Skyrmion Dynamics Research Articles

Skyrmion Dynamics in the Presence of Deformation

The nonlinear dynamics of current-driven skyrmions are essential for designing skyrmion-based spintronic devices. However, Thiele's approach uses a rigid-body assumption that is not suitable here, as skyrmions may change shape at high speeds. This study extends Thiele's equation by including the radial and tangential force components. With this approach, one may depict the inner structure of a current-driven skyrmion and propose a way to suppress deformation with an in-plane magnetic field. This extended analytic formulation may help to describe the nonlinear dynamics of other spin textures as well, and to promote applications based on such dynamics.

Current-Driven Dynamics of Skyrmions in the Presence of Pinning at Finite Temperatures

Current-Driven Dynamics of Skyrmions in the Presence of Pinning at Finite Temperatures

Current-Driven Dynamics of Skyrmions in the Presence of Pinning at Finite Temperatures

Current-Driven Dynamics of Skyrmions in the Presence of Pinning at Finite Temperatures

Dynamical Mass Generation for Ferromagnetic Skyrmions in Two Dimensions

Magnetic skyrmions are topological magnetization textures that are characterized by the homotopy group of two dimensional spheres. Despite years of intensive research on skyrmions, the fundamental problem of the inertia of a skyrmion in driven motion remains unresolved. By properly taking into account a direct coupling between skyrmion motion and the correspondingly excited magnons, we identify a dynamical mass for the skyrmion in motion. The direct coupling between skyrmion motion and magnons can be employed to engineer skyrmion dynamics with magnons through ingenious material and geometry design.

Dynamics of interstitial skyrmions in the presence of temperature gradients

An interstitial skyrmion is the skyrmion state confined in the helical background. While the spin helix naturally provides the one-dimensional channels in helical magnets, the dynamics of an interstitial skyrmion are different from that for free skyrmions in a ferromagnetic or conical background. In this paper, we studied the dynamics of interstitial skyrmions under a temperature gradient numerically and analytically. We show that the interstitial skyrmion moves from the hot area to the cold area in the presence of temperature gradients, in contrast to skyrmions in the ferromagnetic background, where they move towards the hot region. Because the interstitial skyrmion is confined in the one-dimensional channel, it moves in the same direction as the magnon flow induced by the temperature gradient, where the $\ensuremath{\beta}$-type thermomagnonic torque plays an essential role.

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.

Skyrmion dynamics and skyrmion–bimeron crossover in antiferromagnetic thin nanodisks with a random distribution of magnetic impurities

Spin texture interacting with lattice defects is an important topic in condensed matter physics. This work investigates skyrmions in antiferromagnetic nanodisks and how a random distribution of magnetic impurities affects the skyrmion dynamics induced by spin-polarized alternating currents. We consider two kinds of magnetic impurities: planar ones, in which the spin on the impurity atoms has easy-plane anisotropy, and exchange-type impurities, in which the spin of the impurity atoms has local out-of-plane anisotropy. The antiferromagnetic skyrmion (AFM-skyrmion) will be either deformed or even destroyed when it moves around the inhomogeneous region, depending on the impurity strength and concentration. The AFM skyrmion can have also breathe modes while moving in aleatory trajectories. The presence of a random distribution of exchange-type impurities may also induce a transformation of the skyrmion in bimeron and bimeron in skyrmion while the texture travels into the region with defects.

Magnetic skyrmion shape manipulation by perpendicular magnetic anisotropy excitation within geometrically confined nanostructures

Magnetic skyrmions are promising features of spintronic devices including race-track memory and nano-oscillators. Skyrmion shape can act as an additional degree of freedom along with other properties including topological charge, polarity and helicity etc. Skyrmion excitation associated with shape deformation is significant for microwave devices. By means of micromagnetic simulation study, we report skyrmion excitation within nanodiscs by dynamically modulated perpendicular magnetic anisotropy (PMA). At higher resonance frequencies, skyrmion shows shape deformation into regular polygons including elliptic, trigon, tetragon, up to decagon, characterized as n = 2, 3, 4 …, 10, respectively. We build a phase diagram showing that regular polygon shape deformation occurs within a PMA amplitude window with minimum and maximum limits depending on resonance frequency and disc radius. Further analysis reveals that with increase in disc radius, modes with higher n appear, however, skyrmion is distorted into irregular shape, with no specific polygon-like pattern, even for smaller PMA. With a semi-quantitative analysis, we relate n for different modes to resonance frequency, disc size and PMA magnitude. These findings can assist in getting fundamental physics underlying skyrmion deformation and can help in designing energy-efficient microwave generator/detector and nano-oscillator where skyrmion dynamics are very important.

Suppression of Skyrmion Hall Motion in Antiferromagnets Driven by Circularly Polarized Spin Waves

An investigation of spin waves interacting with antiferromagnetic spin textures is meaningful for future spintronic and magnonic-based memory and logic applications. In this work, we numerically study the skyrmion dynamics driven by circularly polarized spin waves in antiferromagnets and propose a method of suppressing the Hall motion. It is demonstrated that the application of two circularly polarized spin waves with opposite chirality allows the skyrmion motion straightly along the intersection line of the two spin wave sources. The skyrmion speed depending on these parameters of the spin waves and system is estimated, and a comparison with other methods is provided. Furthermore, two depinning behaviors of the skyrmion related to the strengths of the defect are also observed in the simulations. Thus, the proposed method could be used in precisely modulating the skyrmion dynamics, contributing to skyrmion-based memory device design.

The rectilinear motion of the individual asymmetrical skyrmion driven by temperature gradients

Engineering the dynamic motion of the bubble-like magnetic skyrmion exhibits great potential in the application of spintronics. Especially, as a natural property, temperature plays an important role in the skyrmion motion. For example, the non-linear motion and the random Brownian motion of skyrmions driven by temperature gradient induced spin-transfer torque and temperature fluctuation have been explored respectively. However, due to the limitation of existing hypothesis-based simulation methods, the study of the motion of individual skyrmion in temperature gradient from the perspective of the thermodynamic free energy is absent, and its kinematic equation is unclear. Here, we employed a temperature-related phase field model to demonstrate the rectilinear motions of an individual skyrmion in temperature gradients. And the thermodynamics analysis reveals that the temperature gradient induced energy imbalance of both sides of skyrmions is the driving force of skyrmion motions. Furthermore, a kinematic equation is proposed to describe the skyrmion motion in temperature gradients. Therefore, this study provides the thermodynamics mechanism and kinematic equation for skyrmion rectilinear thermal motions, which is anticipated to be the theoretical guidance for further research about dynamics of skyrmions and its potential applications in functional devices.

Ultrahigh frequency spin-torque nano-oscillator based on bilayer-skyrmions

A skyrmion in a nanodisk with a single free layer (Single-layer Skyrmion) can be excited by the spin-polarized current to a steady state of circular motion for high-frequency applications. However, limited by the threshold of the driving current owning to the skyrmion Hall effect (SkHE), the maximum frequency of the skyrmion oscillation is usually 1 ∼ 3 GHz. In this work, the dynamics of skyrmions in the nanodisk with two antiferromagnetic-coupled free layers (Bilayer-skyrmions) are investigated. Our simulations show that the maximum frequency of Bilayer-skyrmions can be increased up to above 10 GHz, about one order of magnitude larger than that of Single-layer Skyrmion because of the disappearance of the SkHE in the antiferromagnetic-coupled system. In addition, it is found that the oscillation frequency of Bilayer-skyrmions linearly increases with the current density. Finally, spin-torque nano-oscillators based on multiple pairs of Bilayer-skyrmions are further demonstrated to increase the frequency limit up to 36.5 GHz. Our results may be useful for the design and applications of current-induced skyrmion-based oscillators for ultrahigh-frequency applications.

Thermally activated dynamics of current-driven skyrmions in random media

Based on the Landau-Lifshitz-Gilbert equation, we perform large-scale numerical simulations of the skyrmion dynamics with quench disorder at finite temperatures. Two universal creep behaviors are observed below the depinning transition current, and the creep exponents are accurately determined. The thermal rounding exponents at the depinning transition indicate an anisotropic temperature dependence in the perpendicular and parallel directions of the current. Further, the temperature-current phase diagram of the skyrmion Hall angle is builded, and the thermally activated forces are analyzed. Our results provide comprehensive understanding for the role of temperature in the current-driven skyrmion dynamics.

Probe of skyrmion phases and dynamics in MnSi via the magnetoelectric effect in a composite configuration

We have developed a sensitive technique to probe the magnetic skyrmion phases and dynamics by employing the interfacial coupling effect in a magnetoelectric composite configuration. The study on a MnSi single crystal sample using this technique provides clear evidence for the skyrmion lattice phase and coexistence of skyrmion and conical phase. Above the Curie temperature ${T}_{\mathrm{C}}$, a region with strong spin fluctuation is revealed as well. By tuning the density of skyrmion or disorder, a transition from the skyrmion lattice to skyrmion-conical coexisting phase is observed. The observation is in good agreement with a theoretical model which predicts the dissipation behavior in the coexistence phase.

Spontaneous creation and annihilation dynamics of magnetic skyrmions at elevated temperature

Skyrmions are topologically protected nanoscale magnetic structures with a wide range of potential applications. Here we determine the life cycle of skyrmions from their creation to their intrinsic dynamics and thermal stability to their eventual thermodynamic demise. Using atomistic simulations of Ir/Co/Pt, parameterized from ab initio calculations, we demonstrate the thermal phase transition to a skyrmion state under application of a perpendicular magnetic field. The created skyrmions exhibit Brownian particlelike dynamics driven by the underlying thermal spin fluctuations. At an elevated temperature window well below the Curie temperature, the skyrmions are metastable and can collapse to a uniform magnetic state. With application of an external magnetic field, the intrinsic local thermal spin fluctuations at this elevated temperature window are sufficiently large to allow the spontaneous formation of new skyrmions in thermodynamic equilibrium analogous to a spontaneous skyrmion gas. Such a system could be used to implement a skyrmion-based true random number generator.

Controlled Domain-Wall Pair to Skyrmion Conversion in Typical Junction Geometry Useful for Magnetic Memory Devices

One of the important goals of modern spintronics research is to develop energy efficient magnetic memory devices. It has been recently proposed that race track memory based on skyrmion can be used as energy efficient magnetic memory due to the small threshold current required for setting its motion. Here, using micromagnetic simulation, we studied the mechanism of skyrmion creation from a pair of domain walls in a magnetic nano track geometry composed of two narrow channels and a wide channel. Interestingly, by using optimum material parameters, fixed current density, and separation between the narrow channels, we obtained velocity up to ∼450 m s−1 during the skyrmion dynamics. The selected material parameters and geometry allow the stabilization as well as controlled manipulation of topological magnetic texture. Based on these results we propose that the skyrmion based race-track memory with more than one narrow channel in a junction geometry with suitable magnetic parameters relevant for spintronic devices will enable better control of skyrmion dynamics.

Transcription and logic operations of magnetic skyrmions in bilayer cross structures

Magnetic skyrmions are potential building blocks for future information storage and computing devices. Here, we computationally study the skyrmion dynamics in a cross structure made of two ferromagnetic nanotracks. We show that by controlling the skyrmion motion in the cross structure using spin currents, it is possible to realize the transcription of skyrmion at the intersection of the cross structure at certain conditions. Based on the transcription of skyrmion, we computationally demonstrate the AND, OR and NOT logical gates using the cross structures with modified geometries and appropriate magnetic parameters. Our results may provide guidelines to design future three-dimensional spintronics devices based on magnetic skyrmions.

Skyrmion Dynamics at Finite Temperatures: Beyond Thiele's Equation.

Magnetic textures are often treated as quasiparticles following Thiele's equation of motion. We demonstrate via spin model simulations of the current-driven and Brownian motion of ferromagnetic skyrmions that the existing theory based on Thiele's equation is insufficient to describe the dynamics of skyrmions at finite temperatures. We propose an extended equation of motion that goes beyond Thiele's equation by taking into account the coupling of the skyrmion to the magnonic heat bath leading to an additional dissipative term that is linear in temperature. Our results indicate that this so-far-neglected magnon-induced friction dominates for finite temperatures and Gilbert damping values typical for thin films and multilayers.

Logic Gates Based on Synthetic Antiferromagnetic Bilayer Skyrmions

Technologies based on magnetic skyrmions, such as computational devices that can operate at high speed or with low energy consumption, have been proposed by many researchers. Recently, synthetic antiferromagnetic (SAF) structures have been proposed to increase the stability and mobility of skyrmions by reducing or eliminating the skyrmion Hall effect. Here, we numerically study the current-induced dynamics of skyrmions on SAF bilayer structures. We demonstrate the effective control and manipulation of SAF skyrmions, including directional displacement and alignment. Furthermore, we design SAF-skyrmion-based logic gates, such as the and, or, xor, and not gates. Our design provides guidance for future development of spintronic computing devices that use topological nanoscale spin textures as information carriers.

Visualizing the strongly reshaped skyrmion Hall effect in multilayer wire devices

Magnetic skyrmions are nanoscale spin textures touted as next-generation computing elements. When subjected to lateral currents, skyrmions move at considerable speeds. Their topological charge results in an additional transverse deflection known as the skyrmion Hall effect (SkHE). While promising, their dynamic phenomenology with current, skyrmion size, geometric effects and disorder remain to be established. Here we report on the ensemble dynamics of individual skyrmions forming dense arrays in Pt/Co/MgO wires by examining over 20,000 instances of motion across currents and fields. The skyrmion speed reaches 24 m/s in the plastic flow regime and is surprisingly robust to positional and size variations. Meanwhile, the SkHE saturates at ∼22∘, is substantially reshaped by the wire edge, and crucially increases weakly with skyrmion size. Particle model simulations suggest that the SkHE size dependence — contrary to analytical predictions — arises from the interplay of intrinsic and pinning-driven effects. These results establish a robust framework to harness SkHE and achieve high-throughput skyrmion motion in wire devices.

Directional locking and the influence of obstacle density on skyrmion dynamics in triangular and honeycomb arrays

We numerically examine the dynamics of a single skyrmion driven over triangular and honeycomb obstacle arrays at zero temperature. The skyrmion Hall angle θ sk, defined as the angle between the applied external drive and the direction of the skyrmion motion, increases in quantized steps or continuously as a function of the applied drive. For the obstacle arrays studied in this work, the skyrmion exhibits two main directional locking angles of θ sk = −30° and −60°. We show that these directions are privileged due to the obstacle landscape symmetry, and coincide with channels along which the skyrmion may move with few or no obstacle collisions. Here we investigate how changes in the obstacle density can modify the skyrmion Hall angles and cause some dynamic phases to appear or grow while other phases vanish. This interesting behavior can be used to guide skyrmions along designated trajectories via regions with different obstacle densities. For fixed obstacle densities, we investigate the evolution of the locked θ sk = −30° and −60° phases as a function of the Magnus force, and discuss possibilities for switching between these phases using topological selection.