Session M47: Dynamics of Skyrmions and Chiral Magnetic Textures

Domain wall dynamics in metallic and insulating ferrimagnets

In ferromagnet systems, engineered interfaces can give rise to the chiral Dzyaloshinskii-Moriya interaction (DMI) in otherwise symmetric systems¹. Research has primarily focused on the study of chiral solitons in metallic systems, where heavy metal underlayers provide a large spin-orbit torque and an interfacial DMI. This resulted in extensive research of chiral solitons in ferromagnetic systems^1,2. However, damping in metals is generally high, which limits soliton mobility. The low damping and ferrimagnetic dynamics of insulating garnets make them ripe candidates for ultrafast spin textures. Moreover, spin-orbit effects and spin-transport phenomenon from adjacent heavy metal layers have been used to manipulate the magnetisation in these materials³. Here, we use a pure spin current from an adjacent Pt overlayer to characterise chiral domain wall motion and DMI in epitaxial iron garnet films with perpendicular magnetic anisotropy. We use the significant interfacial DMI and a large spin-orbit torque to drive chiral domain walls to record velocities of a few thousand meters per second.
1 Emori, S. et al. Nat. Mater. 12, 611–616 (2013)
2 Woo, S. et al. Nat. Mater. 15, 501–506 (2016)
3 Avci, C. O. et al. Nat. Mater. 16, 309–314 (2017)   

Universal high-speed dynamics of distorted bubble skyrmions in an uncompensated amorphous ferrimagnet

Magnetic skyrmions are topologically stabilized spin configurations that, like domain walls (DWs), can react to external stimuli by collective displacement, which is both physically intriguing and bears promises to realize next generation non-volatile data storage technologies.
Analytical equations of motion describe straight 180° DWs in the one-dimensional (1D) model while rigid, circular bubble domains and skyrmions move according to the Thiele equation. However, DWs and skyrmions are often not perfectly straight or circular.
Here, we study how strongly deformed DWs and bubble skyrmions move in uncompensated ferrimagnetic Pt/CoGd/W in response to current pulses. We find that all 1D spin textures exhibit velocity saturation at ~300 m/s in agreement with the 1D model, while all fully enclosed spin textures, even if significantly distorted, reach >500 m/s. We attribute this significant difference in the dynamics to the topology and the canting of spins in the skyrmion’s encircling DWs.   

Chiral Edge Currents for ac Driven Skyrmions in Confined Pinning Geometries

We show that ac driven skyrmion lattices in a weak pinning channel confined by regions of strong pinning exhibit edge transport carried by skipping orbits while skyrmions in the bulk of the channel undergo localized orbits with no net transport. The magnitude of the edge currents can be controlled by varying the amplitude and frequency of the ac drive or by changing the ratio of the Magnus force to the damping term. We identify a localized phase in which the orbits are small and edge transport is absent, an edge transport regime, and a fluctuating regime that appears when the ac drive is strong enough to dynamically disorder the skyrmion lattice. In some cases, multiple rows of skyrmions participate in the transport due to a drag effect from the skyrmion-skyrmion interactions. The edge currents are robust for finite disorder and should be a general feature of skyrmions interacting with confined geometries or inhomogeneous disorder under an ac drive. Similar effects can occur for skyrmion lattices at interfaces or along domain boundaries for multiple coexisting skyrmion species. The edge current effect provides a new method to control skyrmion motion that has similarities to the emergence of edge currents in chiral active matter systems and gyroscopic metamaterials.   

Antiferromagnet-based Neuromorphics using dynamics of topological charges

Compared with conventional computers, the human brain is extremely energy efficient and can perform complicated cognitive tasks. Spintronics-based hardware implementations of neuromorphic computing has several advantages, such as low energy dissipation, consistent material platform, and nonvolatile memory. In this work, we propose a new candidate for neuromorphic hardware based on the dynamics of topological charges in an antiferromagnet. The two basic elements—neuron and synapse—are realized and we demonstrate their functionalities that are crucial to form a spiking neural network. A single magnetic domain exhibits binary switch and performs leaky integrate-and-fire as a neuron. A synapse with spike-timing-dependent plasticity is realized by a one-dimensional interacting gas of domain walls, where the synaptic weight is simply the degree of saturation of domain walls. Due to the full compatibility of our artificial neurons and synapses, Hebbian learning can be achieved by simple action rules in the connected system.   

Three-dimensional current-induced magnetic hopfion dynamics

Magnetic hopfions are three-dimensional (3D) topological spin textures characterized by the Hopf invariant. As manifesting by their 3D real-space topologies, magnetic hopfions may exhibit interesting dynamics. Here, we study the current-induced dynamics of a magnetic hopfion in 3D space. The current mainly drives a translational hopfion motion. Depending on the applied current direction, hopfion also shows different moving patterns. We then analyze the equation of motion and find these current-induced dynamics further reflect the 3D nature of hopfion. Such 3D hopfion dynamics may shed light on the study of novel 3D topological spin textures and provides a new pathway to the development of 3D spintronics.   

Skyrmions Diffusion enabling stochastic computing

Skyrmions have been suggested for a variety of applications including memory but in particular also non-conventional computing such as probabilistic computing [1]. A key problem for probabilistic computing is that cascading gates propagate undesired correlations. Therefore one needs to reshuffle the signals to keep them uncorrelated. While for many non-conventional computing approaches non-magnetic implementations are most promising, for building a “reshuffler”, skyrmions might be ideally suited due to the low footprint and low power compared to e.g. CMOS implementations [1].
We have studied low skyrmion pinning materials where we can stabilize skyrmions and controllably nucleate and displace them by current pulses due to spin-orbit torques [2]. We find topologically non-trivial N=1 skyrmions that move in the direction of the current pulses . At zero applied current, we find thermally activated skyrmion motion. We track the trajectories of skyrmions and from the dependence of their mean-square-displacement (MSD) on time, we can identify motion by diffusion and obtain the diffusion constant [2]. There is a strong dependence of the skyrmion diffusion parameter on temperature and the skyrmion size. Finally we patterning the reshuffler geometry and ascertain its performance.
Beyond ferromagnetic skyrmions, we are evaluating the efficiency of skyrmion spin structures in antiferromagnets, which have major advantages. In addition to the absence of a skyrmion Hall effect [3], also antiskyrmions can be stabilized for which first indications have been found.
[1] D. Pinna et al., Phys. Rev. Appl. 9, 064018 (2018)
[2] J. Zazvorka et al., Nature Nano. 14, 658 (2019)
[3] K. Litzius et al. Nature Phys. 13, 170 (2017)
[4] J. Barker et al., Phys. Rev. Lett. 116, 147203 (2016)
  

Skyrmion Pinball and Topological Sorting

In this work we simulate the dynamic behavior of skyrmions under the influence of a square lattice of obstacles [1,2]. First, we consider a single skyrmion while varying the size and strength of the obstacles. We find that as the obstacle size is changed, several dynamic phases may appear or vanish. For smaller obstacles, the system exhibits fewer dynamic phases because as the obstacle size is reduced. On the other hand, if the obstacle size is too large, the system may also exhibit fewer dynamic phases due to the reduction in the size of the gaps between the obstacles, which confines the skyrmion motion. Thus, the highest number of dynamic phases appears for intermediate obstacle sizes. Motivated by these results, we consider the behavior of skyrmions of different species [3] under the influence of the square obstacle array. Our preliminary results indicate that is possible to separate the species according to their different skyrmion Hall angles when a driving current is applied.

[1] S.-Z. Lin, C. Reichhardt, C. D. Batista, and A. Saxena, Phys. Rev. B 87, 214419 (2013).
[2] A. Rosch, Nat. Nanotechnol. 8, 160 (2013).
[3] C. J. O. Reichhardt and C. Reichhardt, Phys. Rev. E 99, 012606 (2019).   

Quantum Depinning of a Magnetic Skyrmion

We investigate the quantum depinning of a weakly driven skyrmion out of an impurity potential in a mesoscopic magnetic insulator. For small barrier height, the Magnus force dynamics dominates over the inertial one, and the problem is reduced to a massless charged particle in a strong magnetic field. The universal form of the WKB exponent, the rate of tunneling, and the crossover temperature between thermal and quantum tunneling is provided, independently of the detailed form of the pinning potential. The results are discussed in terms of macroscopic parameters of the insulator Cu2OSeO3 and various skyrmion radii. We demonstrate that small enough magnetic skyrmions, with a radius of ∼10 lattice sites, consisting of some thousands of spins, can behave as quantum objects at low temperatures in the mK regime [1].

[1] C. Psaroudaki and D. Loss, arXiv:1910.09585v1 (2019).   

Thermal Decay of a Single Néel Skyrmion via Helicity Slip in a Nanodisk

Dynamics of the decay of a single skyrmion confined in a ferromagnetic nanodisk in the presence of stochastic thermal noise are studied using micromagnetic simulations. By analyzing the time-varying oscillations of the in-plane and out-of-plane magnetization under the influence of the thermal field, we identified the presence of two skyrmion eigenmodes with frequencies differing by an order of magnitude– a low-frequency mode associated with gyration of skyrmion core, and a high-frequency breathing mode associated with the oscillations of the skyrmion radius. We show that the thermal fluctuations not only affects the topological charge but also the helicity of the skyrmion, changing the helicity to oscillate around ±π/4-a value which is in between that of the Néel skyrmion and a vortex. We also reveal a phenomenon of helicity slip between +π/4 and -π/4 due to the thermal fluctuations. We explain the helicity slip based on an energy barrier that arises due to a combination of thermally induced deformation of skyrmion and the finite size of the disk.   

Electron Induced Massive Dynamics of Magnetic Domain Walls

We study the effect of conduction electrons on domain walls (DWs) in metallic, ferromagnetic nanowires. Using the Keldysh collective coordinate technique, we show how electrons act as an external bath and derive the Langevin equations of motion for a DW. The DW dynamics is described by two collective degrees of freedom: position and tilt-angle. The coupled Langevin equations therefore involve two correlated noise sources, leading to a generalized fluctuation-dissipation theorem (FDT). The DW response kernel due to electrons contains two parts: one related to dissipation via FDT, and another `inertial' part. We prove that the latter term leads to a mass for both DW degrees of freedom, even though the intrinsic bare mass is zero. The resulting equations of motion contain rich dynamical solutions and point toward a new way to control domain wall motion in metals via the electronic system properties. We discuss experimental consequences including two observable signatures of the mass: hysteresis in the DW dynamics and resonant response to ac current.   

Fast, low-power defect-induced polarity switching of a magnetic vortex core

The core polarity of a topologically-protected magnetic vortex state is predicted to be extremely stable, and as such is considered as a candidate for non-volatile memory storage. However, here we show that the vortex core (VC) polarity is susceptible to rapid, repeatable switching even under low-amplitude motion. We excite vortices in thin permalloy disks with a magnetic field pulse, and observe the dynamic response using 3D time-resolved Kerr microscopy. In as-fabricated samples, we observe typical gyrations of the VC as it relaxes back to equilibrium. However, we observe a radically altered VC trajectory as prolonged pulsed laser exposure begins to change the VC pinning behavior near the disk center. In this region, the sense of gyration switches multiple times over tens of nanoseconds, indicating highly deterministic switches of the VC polarity that remain clear over >10⁶ averaged repetitions. By translating the VC equilibrium position, we can tune the number of switches to zero, or obtain single deterministic switches using field pulses of less than 0.5 mT amplitude and 3 ns duration. Finally, we show simulation results of VC-defect interaction that shed light on this phenomenon.   

Energy Storage in Spin System via Vortices

We formulate an energy-storage concept based on the topological spin textures in magnetic insulators. These textures, such as vortices, are metastable states associated with free energy. Here we propose to store energy in the topological texture of an XY ferromagnetic or antiferromagnetic annulus with easy plane anisotropy. Injecting vortices into the system will establish a net winding texture (energy density) within the bulk as vortices pass through the magnetic system. Once we complete the charging process, we can turn off the vortex conductivity and thus the energy associated with the winding texture is stored.   

Current-driving skyrmion motion in inhomogeneous films

In this talk, I will discuss current-driven skyrmion motion in disordered films. There are three phases: pinning phase, disorder-boosted transverse motion, and disordered-suppressed transverse motion. I will focus on the origin of the transverse motion boosting. Random potential landscape generate a force on a skyrmion. The force is perpendicular to the current direction when the skyrmion is pinned. The disorder-induced force is opposite to the skyrmion velocity when it is moving. Under a sufficient high current, disorders below a critical strength can boost the transverse skyrmion motion and hinder the longitudinal motion. The boosting comes mainly from the pinning force that is opposite to the driving force of the current. Skyrmions are pinned under a low current and above the critical disorder strength. Both transverse and longitudinal skyrmion motions are hindered at an intermediate current. The phase diagram will also be discussed.