Skyrmion Dynamics Research Articles

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.

Switching of a target skyrmion by a spin-polarized current

We study the spin-transfer-induced dynamics of a target skyrmion in the free layer of nanopillar structures, in which the polarizer layer has a perpendicular magnetization. By using micromagnetic simulations, it is shown that three distinct modes can be excited. As a consequence of the evolution of the lowest frequency mode, breathing mode, the polarized direction of the skyrmion core can be switched via Bloch point injection and propagation.

Generation of spin currents in the skyrmion phase of a helimagnetic insulator Cu2OSeO3

We report spin-current generation related to skyrmion dynamics resonantly excited by a microwave in a helimagnetic insulator Cu2OSeO3. A Pt layer was fabricated on Cu2OSeO3 and voltage in the Pt layer was measured upon magnetic upon magnetic resonance of Cu2OSeO3 to electrically detect injected spin currents via the inverse spin Hall effect (ISHE) in Pt. We found that ISHE-induced electromotive forces appear in the skyrmion phase of Cu2OSeO3 as well as in the ferrimagnetic phase, which shows that magnetic skyrmions can contribute to the spin pumping effect.

Dynamics and inertia of skyrmionic spin structures

Understanding the motion of magnetic skyrmions is essential if they are to be used as information carriers in devices. It is now shown that topological confinement endows the skyrmions with an unexpectedly large mass, which plays a key role in their dynamics. Skyrmions are topologically protected winding vector fields characterized by a spherical topology1. Magnetic skyrmions can arise as the result of the interplay of various interactions, including exchange, dipolar and anisotropy energy in the case of magnetic bubbles2,3,4 and an additional Dzyaloshinskii–Moriya interaction in the case of chiral skyrmions5. Whereas the static and low-frequency dynamics of skyrmions are already well under control6,7,8,9, their gigahertz dynamical behaviour2 has not been directly observed in real space. Here, we image the gigahertz gyrotropic eigenmode dynamics of a single magnetic bubble and use its trajectory to experimentally confirm its skyrmion topology. The particular trajectory points to the presence of strong inertia, with a mass much larger than predicted by existing theories. This mass is endowed by the topological confinement of the skyrmion and the energy associated with its size change. It is thereby expected to be found in all skyrmionic structures in magnetic systems and beyond. Our experiments demonstrate that the mass term plays a key role in describing skyrmion dynamics.

Inertia, diffusion, and dynamics of a driven skyrmion

Skyrmions recently discovered in chiral magnets are a promising candidate for magnetic storage devices because of their topological stability, small size ($\sim 3-100$nm), and ultra-low threshold current density ($\sim 10^{6}$A/m$^2$) to drive their motion. However, the time-dependent dynamics has hitherto been largely unexplored. Here we show, by combining the numerical solution of the Landau-Lifshitz-Gilbert equation and the analysis of a generalized Thiele's equation, that inertial effects are almost completely absent in skyrmion dynamics driven by a time-dependent current. In contrast, the response to time-dependent magnetic forces and thermal fluctuations depends strongly on frequency and is described by a large effective mass and a (anti-) damping depending on the acceleration of the skyrmion. Thermal diffusion is strongly suppressed by the cyclotron motion and is proportional to the Gilbert damping coefficient $\alpha$. This indicates that the skyrmion position is stable, and its motion responds to the time-dependent current without delay or retardation even if it is fast. These findings demonstrate the advantages of skyrmions as information carriers.

Skyrmion to ferromagnetic state transition: A description of the topological change as a finite-time singularity in the skyrmion dynamics

We investigate the topological change of a Belavin-Polyakov skyrmion under the action of a spin-polarized current. The dynamics is described by the Schr\"odinger equation for the electrons carrying the current coupled to the Landau-Lifshitz equation for the evolution of the magnetic texture in a square lattice. We show that the addition of an exchange dissipation term, tends to smooth the transition from the skyrmion state to the ferromagnetic state. We demonstrate that this topological change, in the continuum dissipationless limit, can be described as a self-similar finite-time singularity by which the skyrmion core collapses.

A strategy for the design of skyrmion racetrack memories

Magnetic storage based on racetrack memory is very promising for the design of ultra-dense, low-cost and low-power storage technology. Information can be coded in a magnetic region between two domain walls or, as predicted recently, in topological magnetic objects known as skyrmions. Here, we show the technological advantages and limitations of using Bloch and Néel skyrmions manipulated by spin current generated within the ferromagnet or via the spin-Hall effect arising from a non-magnetic heavy metal underlayer. We found that the Néel skyrmion moved by the spin-Hall effect is a very promising strategy for technological implementation of the next generation of skyrmion racetrack memories (zero field, high thermal stability, and ultra-dense storage). We employed micromagnetics reinforced with an analytical formulation of skyrmion dynamics that we developed from the Thiele equation. We identified that the excitation, at high currents, of a breathing mode of the skyrmion limits the maximal velocity of the memory.

Magnon-skyrmion scattering in chiral magnets

Understanding interactions between skyrmions and magnons is an active area of research pursued by several groups. The authors of this manuscript present a comprehensive analytical theory for the effects of skyrmions on the magnon spectrum that can lead to a topological magnon Hall effect. Conversely, magnons affect the dynamics of skyrmions via an effective reactive force resulting in a large skyrmion Hall effect.

Breathing modes of confined skyrmions in ultrathin magnetic dots

The dynamics of individual magnetic skyrmions confined in ultrathin film dots is studied theoretically. The systems considered are transition metal ferromagnets possessing perpendicular magnetic anisotropy and particular attention is given to the dynamic response of the skyrmions to perpendicular driving fields. By using micromagnetics simulations, it is shown that breathing modes can hybridize with geometrically-quantized spin wave eigenmodes of the circular dots considered, leading to distinct features in the power spectrum that differ to the behavior expected for uniformly magnetized systems. The field dependence of the breathing modes offers a direct means of detecting and characterizing such skyrmion states in experiment.

Comparing the dynamics of skyrmions and superconducting vortices

Vortices in type-II superconductors have attracted enormous attention as ideal systems in which to study nonequilibrium collective phenomena, since the self-ordering of the vortices competes with quenched disorder and thermal effects. Dynamic effects found in vortex systems include depinning, nonequilibrium phase transitions, creep, structural order–disorder transitions, and melting. Understanding vortex dynamics is also important for applications of superconductors which require the vortices either to remain pinned or to move in a controlled fashion. Recently, topological defects called skyrmions have been realized experimentally in chiral magnets. Here we highlight similarities and differences between skyrmion dynamics and vortex dynamics. Many of the previous ideas and experimental setups that have been applied to superconducting vortices can also be used to study skyrmions. We also discuss some of the differences between the two systems, such as the potentially large contribution of the Magnus force in the skyrmion system that can dramatically alter the dynamics and transport properties.

Creation and dynamics of two-dimensional skyrmions in antiferromagnetic spin-1 Bose-Einstein condensates

We numerically simulate the creation process of two-dimensional skyrmionic excitations in antiferromagnetic spin-1 Bose--Einstein condensates by solving the full three-dimensional dynamics of the system from the Gross--Pitaevskii equation. Our simulations reproduce quantitatively the experimental results of [Choi et al., Phys. Rev. Lett. 108, 035301 (2012)] without any fitting parameters. Furthermore, we examine the stability of the skyrmion by computing the temporal evolution of the condensate in a harmonic potential. The presence of both the quadratic Zeeman effect and dissipation in the simulations is vital for reproducing the experimentally observed decay time.

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.

Dynamics of skyrmions in chiral magnets: Dynamic phase transitions and equation of motion

We study the dynamics of skyrmions in a metallic chiral magnet. First, we show that skyrmions can be created dynamically by destabilizing the ferromagnetic background state through a spin polarized current. We then treat skyrmions as rigid particles and derive the corresponding equation of motion. The dynamics of skyrmions is dominated by the Magnus force, which accounts for the weak pinning of skyrmions observed in experiments. Finally, we discuss the quantum motion of skyrmions.

The dynamics of domain wall Skyrmions

It has recently been shown that Skyrmions with a fixed size can exist in theories without a Skyrme term, providing the Skyrmion is located on a domain wall. Here we numerically compute domain wall Skyrmions of this type, in a (2+1)-dimensional O(3) sigma model with a potential term. Moreover, we investigate Skyrmion dynamics, to study both Skyrmion stability and the scattering of multi-Skyrmions. We demonstrate that scattering events in which both Skyrmions remain on the same domain wall are effectively one-dimensional, and at low speeds are well-approximated by kink scattering in the integrable sine–Gordon model. However, more exotic fully two-dimensional scatterings are also presented, in which Skyrmions that are initially on different domain walls emerge on the same domain wall.

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.

Microwave magnetoelectric effect via skyrmion resonance modes in a helimagnetic multiferroic

Magnetic skyrmion, a topologically stable spin-swirling object, can host emergent electromagnetism, as exemplified by the topological Hall effect and electric-current-driven skyrmion motion. To achieve efficient manipulation of nano-sized functional spin textures, it is imperative to exploit the resonant motion of skyrmions, analogously to the role of the ferromagnetic resonance in spintronics. The magnetic resonance of skyrmions has recently been detected with oscillating magnetic fields at 1-2 GHz, launching a search for new skyrmion functionality operating at microwave frequencies. Here we show a microwave magnetoelectric effect in resonant skyrmion dynamics. Through microwave transmittance spectroscopy on the skyrmion-hosting multiferroic crystal Cu₂OSeO₃ combined with theoretical simulations, we reveal nonreciprocal directional dichroism (NDD) at the resonant mode, that is, oppositely propagating microwaves exhibit different absorption. The microscopic mechanism of the present NDD is not associated with the conventional Faraday effect but with the skyrmion magnetoelectric resonance instead, suggesting a conceptually new microwave functionality.

Dynamics of an Insulating Skyrmion under a Temperature Gradient

We study the Skyrmion dynamics in thin films under a temperature gradient. Our numerical simulations show that both single and multiple Skyrmions in a crystal move towards the high temperature region, which is contrary to particle diffusion. Noticing a similar effect in the domain wall motion, we employ a theory based on magnon dynamics to explain this counterintuitive phenomenon. Unlike the temperature driven domain wall motion, the Skyrmion's topological charge plays an important role, and a transverse Skyrmion motion is observed. Our theory turns out to be in agreement with numerical simulations, both qualitatively and quantitatively. Our calculation indicates that a very promising Skyrmion dynamic phenomenon can be observed in experiments.

Dynamics and complex structure of two-dimensional skyrmions in antiferromagnetic spin-1 Bose-Einstein condensates

Motivated by the recent experiment of Choi et al. [Phys. Rev. Lett. 108, 035301 (2012)], we simulate, within the Gross-Pitaevskii equation, the process of creating a skyrmion in an antiferromagnetic spin-1 Bose-Einstein condensate via the magnetic-field rotation method. Complex skymion structures are found and the factors influencing them are discussed. The dynamics of the system is mainly quasiperiodic. When the center of the skyrmion is displaced from the trap center, half vortices can be found at an intermediate stage of the dynamical evolution, but they do not necessarily lead to the destruction of the skyrmions.

Driven Skyrmions and dynamical transitions in chiral magnets.

We study the dynamics of Skyrmions in chiral magnets in the presence of a spin polarized current. The motion of Skyrmions in the ferromagnetic background excites spin waves and contributes to additional damping. At a large current, the spin wave spectrum becomes gapless and Skyrmions are created dynamically from the ferromagnetic state. At an even higher current, these Skyrmions are strongly deformed due to the damping and become unstable at a threshold current, leading to a chiral liquid. We show how Skyrmions can be created by increasing the current in the magnetic spiral state. We then construct a dynamic phase diagram for a chiral magnet with a current. The instability transitions between different states can be observed as experimentally clear signatures in the transport measurements, such as jumps and hysteresis.

Magnetoelectric nature of skyrmions in a chiral magnetic insulator Cu2OSeO3

Dielectric properties were investigated under various magnitudes and directions of magnetic field (H) for a chiral magnetic insulator Cu2OSeO3. We found that the skyrmion crystal induces electric polarization (P) along either in-plane or out-of-plane direction of the spin vortices depending on the applied H-direction. The observed H-dependence of P in ferrimagnetic, helimagnetic, and skyrmion crystal state can be consistently described by the d-p hybridization model, highlighting an important role of relativistic spin-orbit interaction in the magnetoelectric coupling in Cu2OSeO3. Our analysis suggests that each skyrmion particle can locally carry electric dipole or quadrupole, which implies that the dynamics of skyrmions are controllable by the external electric field.