriers with distinctive protection. Though the realization of skyrmion‐based devices requires flexible control of a skyrmion motion, achieving such a skyrmion motion has been hampered by the skyrmion Hall effect (SkHE), which refers to the presence of a finite angle between a current and the skyrmion trajectory. Here, new insight for the precise control of half‐skyrmion motion is presented, including complete suppression of the SkHE by deforming the internal structure of skyrmions, which is experimentally achieved by external magnetic field to steer current‐driven half‐skyrmions in the desired direction. Furthermore, based on the unique advantages in half‐skyrmions, the potential of half‐skyrmions application beyond skyrmion‐based electronics is also demonstrated by presenting simple half‐skyrmion‐based addition/subtraction operation. The findings of controllability of 2D half‐skyrmion motion will provide new perspectives on utilization of topological solitons for device applications.

Dynamics of antiferromagnetic skyrmions in the absence or presence of pinning defects

A theoretical study on the dynamics of an antiferromagnetic (AFM) skyrmion is indispensable for revealing the underlying physics and understanding the numerical and experimental observations. In this work, we present a reliable theoretical treatment of the spin current induced motion of an AFM skyrmion in the absence and presence of pinning defect. For an ideal AFM system free of defect, the skyrmion motion velocity as a function of the intrinsic parameters can be derived, based on the concept that the skyrmion profile agrees well with the 360 domain wall formula, leading to an explicit description of the skyrmion dynamics. However, for an AFM lattice containing a defect, the skyrmion can be pinned and the depinning field as a function of damping constant and pinning strength can be described by the Thiele approach. It is revealed that the depinning behavior can be remarkably influenced by the time dependent oscillation of the skyrmion trajectory. The present theory provides a comprehensive scenario for manipulating the dynamics of AFM skyrmion, informative for future spintronic applications based on antiferromagnets.

Impurity-dependent gyrotropic motion, deflection and pinning of current-driven ultrasmall skyrmions in PdFe/Ir(111) surface

Resting on multi-scale modelling simulations, we explore dynamical aspects characterizing magnetic skyrmions driven by spin-transfer-torque towards repulsive and pinning 3d and 4d single atomic defects embedded in a Pd layer deposited on the Fe/Ir(111) surface. The latter is known to host sub-10 nm skyrmions which are of great interest in information technology. The Landau–Lifshitz–Gilbert equation is parametrized with magnetic exchange interactions extracted from the ab-initio all-electron full potential Korringa–Kohn–Rostoker Green function method, where spin–orbit coupling is added self-consistently. Depending on the nature of the defect and the magnitude of the applied magnetic field, the skyrmion deforms by either shrinking or increasing in size, experiencing thereby elliptical distortions. After applying a magnetic field of 10 T, ultrasmall skyrmions are driven along a straight line towards the various defects which permits a simple analysis of the impact of the impurities. Independently from the nature of the skyrmion-defect complex interaction, being repulsive or pinning, a gyrotropic motion is observed. A repulsive force leads to a skyrmion trajectory similar to the one induced by an attractive one. We unveil that the circular motion is clockwise around pinning impurities but counter clockwise around the repulsive ones, which can be used to identify the interaction nature of the defects by observing the skyrmions trajectories. Moreover, and as expected, the skyrmion always escapes the repulsive defects in contrast to the pinning defects, which require a minimal depinning current to observe impurity avoidance. This unveils the richness of the motion regimes of skyrmions. We discuss the results of the simulations in terms of the Thiele equation, which provides a reasonable qualitative description of the observed phenomena. Finally, we show an example of a double track made of pinning impurities, where the engineering of their mutual distance allows to control the skyrmion motion with enhanced velocity.

Diameter-independent skyrmion Hall angle observed in chiral magnetic multilayers

Magnetic skyrmions are topologically non-trivial nanoscale objects. Their topology, which originates in their chiral domain wall winding, governs their unique response to a motion-inducing force. When subjected to an electrical current, the chiral winding of the spin texture leads to a deflection of the skyrmion trajectory, characterised by an angle with respect to the applied force direction. This skyrmion Hall angle is predicted to be skyrmion diameter-dependent. In contrast, our experimental study finds that the skyrmion Hall angle is diameter-independent for skyrmions with diameters ranging from 35 to 825 nm. At an average velocity of 6 ± 1 ms−1, the average skyrmion Hall angle was measured to be 9° ± 2°. In fact, the skyrmion dynamics is dominated by the local energy landscape such as materials defects and the local magnetic configuration.

The role of temperature and drive current in skyrmion dynamics

Magnetic skyrmions are topologically stabilized nanoscale spin structures that could be of use in the development of future spintronic devices. When a skyrmion is driven by an electric current it propagates at an angle relative to the flow of current-known as the skyrmion Hall angle (SkHA)-that is a function of the drive current. This drive dependence, as well as thermal effects due to Joule heating, could be used to tailor skyrmion trajectories, but are not well understood. Here we report a study of skyrmion dynamics as a function of temperature and drive amplitude. We find that the skyrmion velocity depends strongly on temperature, while the SkHA does not and instead evolves differently in the low- and high-drive regimes. In particular, the maximum skyrmion velocity in ferromagnetic devices is limited by a mechanism based on skyrmion surface tension and deformation (where the skyrmion transitions into a stripe). Our mechanism provides a complete description of the SkHA in ferromagnetic multilayers across the full range of drive strengths, illustrating that skyrmion trajectories can be engineered for device applications. An analysis of skyrmion dynamics at different temperatures and electric drive currents is used to develop a complete description of the skyrmion Hall angle in ferromagnetic multilayers from the creep to the flow regime and illustrates that skyrmion trajectories can be engineered for device applications.

Antiferromagnetic skyrmions overcoming obstacles in a racetrack

Topological objects interacting with lattice defects is an important topic in condensed matter physics. In this paper, we would like to explore the ballistic trajectory of an antiferromagnetic skyrmion in a racetrack to study processes such as collisions of skyrmions and holes in the magnetic sample. The skyrmion is impelled against the hole-obstacle by means of a spin polarized current. Depending on the skyrmion velocity (associated to the strength of the applied current) and the type of collision (frontal or lateral), it will be captured, scattered or completely destroyed by the hole. In some cases, this obstacle can shift the skyrmion center from a straight line to another one, and it appears as an effective way of manipulating skyrmion trajectories and dynamics.

Current-driven skyrmion depinning in magnetic granular films

We consider current-driven motion of magnetic skyrmions in granular magnetic films. The study uses micromagnetic modeling and phenomenological analysis based on the Thiele formalism. Remarkably, disorder enhances the effective skyrmion Hall effect that depends on the magnitude of the driving force (current density and non-adiabaticity parameter). The origin is sliding motion of the skyrmion along the grain boundaries, followed by pinning and depinning at the grain junctions. A side-jump can occur during this depinning process. In addition, the critical current that triggers the skyrmion motion depends on the relative size of the crystallites with respect to the skyrmion size. Finally, when the skyrmion trajectory is confined along an edge by the non-adiabatic Magnus force, the critical current density can be significantly reduced. Our results imply that narrow nanowires have higher skyrmion mobilities.

Reversible to irreversible transitions in periodically driven skyrmion systems

We examine skyrmions driven periodically over random quenched disorder and show that there is a transition from reversible motion to a state in which the skyrmion trajectories are chaotic or irreversible. We find that the characteristic time required for the system to organize into a steady reversible or irreversible state exhibits a power law divergence near a critical ac drive period, with the same exponent as that observed for reversible to irreversible transitions in periodically sheared colloidal systems, suggesting that the transition can be described as an absorbing phase transition in the directed percolation universality class. We compare our results to the behavior of an overdamped system and show that the Magnus term enhances the irreversible behavior by increasing the number of dynamically accessible orbits. We discuss the implications of this work for skyrmion applications involving the long time repeatable dynamics of dense skyrmion arrays.

Motion of skyrmions in nanowires driven by magnonic momentum-transfer forces

We study the motion of magnetic skyrmions in a nanowire induced by a spin-wave current J flowing out of a driving layer close to the edge of the wire. By applying micromagnetic simulation and an analysis of the effective Thiele equation, we find that the skyrmion trajectory is governed by an interplay of both forces due to the magnon current and the wire boundary. The skyrmion is attracted to the driving layer and is accelerated by the repulsive force due to the wire boundary. We consider both cases of longitudinal and transverse driving to the nanowire, but a steady-state motion of the skyrmion is only obtained for a transverse magnon current. For the latter case, we find in the limit of low current densities J the velocity–current relation where v is the skyrmion velocity and α is the Gilbert damping. For large J, in case of strong driving, the skyrmion is pushed into the driving layer, resulting in a drop in skyrmion velocity and, eventually, the destruction of the skyrmion.

Topological dynamics and current-induced motion in a skyrmion lattice

We study the Thiele equation for current-induced motion in a skyrmion lattice through two soluble models of the pinning potential. Comprised by a Magnus term, a dissipative term and a pinning force, Thiele’s equation resembles Newton’s law but in virtue of the topological character to the first, it differs significantly from Newtonian mechanics and because the Magnus force is dominant, unlike its mechanical counterpart—the Coriolis force—skyrmion trajectories do not necessarily have mechanical counterparts. This is important if we are to understand skyrmion dynamics and tap into its potential for data-storage technology. We identify a pinning threshold velocity for the one-dimensional pinning potential and for a two-dimensional attractive potential we find a pinning point and the skyrmion trajectories toward that point are spirals whose frequency (compare Kepler’s second law) and amplitude-decay depend only on the Gilbert constant and potential at the pinning point. Other scenarios, e.g. other choices of initial spin velocity, a repulsive potential, etc are also investigated.