We examine ac driven skyrmions interacting with the interface between two different obstacle array structures. We consider drive amplitudes at which skyrmions in a bulk obstacle lattice undergo only localized motion and show that when an obstacle lattice interface is introduced, directed skyrmion transport can occur along the interface. The skyrmions can be guided by a straight interface and can also turn corners to follow the interface. For a square obstacle lattice embedded in a square pinning array with a larger lattice constant, we find that skyrmions can undergo transport in all four primary symmetry directions under the same fixed ac drive. We map where localized or translating motion occurs as a function of the ac driving parameters. Our results suggest a new method for controlling skyrmion motion based on transport along obstacle lattice interfaces.
High precision skyrmion pinning by an intentionally created magnetic structure is important in skyrmion manipulation. Here, we consider skyrmion pinning by various types of disks. Among other findings, we clarify that, in terms of pinning position and pinning potential landscape, one needs to distinguish thin-wall skyrmions from thick-wall skyrmions because of fundamental differences. A skyrmion wall prefers areas with a weaker exchange stiffness, a larger DMI constant, or a smaller magnetic anisotropy while a skyrmion core experiences only the magnetic anisotropy, not exchange stiffness and D…
An understanding of the pinning of magnetic skyrmions to defects is crucial for the development of future spintronic applications. While pinning is desirable for a precise positioning of magnetic skyrmions it is detrimental when they are to be moved through a material. We use scanning tunneling microscopy to study the interaction between atomic scale defects and magnetic skyrmions that are only a few nanometers in diameter. The studied pinning centers range from single atom inlayer defects and adatoms to clusters adsorbed on the surface of our model system. We find very different pinning stren…
Resting on multi-scale modelling simulations, we explore dynamical aspects characterizing 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 first-principles. Depending on the nature of the defect and the magnitude of the applied magnetic field, the skyrmion deforms by either shri…
A key issue for skyrmion dynamics and devices are pinning effects present in real systems. While posing a challenge for the realization of conventional skyrmionics devices, exploiting pinning effects can enable non-conventional computing approaches if the details of the pinning in real samples are quantified and understood. We demonstrate that using thermal skyrmion dynamics, we can characterize the pinning of a sample and we ascertain the spatially resolved energy landscape. To understand the mechanism of the pinning, we probe the strong skyrmion size and shape dependence of the pinning. Magn…
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 of the first two, 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 skykrmion dynamics and tap into its pot…
Skyrmions are nanoscale magnetic structures with features promising for future low-power memory or logic devices. In this work, we demonstrate novel scanning techniques based on nitrogen vacancy center magnetometry that simultaneously probe both the magnetic dynamics and structure of room temperature skyrmion bubbles in a thin film system Ta/CoFeB/MgO. We confirm the handedness of the Dzyaloshinskii-Moriya interaction in this material and extract the helicity angle of the skyrmion bubbles. Our measurements also show that the skyrmion bubbles in this material change size in discrete steps, depe…
We have imaged Néel skyrmion bubbles in perpendicularly magnetised polycrystalline multilayers patterned into 1 μm diameter dots, using scanning transmission x-ray microscopy. The skyrmion bubbles can be nucleated by the application of an external magnetic field and are stable at zero field with a diameter of 260 nm. Applying an out of plane field that opposes the magnetisation of the skyrmion bubble core moment applies pressure to the bubble and gradually compresses it to a diameter of approximately 100 nm. On removing the field the skyrmion bubble returns to its original diameter via a hyste…
Using particle-based simulations, we examine the collective dynamics of skyrmions interacting with periodic pinning arrays, focusing on the impact of the Magnus force on the sliding phases. As a function of increasing pinning strength, we find a series of distinct dynamical phases, including an interstitial flow phase, a moving disordered state, a moving crystal, and a segregated cluster state. The transitions between these states produce signatures in the skyrmion lattice structure, the skyrmion Hall angle, the velocity fluctuation distributions, and the velocity-force curves. The moving clus…
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 descri…
Using numerical simulations, we examine the nonlinear dynamics of skyrmions driven over random pinning. For weak pinning, the skyrmions depin elastically, retaining sixfold ordering; however, at the onset of motion there is a dip in the magnitude of the structure factor peaks due to a decrease in positional ordering, indicating that the depinning transition can be detected using the structure factor even within the elastic depinning regime. At higher drives the moving skyrmion lattice regains full ordering. For increasing pinning strength, we find a transition from elastic to plastic depinning…
Recently spin textures called skyrmions have been discovered in certain chiral magnetic materials without spatial inversion symmetry, and have attracted enormous attention due to their promising application in spintronics since only a low applied current is necessary to drive their motion. When a conduction electron moves around the skyrmion, its spin is fully polarized by the spin texture and acquires a quantized phase; thus, the skyrmion yields an emergent electrodynamics that in turn determines skyrmion motion and gives rise to a finite Hall angle. While Skyrmions behave as particles, no pa…
In the cubic chiral magnet Fe$_{1-x}$Co$_{x}$Si a metastable state comprising of topologically nontrivial spin whirls, so-called skyrmions, may be preserved down to low temperatures by means of field cooling the sample. This metastable skyrmion state is energetically separated from the topologically trivial ground state by a considerable potential barrier, a phenomenon also referred to as topological protection. Using magnetic force microscopy on the surface of a bulk crystal, we show that certain positions are preferentially and reproducibly decorated with metastable skyrmions, indicating tha…
Current-driven skyrmion motion in random granular films is investigated with interesting findings. For a given current, there exists a critical disorder strength below which its transverse motion could either be boosted below a critical damping or be hindered above the critical damping, resulting in current and disorder dependences of skyrmion Hall angle. The boosting comes mainly from the random force that is opposite to the driving force (current). The critical damping depends on the current density and disorder strength. However, the longitudinal motion of a skyrmion is always hindered by t…
Spin torque nano-oscillator has been extensively studied both theoretically and experimentally in recent decades due to its potential applications in future microwave communication technology and neuromorphic computing. In this work, we present a skyrmion-based spin torque nano-oscillator driven by a spatially uniform direct current, where the skyrmion is confined by two pinning sites. Different from other skyrmion-based oscillators that arise from the circular motion or the breathing mode of a skyrmion, the steady-state oscillatory motions are produced by the periodic deformation of an elonga…
We report on the effect of the lateral confinement and a perpendicular magnetic field on isolated room-temperature magnetic skyrmions in sputtered Pt/Co/MgO nanotracks and nanodots. We show that the skyrmions size can be easily tuned by playing on the lateral dimensions of the nanostructures and by using external magnetic field amplitudes of a few mT, which allow to reach sub-100 nm diameters. Our XMCD-PEEM observations also highlight the important role of the pinning on the skyrmions size and stability under an out-of-plane magnetic field. Micromagnetic simulations reveal that the effect of l…
Topological spin textures can serve as non-volatile information carriers. Here we study the current-induced dynamics of an isolated magnetic skyrmion on a nanoscale square-grid pinning pattern formed by orthogonal defect lines with reduced magnetic anisotropy. The skyrmion on the square grid can be pixelated with a quantized size of the grid. We demonstrate that the position, size, and shape of skyrmion on the square grid are electrically configurable. The skyrmion center is quantized to be on the grid and the skyrmion may show a hopping motion instead of a continuous motion. We find that the …
We study the behavior of skyrmions in thin films under the action of stochastic torques arising from thermal fluctuations. We find that the Brownian motion of skyrmions is described by a stochastic Thiele's equation and its corresponding Fokker-Planck equation. The resulting Fokker-Planck equation is recognized as the one for a high-friction Brownian particle which has been studied extensively in different physical contexts. It is shown that thermal fluctuations favor the skyrmion motion allowing a finite mobility even in presence of pinning traps. We calculate explicitly the mobility tensor o…
We numerically examine thermal effects on the skyrmion Hall angle for driven skyrmions interacting with quenched disorder. We identify a creep regime in which motion occurs via intermittent jumps between pinned and flowing states. Here the skyrmion Hall angle is zero since the skyrmions have time to relax into equilibrium positions in the pinning sites, eliminating the side-jump motion induced by the Magnus force. At higher drives we find a crossover to a viscous flow regime where the skyrmion Hall angle is finite and increases with increasing drive or temperature. Our results are in agreement…
We study theoretically the dynamics of the spin textures, i.e., Skyrmion crystal (SkX) and spiral structure (SS), in two-dimensional helical magnets under external current. By numerically solving the Landau-Lifshitz-Gilbert equation, it is found that (i) the critical current density of the motion is much lower for SkX compared with SS in agreement with the recent experiment, (ii) there is no intrinsic pinning effect for SkX and the deformation of the internal structure of Skyrmion reduces the pinning effect dramatically, (iii) the Bragg intensity of SkX shows strong time-dependence as can be o…
We study the dynamical control of a magnetic skyrmion bubble by using counter-propagating surface acoustic waves (SAWs) in a ferromagnet. First, we determine the bubble mass and derive the force due to SAWs acting on a magnetic bubble using Thiele's method. The force that pushes the bubble is proportional to the strain gradient for the major strain component. We then study the dynamical pinning and motion of magnetic bubbles by SAWs in a nanowire. In a disk geometry, we propose a SAWs-driven skyrmion bubble oscillator with two resonant frequencies.
Diameter-modulated nanowires offer an important paradigm to design the magnetization response of 3D magnetic nanostructures by engineering the domain wall pinning. With the aim to understand its nature and to control the process, we analyze the magnetization response in FeCo modulated polycrystalline two-segment nanowires varying the minor diameter. Our modelling indicates a very complex behavior with a strong dependence on the disorder distribution and an important role of topologically non-trivial magnetization structures. We demonstrate that modulated nanowires with a small diameter differe…
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…
We study how impurities influence the current-induced dynamics of magnetic Skyrmions moving in a racetrack geometry. For this, we solve numerically the generalized Landau-Lifshitz-Gilbert equation extended by the current-induced spin transfer torque. In particular, we investigate two classes of impurities, non-conducting and magnetic impurities. The former are magnetically rigid objects and yield to an inhomogeneous current density over the racetrack which we determine separately by solving the fundamental electrostatic equations. In contrast, magnetic impurities leave the applied current dens…
Skyrmion Lattice Domain Formation in a Non-Flat Energy Landscape
Institute of Physics, Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学物理研究所）；Singulus Technologies AG（辛古卢斯技术有限公司）；Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology（挪威科技大学物理系量子自旋电子学中心）
Magnetic skyrmion, vortex-like swirling topologically stable spin configurations, is appealing as information carrier for future nanoelectronics, owing to the stability, small size and extremely low driving current density. One of the most promising applications of skyrmion is to build racetrack memory (RM). Compared to domain wall-based RM (DW-RM), skyrmion-based RM (Sky-RM) possesses quite a few benefits in terms of energy, density and speed etc. Until now, the fundamental behaviors, including nucleation/annihilation, motion and detection of skyrmion have been intensively investigated. Howev…
Magnetic skyrmions are quasiparticles with non-trivial topology, envisioned to play a key role in next-generation data technology while simultaneously attracting fundamental research interest due to their emerging topological charge. In chiral magnetic multilayers, current-generated spin-orbit torques or ultrafast laser excitation can be used to nucleate isolated skyrmions on a picosecond timescale. Both methods, however, produce randomly arranged skyrmions, which inherently limits the precision on the location at which the skyrmions are nucleated. Here, we show that nanopatterning of the anis…
Tunable Emergent Gauge Fields from Skyrmions in a Quasicrystalline Lattice
Department of Physics and Astronomy, The University of Tennessee（田纳西大学物理与天文学系）；Instituto de Física de Líquidos y Sistemas Biológicos, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata（拉普拉塔国立大学精确科学学院液体与生物系统物理研究所，阿根廷国家科学研究委员会）；Departamento de Ciencias Básicas, Facultad de Ingeniería, UNLP（拉普拉塔国立大学工程学院基础科学系）；Neutron Scattering Division and Shull-Wollan Center, Oak Ridge National Laboratory（橡树岭国家实验室中子散射处和舒尔-沃兰中心）；Centro Atómico Bariloche and Instituto Balseiro, CNEA（巴里洛切原子中心巴尔塞罗研究所，阿根廷核能委员会）；Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（阿根廷国家科学研究委员会）；Instituto de Nanociencia y Nanotecnología CNEA-CONICET（CNEA-CONICET纳米科学与技术研究所）
We have employed spin-polarized scanning tunneling microscopy and Monte-Carlo simulations to investigate the effect of lateral confinement onto the nanoskyrmion lattice in Fe/Ir(111). We find a strong coupling of one diagonal of the square magnetic unit cell to the close-packed edges of Fe nanostructures. In triangular islands this coupling in combination with the mismatching symmetries of the islands and of the square nanoskyrmion lattice leads to frustration and triple-domain states. In direct vicinity to ferromagnetic NiFe islands, the surrounding skyrmion lattice forms additional domains. …
Antiferromagnetic Skyrmion Scattering Revealed by Direct Time-Resolved Imaging of Collective Dynamics
Institute of Physics, Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学物理研究所）；Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University（东北大学电气通信研究所纳米电子与自旋电子学实验室）；Singulus Technologies AG（辛古卢斯科技有限公司）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Helmholtz-Zentrum Berlin für Materialien und Energie GmbH（柏林亥姆霍兹材料能源中心有限公司）
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 $R=V_{\perp}/V_{||}$ of the skyrmion velocity perpendicular ($V_{\perp}$) and parallel ($V_{||}$) 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 a…
Using small-angle neutron scattering (SANS), we investigate the deformation of the magnetic skyrmion lattice in bulk single-crystalline MnSi under electric current flow. A significant broadening of the skyrmion-lattice-reflection peaks was observed in the SANS pattern for current densities greater than a threshold value j_t ~ 1 MA/m^2 (10^6 A/m^2). We show this peak broadening to originate from a spatially inhomogeneous rotation of the skyrmion lattice, with an inverse rotation sense observed for opposite sample edges aligned with the direction of current flow. The peak broadening (and the cor…
Chiral magnets like MnSi form lattices of skyrmions, i.e. magnetic whirls, which react sensitively to small electric currents j above a critical current density jc. The interplay of these currents with tiny gradients of either the magnetic field or the temperature can induce a rotation of the magnetic pattern for j>jc. Either a rotation by a finite angle of up to 15 degree or -- for larger gradients -- a continuous rotation with a finite angular velocity is induced. We use Landau-Lifshitz-Gilbert equations extended by extra damping terms in combination with a phenomenological treatment of pinn…
Magnetic skyrmions are chiral spin textures that hold great promise as nanoscale information carriers. Since their first observation at room temperature, progress has been made in their current-induced manipulation, with fast motion reported in stray-field-coupled multilayers. However, the complex spin textures with hybrid chiralities and large power dissipation in these multilayers limit their practical implementation and the fundamental understanding of their dynamics. Here, we report on the current-driven motion of Néel skyrmions with diameters in the 100-nm range in an ultrathin Pt/Co/MgO …
The novel ratchet motion of magnetic skyrmions driven by microwave magnetic fields, with the motion direction and speed tunable by field parameters, provides a promising route to drive magnetic skyrmions in materials with poor conductivity. However, as an indirect motion, skyrmion ratchet motion speed is generally low in comparison with the direct motions driven by current. Toward practical applications, it is important to ask if there are mechanisms to realize ultrafast ratchet motion of magnetic skyrmions and how such novel motion can be integrated into racetrack-type skyrmion devices. In th…
The skyrmion-substrate interaction is an important issue to consider when studying particle-like skyrmions in nanostructures, which may strongly affect the skyrmion dynamics and lead to complex dynamic phenomena. Here, we report the current-driven dynamic behaviors of particle-like skyrmions interacting with the funnel obstacle in a ferromagnetic layer. We computationally demonstrate that a funnel obstacle with enhanced perpendicular magnetic anisotropy can be used to modify the dynamics of skyrmions due to the repulsive skyrmion-funnel interaction, which could generate several nontrivial effe…
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 …
TetMaG-Guided Design and Operando Electron Holography Validation of Current-Induced Domain-Wall Motion in 3D Curved and Cornered Fe Nanobridges
SUPA, School of Physics and Astronomy, University of Glasgow（格拉斯哥大学物理与天文学学院）；Institute for Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心离子束物理与材料研究所）；Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons（恩斯特·鲁斯卡电子显微镜与谱学中心）
