Skyrmion Velocity Research Articles

Skyrmion dynamics in width-varying nanotracks and implications for skyrmionic applications

A comprehensive study of the magnetic skyrmion dynamics in terms of size, velocity, energy, and stability in width-varying nanotracks is reported by micromagnetic simulations. We find that the diameter of a skyrmion reduces with the decrease in the nanotrack width in the spin Hall effect (SHE)-induced skyrmion motion. Accordingly, the skyrmion energy increases giving rise to the growing instability of the skyrmion. It is also numerically demonstrated that the velocity of the skyrmion varies during the motion, since the repulsive force of the nanotrack edges acting on the skyrmion as well as the driving force created by the SHE associated with the size of the skyrmion have a joint impact on the skyrmion motion dynamics in the width-varying nanotrack. In addition, one interesting finding reveals that skyrmions with small sizes, which may be inaccessible to typical approaches by means of directly injecting a spin-polarized current, could be obtained by utilizing this structure. This finding is potential for generating nanoscale skyrmions in skyrmionic applications with ultra-dense density. Finally, inspired by the skyrmion dynamics in the width-varying nanotrack, a general summary on the tradeoff between the nanotrack width (storage density) and the skyrmion velocity (data access speed) is given by further analyzing the skyrmion dynamics in parallel nanotracks with different widths, which may provide guidelines in designing racetrack-type skyrmionic applications.

Skyrmion-based multi-channel racetrack

Magnetic skyrmions are promising for the application of racetrack memories, logic gates, and other nano-devices, owing to their topologically protected stability, small size, and low driving current. In this work, we propose a skyrmion-based multi-channel racetrack memory where the skyrmion moves in the selected channel by applying voltage-controlled magnetic anisotropy gates. It is demonstrated numerically that a current-dependent skyrmion Hall effect can be restrained by the additional potential of the voltage-controlled region, and the skyrmion velocity and moving channel in the racetrack can be operated by tuning the voltage-controlled magnetic anisotropy, gate position, and current density. Our results offer a potential application of racetrack memory based on skyrmions.

Fluctuations and noise signatures of driven magnetic skyrmions

Magnetic skyrmions are particle-like objects with topologically-protected stability which can be set into motion with an applied current. Using a particle-based model we simulate current-driven magnetic skyrmions interacting with random quenched disorder and examine the skyrmion velocity fluctuations parallel and perpendicular to the direction of motion as a function of increasing drive. We show that the Magnus force contribution to skyrmion dynamics combined with the random pinning produces an isotropic effective shaking temperature. As a result, the skyrmions form a moving crystal at large drives instead of the moving smectic state observed in systems with a negligible Magnus force where the effective shaking temperature is anisotropic. We demonstrate that spectral analysis of the velocity noise fluctuations can be used to identify dynamical phase transitions and to extract information about the different dynamic phases, and show how the velocity noise fluctuations are correlated with changes in the skyrmion Hall angle, transport features, and skyrmion lattice structure.

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.

Current-driven skyrmion dynamics in disordered films

A theoretical study of the current-driven dynamics of magnetic skyrmions in disordered perpendicularly magnetized ultrathin films is presented. The disorder is simulated as a granular structure, in which the local anisotropy varies randomly from grain to grain. The skyrmion velocity is computed for different disorder parameters and ensembles. Similar behavior is seen for spin-torques due to in-plane currents and the spin Hall effect, where a pinning regime can be identified at low currents with a transition towards the disorder-free case at higher currents, similar to domain wall motion in disordered films. Moreover, a current-dependent skyrmion Hall effect and fluctuations in the core radius are found, which result from the interaction with the pinning potential.

Magnus-induced dynamics of driven skyrmions on a quasi-one-dimensional periodic substrate

We numerically examine driven skyrmions interacting with a periodic quasi-one dimensional substrate where the driving force is applied either parallel or perpendicular to the substrate periodicity direction. For perpendicular driving, the particles in a purely overdamped system simply slide along the substrate minima; however, for skyrmions where the Magnus force is relevant, we find that a rich variety of dynamics can arise. In the single skyrmion limit, the skyrmion motion is locked along the driving or longitudinal direction for low drives, while at higher drives a transition occurs to a state in which the skyrmion moves both transverse and longitudinal to the driving direction. Within the longitudinally locked phase we find a pronounced speed up effect that occurs when the Magnus force aligns with the external driving force, while at the transition to transverse and longitudinal motion, the skyrmion velocity drops, producing negative differential conductivity. For collectively interacting skyrmion assemblies, the speed up effect is still present and we observe a number of distinct dynamical phases, including a sliding smectic phase, a disordered or moving liquid phase, a moving hexatic phase, and a moving crystal phase. The transitions between the dynamic phases produce distinct features in the structure of the skyrmion lattice and in the velocity-force curves. We map these different phases as a function of the ratio of the Magnus term to the dissipative term, the substrate strength, the commensurability ratio, and the magnitude of the driving force.

Noise fluctuations and drive dependence of the skyrmion Hall effect in disordered systems

Using a particle-based simulation model, we show that quenched disorder creates a drive-dependent skyrmion Hall effect as measured by the change in the ratio of the skyrmion velocity perpendicular (V⊥) and parallel () to an external drive. R is zero at depinning and increases linearly with increasing drive, in agreement with recent experimental observations. At sufficiently high drives where the skyrmions enter a free flow regime, R saturates to the disorder-free limit. This behavior is robust for a wide range of disorder strengths and intrinsic Hall angle values, and occurs whenever plastic flow is present. For systems with small intrinsic Hall angles, we find that the Hall angle increases linearly with external drive, as also observed in experiment. In the weak pinning regime where the skyrmion lattice depins elastically, R is nonlinear and the net direction of the skyrmion lattice motion can rotate as a function of external drive. We show that the changes in the skyrmion Hall effect correlate with changes in the power spectrum of the skyrmion velocity noise fluctuations. The plastic flow regime is associated with noise, while in the regime in which R has saturated, the noise is white with a weak narrow band signal, and the noise power drops by several orders of magnitude. At low drives, the velocity noise in the perpendicular and parallel directions is of the same order of magnitude, while at intermediate drives the perpendicular noise fluctuations are much larger.

Phenomenology of current-induced skyrmion motion in antiferromagnets

We study current-driven skyrmion motion in uniaxial thin film antiferromagnets in the presence of the Dzyaloshinskii–Moriya interactions and in an external magnetic field. We phenomenologically include relaxation and current-induced torques due to both spin–orbit coupling and spatially inhomogeneous magnetic textures in the equation for the Néel vector of the antiferromagnet. Using the collective coordinate approach we apply the theory to a two-dimensional antiferromagnetic skyrmion and estimate the skyrmion velocity under an applied DC electric current.

Effect of external field on current-induced skyrmion dynamics in a nanowire

We investigate the effect of external field on current-induced skyrmion dynamics in bilayer structures with interfacial Dzyaloshinskii-Moriya interaction. We find that the skyrmion velocity can be changed depending on the direction and magnitude of external magnetic field. Perpendicular magnetic field changes the velocity through the change in the skyrmion size. On the other hand, in-plane magnetic fields distort the magnetic skyrmion, which in turn affects the maximum skyrmion velocity obtained just before the annihilation of skyrmion at nanowire edges. Our results show that skyrmion velocity can be increased by applying magnetic fields along a proper direction.

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

We study the dynamics and velocity-force curves of a skyrmion moving over a two-dimensional periodic substrate using simulations of a particle-based skyrmion model, focusing on the role of the non-dissipative Magnus term. In the overdamped limit, the skyrmion depins into a sliding state with a Hall angle of zero. When a Magnus term is included, the Hall angle is nonzero in the absence of a substrate. On a periodic substrate, the Hall angle varies with the drive amplitude. Due to the substrate symmetry the Hall angle does not change continuously with drive, but forms a series of discrete steps at rational ratios of the skyrmion velocity components perpendicular and parallel to the drive direction, when the skyrmion motion locks to symmetry directions of the substrate for fixed intervals of the drive amplitude. On each step, the Hall angle is constant and the skyrmion motion is orderly. Transitions between locked phases generate pronounced cusps in the velocity-force curves, as well as regions of negative differential mobility. The number of observable locking steps increases when the relative strength of the Magnus term increases. We find an overshoot phenomena where the Hall angle exceeds the clean limit value, as well as an acceleration effect where the skyrmion moves faster over a substrate than through a clean sample. These effects are robust for different types of periodic substrates. With a simple model for a skyrmion interacting with a single pin, we can capture the behavior of the Hall angle. The Magnus term induces a curvature in the skrymion orbit as it moves through the pin, resulting in a side step phenomenon that decreases with increasing drive. When the Magnus term is large, the range of impact parameters that permit the skyrmion to be trapped by the pin is small, which is a reasons that strong Magnus force effects reduce the pinning in skyrmion systems.

Manipulating current induced motion of magnetic skyrmions in the magnetic nanotrack

In this paper we investigate the current induced motion of magnetic skyrmions in a magnetic nanotrack with perpendicular magnetic anisotropy (PMA) using micromagnetic simulation. It is found that the size of the skyrmion can be tuned not only by the intrinsic parameters, such as Dzyaloshinskii–Moriya interaction strength and PMA constant, but also by the external magnetic field. Furthermore, the skyrmion velocity linearly depends on the size of the skyrmion. In the presence of the defects in the nanotrack, the motion of skyrmions in the chain depends not only on the current induced driving torque, but also on the repulsive skyrmion–skyrmion interaction. The critical current density of depinning can be further reduced due to the additional repulsive skyrmion–skyrmion interaction. Our work gives guidance for the future development of spintronics devices based on magnetic skyrmions.

Spin-orbit torques and anisotropic magnetization damping in skyrmion crystals

The length scale of the magnetization gradients in chiral magnets is determined by the relativistic Dzyaloshinskii-Moriya interaction. Thus, even conventional spin-transfer torques are controlled by the relativistic spin-orbit coupling in these systems, and additional relativistic corrections to the current-induced torques and magnetization damping become important for a complete understanding of the current-driven magnetization dynamics. We theoretically study the effects of reactive and dissipative homogeneous spin-orbit torques and anisotropic damping on the current-driven skyrmion dynamics in cubic chiral magnets. Our results demonstrate that spin-orbit torques play a significant role in the current-induced skyrmion velocity. The dissipative spin-orbit torque generates a relativistic Magnus force on the skyrmions, whereas the reactive spin-orbit torque yields a correction to both the drift velocity along the current direction and the transverse velocity associated with the Magnus force. The spin-orbit torque corrections to the velocity scale linearly with the skyrmion size, which is inversely proportional to the spin-orbit coupling. Consequently, the reactive spin-orbit torque correction can be the same order of magnitude as the non-relativistic contribution. More importantly, the dissipative spin-orbit torque can be the dominant force that causes a deflected motion of the skyrmions if the torque exhibits a linear or quadratic relationship with the spin-orbit coupling. In addition, we demonstrate that the skyrmion velocity is determined by anisotropic magnetization damping parameters governed by the skyrmion size.

Current-induced skyrmion dynamics in constricted geometries

Magnetic skyrmions--vortex-like swirling spin structures with a quantized topological number that are observed in chiral magnets--are appealing for potential applications in spintronics because it is possible to control their motion with ultralow current density. To realize skyrmion-based spintronic devices, it is essential to understand skyrmion motions in confined geometries. Here we show by micromagnetic simulations that the current-induced motion of skyrmions in the presence of geometrical boundaries is very different from that in an infinite plane. In a channel of finite width, transverse confinement results in steady-state characteristics of the skyrmion velocity as a function of current that are similar to those of domain walls in ferromagnets, whereas the transient behaviour depends on the initial distance of the skyrmion from the boundary. Furthermore, we show that a single skyrmion can be created by an electric current in a simple constricted geometry comprising a plate-shaped specimen of suitable size and geometry. These findings could guide the design of skyrmion-based devices in which skyrmions are used as information carriers.