Skyrmion Size Research Articles

Dynamic Behavior of Above-Room-Temperature Robust Skyrmions in 2D Van der Waals Magnet.

Magnetic skyrmions are swirl-like spin configurations that present topological properties, which have great potential as information carriers for future high-density and low-energy-consumption devices. The optimization of skyrmion-hosting materials that can be integrated with semiconductor-based circuits is the primary challenge for their industrialization. Two-dimensional van der Waals ferromagnets are emerging materials that have excellent carrier mobility and compatibility with integrated circuits, making them an ideal candidate for spintronic devices. Here, we report the realization of skyrmions at above room temperature in the 2D ferromagnet Fe3GaTe2. The thickness tunability of their skyrmion size and the formation of the skyrmion lattice are revealed. Furthermore, we demonstrate that the skyrmions can be moved by a low-density current at room temperature, together with an apparent skyrmion Hall effect, which is consistent with our quantitative micromagnetic simulation. Our work offers a promising 2D material platform for harnessing magnetic skyrmions in practical device applications.

The electron resistance of a single skyrmion within ballistic approach

An alternative way of skyrmion quasi-particle detection is simulated at low voltage bias. The point contact (PC), attached to the strip with a Néel-type skyrmion, can detect it with a higher efficiency than a magnetic tunnel junction. The method is based on detecting the skyrmion via the ballistic magnetoresistance ratio (BRR). PC's resistance with skyrmion significantly differs from the one without it. BRR is estimated in the framework of the point contact model for two directions of spin-polarized current: perpendicular to the transport direction (case 1) and along one (case 2). Skyrmion's size is assumed to be around 3.6 nm in diameter—smaller, or comparable, to the mean free path of electrons, allowing it to utilize the ballistic transport approach. As a result, resistance values for the considered Néel type skyrmion within the related size are estimated as 157 Ω for case 1 and 452.2 Ω for case 2 with optimistic BRR 101.3% and 291.7%, respectively. BRR for case 2 is higher due to the spin-filtering effect. The method also has the potential to detect the skyrmion type, or other magnetic nano structures such as bimeron, domain wall (DW), etc.

Manipulation of hybrid skyrmion dynamics by step Dzyaloshinskii–Moriya interaction approach

The topological protected magnetic state, which plays a pivotal role against any continuous deformation of a magnetic skyrmion, comes with an unwanted skyrmion Hall effect (SkHE) that poses a significant challenge in practical applications. Here, we present a detailed micromagnetic simulation study that delves into the controlled manipulation of skyrmion dynamics through subtle engineering of the Dzyaloshinskii–Moriya interaction (DMI) in a hybrid skyrmion-based racetrack. In particular, we introduce a gradient variation of bulk and interfacial DMIs, which results in a parabolic trajectory of the skyrmion motion, thereby allowing us to find a critical DMI ratio with almost zero SkHE. Most importantly, we present a novel approach involving the engineering of a racetrack with strategically placed step DMI regions that gives us meticulous control over the size and speed of the hybrid skyrmions. The present study gives a new direction for the simultaneous realization of stable skyrmions without SkHE and an increased skyrmion speed with optimized DMI engineering.

Simulation-trained machine learning models for Lorentz transmission electron microscopy

Understanding the collective behavior of complex spin textures, such as lattices of magnetic skyrmions, is of fundamental importance for exploring and controlling the emergent ordering of these spin textures and inducing phase transitions. It is also critical to understand the skyrmion–skyrmion interactions for applications such as magnetic skyrmion-enabled reservoir or neuromorphic computing. Magnetic skyrmion lattices can be studied using in situ Lorentz transmission electron microscopy (LTEM), but quantitative and statistically robust analysis of the skyrmion lattices from LTEM images can be difficult. In this work, we show that a convolutional neural network, trained on simulated data, can be applied to perform segmentation of spin textures and to extract quantitative data, such as spin texture size and location, from experimental LTEM images, which cannot be obtained manually. This includes quantitative information about skyrmion size, position, and shape, which can, in turn, be used to calculate skyrmion–skyrmion interactions and lattice ordering. We apply this approach to segmenting images of Néel skyrmion lattices so that we can accurately identify skyrmion size and deformation in both dense and sparse lattices. The model is trained using a large set of micromagnetic simulations as well as simulated LTEM images. This entirely open-source training pipeline can be applied to a wide variety of magnetic features and materials, enabling large-scale statistical studies of spin textures using LTEM.

All-optical control of skyrmion configuration in CrI monolayer.

The potential for manipulating characteristics of skyrmions in a CrI monolayer using circularly polarised light is explored. The effective skyrmion-light interaction is mediated by bright excitons whose magnetization is selectively influenced by the polarization of photons. The light-induced skyrmion dynamics is illustrated by the dependencies of the skyrmion size and the skyrmion lifetime on the intensity and polarization of the incident light pulse. Two-dimensional magnets hosting excitons thus represent a promising platform for the control of topological magnetic structures by light.

All-electrical skyrmionic magnetic tunnel junction.

Topological whirls or 'textures' of spins such as magnetic skyrmions represent the smallest realizable emergent magnetic entities1-5. They hold considerable promise as robust, nanometre-scale, mobile bits for sustainable computing6-8. A longstanding roadblock to unleashing their potential is the absence of a device enabling deterministic electrical readout of individual spin textures9,10. Here we present the wafer-scale realization of a nanoscale chiral magnetic tunnel junction (MTJ) hosting a single, ambient skyrmion. Using a suite of electrical and multimodal imaging techniques, we show that the MTJ nucleates skyrmions of fixed polarity, whose large readout signal-20-70% relative to uniformly magnetized states-corresponds directly to skyrmion size. The MTJ exploits complementary nucleation mechanisms to stabilize distinctly sized skyrmions at zero field, thereby realizing three non-volatile electrical states. Crucially, it can electrically write and delete skyrmions to both uniform states with switching energies 1,000 times lower than the state of the art. Here, the applied voltage emulates a magnetic field and, in contrast to conventional MTJs, it reshapes both the energetics and kinetics of the switching transition, enabling deterministic bidirectional switching. Our stack platform enables large readout and efficient switching, and is compatible with lateral manipulation of skyrmionic bits, providing the much-anticipated backbone for all-electrical skyrmionic device architectures9,10. Its wafer-scale realizability provides a springboard to harness chiral spin textures for multibit memory and unconventional computing8,11.

Annihilation mechanisms for interacting skyrmions in magnetic nanowire

Abstract Magnetic skyrmions are considered potential candidates for spintronics-based memory and logic devices. For achieving high-density and high-speed devices, it is essential to study their interactions. In this paper, the interaction, dynamics, and annihilation mechanisms of Néel skyrmions in nanowire confinement under the influence of spin-transfer torque (STT) and edge forces have been studied. Initially isolated, two Néel skyrmions are brought into proximity, leading to distinct interaction scenarios characterized by varying current densities. We explore the impact of these interactions on skyrmion trajectories, size evolution, and annihilation phenomena. Our findings reveal the interplay of skyrmion-skyrmion repulsive forces, edge effects, and the influence of STT, shedding light on the rich dynamics of these topological magnetic textures. Furthermore, we unveil the distinct annihilation mechanisms of the leading and trailing skyrmions under different forces, providing valuable insights into the fundamental physics of skyrmion behavior in confined geometries.

Controlling the Skyrmion Density and Size for Quantized Convolutional Neural Network

Controlling the Skyrmion Density and Size for Quantized Convolutional Neural Network

Skyrmion size and density in lattices

The effect of changing magnetic parameters on the size and density of skyrmions in a hexagonal lattice is investigated using micromagnetic simulations. Achieving control of the skyrmion density, for instance, by applied voltages, is a route to magnetic neuromorphic computing devices. Here, we show how small changes in the uniaxial magnetic anisotropy and Dzyaloshinskii–Moriya interaction lead to large changes in the skyrmion size and density, which occurs for parameters that do not support isolated skyrmions. The effect of a grain structure on the density of skyrmions is modeled through the introduction of a locally varying anisotropy. This shows that a higher density of skyrmions is favored for a wider distribution of magnetic anisotropy. The results provide a clear understanding of systems where the skyrmion density can be externally controlled and assist the design of functional skyrmion-based devices.

Dynamic Motion of Polar Skyrmions in Oxide Heterostructures.

Polar skyrmions have been widely investigated in oxide heterostructures due to their exotic properties and intriguing physical insights. However, the field-driven motion of polar skyrmions, akin to that of the magnetic counterpart, remains elusive. Herein, using phase-field simulations, we demonstrate the dynamic motion of polar skyrmions with integrated external thermal, electrical, and mechanical stimuli. External heating reduced the spontaneous polarization, while an applied electric field decreased the skyrmion size and weakened the interactions between the skyrmions. Together, the skyrmion motion barrier is significantly reduced from 40 to 2 eV under 9 V at 500 K. An applied mechanical force transformed the skyrmions into a c-domain region near the indenter center under the electric field, providing the space and driving force needed for the motion of the skyrmions. This study confirms that polar skyrmions can move like particles and provides concrete design principles for polar skyrmion-based electronic devices.

Dynamics of skyrmion contraction and expansion in a magnetic film

Contraction and expansion of skyrmions in ferromagnetic films are investigated. In centrosymmetric systems, the dynamics of a collapsing skyrmion is driven by dissipation. The collapse time has a minimum on the damping constant. In systems with broken inversion symmetry, the evolution of skyrmions toward equilibrium size is driven by the Dzyaloshinskii–Moriya interaction. Expressions describing the time dependence of the skyrmion size are derived and their implications for skyrmion-based information processing are discussed.

Size and density control of skyrmions with picometer CoFeB thickness variations—observation of zero-field skyrmions and skyrmion merging

The controlled formation and adjustment of size and density of magnetic skyrmions in Ta/CoFeB/MgO trilayers with low Dzyaloshinskii–Moriya interaction is demonstrated. Close to the out-of-plane to in-plane magnetic spin reorientation transition, we find that small energy contributions enable skyrmion formation in a narrow window of 20 pm in CoFeB thickness. Zero-field stable skyrmions are established with proper magnetic field initialization within a 10 pm CoFeB thickness range. Using magneto-optical imaging with quantitative image processing, variations in skyrmion distribution and diameter are analyzed quantitatively, the latter for sizes well below the optical resolution limit. We demonstrate the controlled merging of individual skyrmions. The overall demonstrated degree of comprehension of skyrmion control aids to the development of envisioned skyrmion based magnetic memory devices.

Theoretical studies of magnetic domain phase diagrams from micromagnetic simulation

A skyrmion is a kind of quasiparticle observed on the surface of a magnetic material, and the topologically protected vortex structure is known to be produced via spintronics. The special properties allow skyrmions to exist in the interface of devices with an ultralow accumulation rate and a high transportation rate. Magnetic domain walls such as the multiple wormhole domain show up from the ground state with different dendritic densities and shapes when the material is stimulated. The Dzyaloshinskii–Moriya interaction (Ms), anisotropy constant (K), and stiffness coefficient (A) are key parameters that affect the magnetic field relative to the representation of the skyrmion. By tuning these parameters, we can adjust the fragmentation of the magnetic domain, the stability, and the radius of the skyrmion. These parameters also modulate characteristics such as the skyrmion number and helicity, which describe the behavior of the spintronic vortex and strongness. This research shows the relation between the parameters and characteristics with the phase diagram and indicates the range of stable skyrmion existence and its size. The higher saturation magnetization Ms and the lower stiffness coefficient A cause the domain wall width to become thicker. Besides, the skyrmion number N decreases with an increase in the skyrmion size until it transforms into a deformed domain.

Direct observation of Néel-type skyrmions and domain walls in a ferrimagnetic DyCo3 thin film

Isolated magnetic skyrmions are stable, topologically protected spin textures that are at the forefront of research interests today due to their potential applications in information technology. A distinct class of skyrmion hosts are rare earth - transition metal (RE-TM) ferrimagnetic materials. To date, the nature and the control of basic traits of skyrmions in these materials are not fully understood. We show that for an archetypal ferrimagnetic material DyCo3 that exhibits a strong perpendicular anisotropy, the ferrimagnetic skyrmion size can be tuned by an external magnetic field. Moreover, by taking advantage of the high spatial resolution of scanning transmission X-ray microscopy (STXM) and utilizing a large x-ray magnetic linear dichroism (XMLD) contrast that occurs naturally at the RE resonant edges, we resolve the nature of the magnetic domain walls of ferrimagnetic skyrmions. We demonstrate that through this method one can easily discriminate between Bloch and Néel type domain walls for each individual skyrmion. For all isolated ferrimagnetic skyrmions, we observe that the domain walls are of Néel-type. This key information is corroborated with results of micromagnetic simulations and allows us to conclude on the nature of the Dzyaloshinskii-Moriya interaction (DMI) which concurs to the stabilisation of skyrmions in this ferrimagnetic system. Establishing that an intrinsic DMI occurs in RE-TM materials will also be beneficial towards a deeper understanding of chiral spin texture control in ferrimagnetic materials.

Elliptical k[formula omitted] skyrmions in the presence of the anisotropic Dzyaloshinskii–Moriya interaction

In this work, using micromagnetic simulations, we studied the stabilization of kπ skyrmions (k =1, …, 5), in the presence of the anisotropic Dzyaloshinskii–Moriya interaction (DMI), in a ferromagnetic dot. Our results show that the shape and size of the kπ skyrmions depend on the values of Dx and Dy (area unit energy densities along the x and y axes). A rich phase diagram was obtained as a function of Dx and Dy. Also, power spectra and the spatial profile of the spin wave modes of the kπ skyrmions were obtained as a function of Dx and Dy. These results show that the distribution of the maximum amplitudes of oscillation of the spin wave modes are distributed in circular or elliptical ring in the ferromagnetic dot, according to values of Dx and Dy.

Analytic theory for Néel skyrmion size, accounting for finite film thickness

The energy of a Néel skyrmion in a magnetic film with interfacial DMI is developed analytically, with the finite thickness of the film taken into account. Many theories for the energy of magnetic skyrmions use models that are only accurate in the limit that the film thickness vanishes. One theory [Büttner et al. Sci. Rep. 8, 4464 (2018)] provides exceptionally accurate expressions for the skyrmion energy for finite thickness films, but does not yield an analytic solution for the skyrmion size, plus it contains contributions which are found using fitting methods. Here, we approximate the demagnetizing energy of a skyrmion by examining the form of magnetostatic Green’s function expressions for the demagnetizing fields. Then, analytic expressions for the skyrmion radius and the skyrmion domain wall width are derived in the limit of zero applied field. Our methods are rigorously compared to other calculation methods and compare well to numerical calculations and experimental results, both with and without an applied magnetic field. The approximations that allow for an analytic result lead to a loss of accuracy for the skyrmion radius of up to 20% but this loss in accuracy may be offset by the simplicity of the developed physical expressions. Finite thickness is important to consider for skyrmions existing in multilayer stacks with total thickness of a few nanometers.

Harnessing Skyrmion Hall Effect by Thickness Gradients in Wedge-Shaped Samples of Cubic Helimagnets.

The skyrmion Hall effect, which is regarded as a significant hurdle for skyrmion implementation in thin-film racetrack devices, is theoretically shown to be suppressed in wedge-shaped nanostructures of cubic helimagnets. Under an applied electric current, ordinary isolated skyrmions with the topological charge 1 were found to move along the straight trajectories parallel to the wedge boundaries. Depending on the current density, such skyrmion tracks are located at different thicknesses uphill along the wedge. Numerical simulations show that such an equilibrium is achieved due to the balance between the Magnus force, which instigates skyrmion shift towards the wedge elevation, and the force, which restores the skyrmion position near the sharp wedge boundary due to the minimum of the edge-skyrmion interaction potential. Current-driven dynamics is found to be highly non-linear and to rest on the internal properties of isolated skyrmions in wedge geometries; both the skyrmion size and the helicity are modified in a non-trivial way with an increasing sample thickness. In addition, we supplement the well-known theoretical phase diagram of states in thin layers of chiral magnets with new characteristic lines; in particular, we demonstrate the second-order phase transition between the helical and conical phases with mutually perpendicular wave vectors. Our results are useful from both the fundamental point of view, since they systematize the internal properties of isolated skyrmions, and from the point of view of applications, since they point to the parameter region, where the skyrmion dynamics could be utilized.

Skyrmion size-tuning in two-dimensional antiferromagnetic monolayers by applying local spin-polarized current-induced spin-transfer torque

Antiferromagnetic (AFM) skyrmions exhibit a variety of outstanding features, including stability, non-volatility, processability, and resistance to the skyrmion Hall effect (SkHE). However, AFM skyrmions are insensitive to an external magnetic field, posing a major challenge for controlling their size. Tuning the key magnetic properties in AFM thin films is a feasible method for controlling skyrmion size, but it may also adversely affect other magnetic characteristics, such as the velocity and stability of the skyrmion, especially for small skyrmion sizes. In this study, we have investigated the size controllability of AFM skyrmions in the presence of the Dzyaloshinskii–Moriya interaction (DMI), applying a pure spin current in a bilayer structure consisting of a 2D AFM nanodisk placed over a thin coating of heavy metal (HM). The method relies on destabilizing the AFM lattice by targeting the 2D AFM nanodisk in a specific area defined by the diameter (dtr) using spin-polarized current-perpendicular-to-plane (CPP), causing a localized magnetization precession induced by spin-transfer torque (STT). As a result, a series of AFM skyrmions of different radii was stabilized depending on the diameter used without resorting to re-tuning the magnetic characteristics of the material. Moreover, we have found that for strong DMI, robust AFM skyrmions of small sizes can also be generated by adopting small diameters. Besides, the impact of spin current and nucleation time has been examined, and it was found that adjusting these parameters does not help to fine-tune the skyrmion size as much as it affects the nucleation process. Finally, we demonstrate how this method may be used to adjust both the radius and site of the skyrmion in the 2D AFM monolayer by simultaneously targeting different locations using pure spin currents. This method allows us to tune the AFM skyrmion size and to directly address the target skyrmion without disturbing the surrounding magnetic environment. Therefore, our results may pave the way for high-functional spintronics applications based on AFM skyrmions.

Improving Néel Domain Walls Dynamics and Skyrmion Stability Using He Ion Irradiation.

Ion irradiation with light ions is an appealing way to finely tune the magnetic properties of thin magnetic films and in particular the perpendicular magnetic anisotropy (PMA). In this work, the effect of He+ irradiation on the magnetization reversal and on the domain wall dynamics of Pt/Co/AlOx trilayers is illustrated. Fluences up to 1.5×1015 ions cm-2 strongly decrease the PMA, without affecting neither the spontaneous magnetization nor the strength of the interfacial Dzyaloshinskii-Moriya interaction (DMI). This confirms experimentally the robustness of the DMI interaction against interfacial chemical intermixing, already predicted by theory. In parallel with the decrease of the PMA, a strong decrease of the domain wall depinning field is observed after irradiation. This allows the domain walls to reach large maximum velocities with a lower magnetic field compared to that needed for the pristine films. Decoupling PMA from DMI can, therefore, be beneficial for the design of low energy devices based on domain wall dynamics. When the samples are irradiated with larger He+ fluences, the magnetization gets close to the out-of-plane/in-plane reorientation transition, where ≈100nm size magnetic skyrmions are stabilized. It is observed that as the He+ fluence increases, the skyrmion size decreases while these magnetic textures become more stable against the application of an external magnetic field, as predicted by theoretical models developed for ultrathin films with labyrinthine domains.

Stability of magnetic skyrmions: Systematic calculations of the effect of size from nanometer scale to microns

The lifetime of a magnetic skyrmion in a two-dimensional lattice is calculated as a function of size, from nanometer scale to microns, while the shape of the skyrmion remains the same. Values of the parameters in the extended Heisenberg Hamiltonian that includes exchange, anisotropy, Dzyaloshinskii-Moriya interaction, and the effect of an external field, are scaled in accordance with a continuous micromagnetic description. The lifetime increases dramatically with increased skyrmion size both because of a decrease in the entropy of the transition state with respect to that of the skyrmion state, resulting in an increase in the pre-exponential factor by four orders of magnitude, and because the activation energy increases towards an upper bound consistent with the energy of the Belavin-Polyakov soliton. While the calculated lifetime of the skyrmion for the Hamiltonian parameter values chosen here is less than a microsecond when the radius is 5 lattice constants, it reaches years when the radius is 100 lattice constants at a temperature of 200 K and an hour at room temperature. The calculations of the largest skyrmion studied here explicitly include over 20 000 000 spins.