Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions

Magnetic vortex: fundamental physics, developments, and device applications

A magnetic vortex is one of the fundamental and topologically nontrivial spin textures in condensed matter physics. Magnetic vortices are usually the ground states in geometrically restricted ferromagnets with zero magnetocrystalline anisotropy. Magnetic vortices have recently been proposed for use in a variety of spintronics applications due to their resistance to thermal perturbations, flexibility in changing core polarity, simple patterning procedure, and potential uses in magnetic data storage with substantial density, sensors for the magnetic field, devices for logic operations, and other related fields. The data storage and computing capabilities of vortex-based devices are highly integrated and energy-efficient, with low drive current requirements. Thus, a comprehensive understanding ranging from basic physics to real-world applications is necessary to realize these devices. This article provides an overview of the recent developments in our knowledge of magnetic vortices and computing and data storage technologies that are based on them. This thorough analysis aims to advance knowledge and awareness of the possibilities of vortex-based spintronic devices in modern technologies.

Realizing Quantitative Quasiparticle Modeling of Skyrmion Dynamics in Arbitrary Potentials

We demonstrate fully quantitative Thiele model simulations of magnetic skyrmion dynamics on previously unattainable experimentally relevant large length and time scales by ascertaining the key missing parameters needed to calibrate the experimental and simulation timescales and current-induced forces. Our work allows us to determine complete spatial pinning energy landscapes that enable quantification of experimental studies of diffusion in arbitrary potentials within the Lifson-Jackson framework. Our method enables us to ascertain the timescales, and by isolating the effect of ultralow current density (order 10^{6}  A/m^{2}) generated torques we directly infer the total force acting on the skyrmion for a quantitative modeling.

Creating and Deleting a Single Dipolar Skyrmion by Surface Spin Twists

We report deterministic operations on single dipolar skyrmions confined in nanostructured cuboids by using in-plane currents. We achieve highly reversible writing and deleting of skyrmions in a simple cuboid without any artificial defects or pinning sites. The current-induced creation of skyrmions is well-understood through the spin-transfer torque acting on surface spin twists of the spontaneous 3D ferromagnetic state, caused by the magnetic dipole-dipole interaction of the uniaxial Fe3Sn2 magnet with a low-quality factor. Current-induced deletions of skyrmions result from the combined effects of magnetic hysteresis and Joule thermal heating. Our results are replicated consistently through 3D micromagnetic simulations. Our approach offers a viable method for achieving reliable single-bit operations in skyrmionic devices for applications such as random-access memories.

Topological Spin Textures: Basic Physics and Devices

In the face of escalating modern data storage demands and the constraints of Moore's Law, exploring spintronic solutions, particularly the devices based on magnetic skyrmions, has emerged as a promising frontier in scientific research. Since the first experimental observation of skyrmions, topological spin textures have been extensively studied for their great potential as efficient information carriers in spintronic devices. However, significant challenges have emerged alongside this progress. This review aims to synthesize recent advances in skyrmion research while addressing the major issues encountered in the field. Additionally, current research on promising topological spin structures in addition to skyrmions is summarized. Beyond 2D structures, exploration also extends to 1D magnetic solitons and 3D spin textures. In addition, a diverse array of emerging magnetic materials is introduced, including antiferromagnets and 2D van der Waals magnets, broadening the scope of potential materials hosting topological spin textures. Through a systematic examination of magnetic principles, topological categorization, and the dynamics of spin textures, a comprehensive overview of experimental and theoretical advances in the research of topological magnetism is provided. Finally, both conventional and unconventional applications are summarized based on spin textures proposed thus far. This review provides an outlook on future development in applied spintronics.

Topological protection of optical skyrmions through complex media

Optical Skyrmions have many important properties that make them ideal units for high-density data applications, including the ability to carry digital information through a discrete topological number and the independence of spatially varying polarization to other dimensions. More importantly, the topological nature of the optical Skyrmion heuristically suggests a strong degree of robustness to perturbations, which is crucial for reliably carrying information in noisy environments. However, the study of the topological robustness of optical Skyrmions is still in its infancy. Here, we quantify this robustness precisely by proving that the topological nature of the Skyrmion arises from its structure on the boundary and, by duality, is resilient to spatially varying perturbations provided they respect the relevant boundary conditions of the unperturbed Skyrmion. We then present experimental evidence validating this robustness in the context of paraxial Skyrmion beams against complex polarization aberrations. Our work provides a framework for handling various perturbations of Skyrmion fields and offers guarantees of robustness in a general sense. This, in turn, has implications for applications of the Skyrmion where their topological nature is exploited explicitly, and, in particular, provides an underpinning for the use of optical Skyrmions in communications and computing.

Enhancing the Thermal Stability of Skyrmion in Magnetic Nanowires for Nanoscale Data Storage

Magnetic skyrmion random switching and structural stability are critical limitations for storage data applications. Enhancing skyrmions' magnetic properties could improve their thermal structural stability. Hence, micromagnetic calculation was carried out to explore the thermal nucleation and stability of skyrmions in magnetic nanodevices. Different magnetic properties such as uniaxial magnetic anisotropy energy (Ku), saturation magnetization (Ms) and Dzyaloshinskii-Moriya interaction (DMI) were used to assess the thermal stability of skyrmions in magnetic nanowires. For some values of Ms and Ku, the results verified that the skyrmion structure is stable at temperatures above 800 K, which is higher than room temperature. Additionally, manipulating the nanowire geometry was found to have a substantial effect on the thermal structural stability of the skyrmion in storage nanodevices. Increasing the nanowire dimensions, such as length or width, enhanced skyrmions' structural stability against temperature fluctuations in nanodevices. Furthermore, the random nucleation of the skyrmions due to the device temperature was examined. It was shown that random skyrmion nucleation occurs at temperature values greater than 700 K. These findings make skyrmion devices suitable for storage applications.

Universal skyrmion logic gates and circuits based on antiferromagnetically coupled skyrmions without a topological Hall effect

Nanoscale skyrmions are spin-based quasiparticles that are promising for nonvolatile logic applications. However, the presence of the skyrmion Hall effect (SkHE) in ferromagnetic skyrmions limits their performance in logic devices. Here, we present a detailed micromagnetic modeling study on low-energy skyrmion logic gate circuits based on skyrmions in synthetic antiferromagnetically coupled (SAF) metallic ferromagnetic layers to eliminate the SkHE while reducing current requirements. First, we demonstrate the functionalities of the SAF skyrmion logic inverter gate and other Boolean gates such as NOR, OR, AND, and NAND using the inverter gate block and show the improved performance over their ferromagnetic skyrmion gate counterparts. We analyzed the operation and energy consumption at different stages of the SAF skyrmion logic operation and found that the SAF gates can operate at lower current densities. We designed a multiplexer circuit as a test case and obtained a fast response and low Joule heating. The skyrmion motion through the gates is shown to be stable and efficient in different regions, and cascading the gates creates longer linear motion without the unwanted transverse SkHE. Overall, the results indicate the feasibility of antiferromagnetically coupled skyrmions for low-energy logic with improved performance over ferromagnetic skyrmionics.

Breakdown of Volterra's Elasticity Theory of Dislocations in Polar Skyrmion Lattices

Emerging polar skyrmion crystals (SkX) have raised much interest for technological applications owing to their nontrivial topologies of electric dipoles, quasiparticle-like behaviors, and unique electrical responses. Understanding SkX defects, especially dislocations, is crucial for their unique lattice dynamics and responses; however, it still remains elusive. Here, we have not only demonstrated that a SkX dislocation exhibits an anomalously deformed core structure with over 50% elongation of skyrmions but also discovered that Volterra's elasticity theory of dislocation is broken down in SkX. Our phase-field simulation reveals that these distinct features of SkX dislocation arise from a rigid to soft quasiparticle transition of skyrmions depending on the electric field and temperature. In SkX, there exist inherent mechanics that mitigate the mismatch by both migration and deformation of skyrmions. This work provides novel insights into a new class of lattice mechanics and related functionality arising from the unique properties of quasi-particle SkX.

Gesture recognition with Brownian reservoir computing using geometrically confined skyrmion dynamics

Physical reservoir computing leverages the dynamical properties of complex physical systems to process information efficiently, significantly reducing training efforts and energy consumption. Magnetic skyrmions, topological spin textures, are promising candidates for reservoir computing systems due to their enhanced stability, non-linear interactions and low-power manipulation. Traditional spin-based reservoir computing has been limited to quasi-static detection or real-world data must be rescaled to the intrinsic timescale of the reservoir. We address this challenge by time-multiplexed skyrmion reservoir computing, that allows for aligning the reservoir's intrinsic timescales to real-world temporal patterns. Using millisecond-scale hand gestures recorded with Range-Doppler radar, we feed voltage excitations directly into our device and detect the skyrmion trajectory evolution. This method scales down to the nanometer level and demonstrates competitive or superior performance compared to energy-intensive software-based neural networks. Our hardware approach's key advantage is its ability to integrate sensor data in real-time without temporal rescaling, enabling numerous applications.

Melting and freezing of a skyrmion lattice

We report comprehensive Monte-Carlo studies of the melting of skyrmion lattices (SkL) in systems of small, medium, and large sizes with the number of skyrmions ranging from 103to over 105. Large systems exhibit hysteresis similar to that observed in real experiments on the melting of SkLs. For sufficiently small systems which achieve thermal equilibrium, a fully reversible sharp solid-liquid transition on temperature with no intermediate hexatic phase is observed. A similar behavior is found on changing the magnetic field that provides the control of pressure in the SkL. We find that on heating the melting transition occurs via a formation of grains with different orientations of hexagonal axes. On cooling, the fluctuating grains coalesce into larger clusters until a uniform orientation of hexagonal axes is slowly established. The observed scenario is caused by collective effects involving defects and is more complex than a simple picture of a transition driven by the unbinding and annihilation of dislocation and disclination pairs.

Bending skyrmion strings under two-dimensional thermal gradients

Magnetic skyrmions are topologically protected magnetization vortices that form three-dimensional strings in chiral magnets. With the manipulation of skyrmions being key to their application in devices, the focus has been on their dynamics within the vortex plane, while the dynamical control of skyrmion strings remained uncharted territory. Here, we report the effective bending of three-dimensional skyrmion strings in the chiral magnet MnSi in orthogonal thermal gradients using small angle neutron scattering. This dynamical behavior is achieved by exploiting the temperature-dependent skyrmion Hall effect, which is unexpected in the framework of skyrmion dynamics. We thus provide experimental evidence for the existence of magnon friction, which was recently proposed to be a key ingredient for capturing skyrmion dynamics, requiring a modification of Thiele's equation. Our work therefore suggests the existence of an extra degree of freedom for the manipulation of three-dimensional skyrmions.

Generation of skyrmions by combining thermal and spin-orbit torque: breaking half skyrmions into skyrmions

Skyrmions, swirling spin textures with topologically protected stability and low critical driven-current density, can be generated from the stripe domain with current pulses, bringing them closer to practical applications in racetrack memory. However, the mechanism of this topological transition from the stripe domain to the skyrmion remains unclear because the transition process occurs at a nanosecond timescale, giving rise to difficulties in observing this process using imaging tools. In this study, we controlled the domain wall - skyrmion transition by combining Joule heating with spin-orbit torque (SOT) and experimentally observed the details of this process, by which we confirmed the mechanism: the spatial variation of the topological charge density induces half skyrmions branching from the stripe domains, and these half skyrmions overcome the surface tension and break away from the stripe domain, resulting in the generation of skyrmions. The details were observed by employing Joule heating to overcome the pinning effect and manipulating the strength of the SOT to induce the branching and breaking of half skyrmions. These findings offer new insights into skyrmion generation and serve as an important step towards the development of highly efficient devices for processing and computing based on skyrmionics.

Observation of Topological Hall Effect in a Chemically Complex Alloy

The topological Hall effect (THE) is the transport response of chiral spin textures and thus can serve as a powerful probe for detecting and understanding these unconventional magnetic orders. So far, the THE is only observed in either noncentrosymmetric systems where spin chirality is stabilized by Dzyaloshinskii-Moriya interactions, or triangular-lattice magnets with Ruderman-Kittel-Kasuya-Yosida-type interactions. Here, a pronounced THE is observed in a Fe-Co-Ni-Mn chemically complex alloy with a simple face-centered cubic (fcc) structure across a wide range of temperatures and magnetic fields. The alloy is shown to have a strong magnetic frustration owing to the random occupation of magnetic atoms on the close-packed fcc lattice and the direct Heisenberg exchange interaction among atoms, as evidenced by the appearance of a reentrant spin glass state in the low-temperature regime and the first principles calculations. Consequently, THE is attributed to the nonvanishing spin chirality created by strong spin frustration under the external magnetic field, which is distinct from the mechanism responsible for the skyrmion systems, as well as geometrically frustrated magnets.

Quantification of Hybrid Topological Spin Textures and Their Nanoscale Fluctuations in Ferrimagnets

Noncolinear spin textures, including chiral stripes and skyrmions, have shown great potential in spintronics. Basic configurations of spin textures are either Bloch or Néel types, and the intermediate hybrid type has rarely been reported. A major challenge in identifying hybrid spin textures is to quantitatively determine the hybrid angle, especially in ferrimagnets with weak net magnetization. Here, we develop an approach to quantify magnetic parameters, including chirality, saturation magnetization, domain wall width, and hybrid angle with sub-5 nm spatial resolution, based on Lorentz four-dimensional scanning transmission electron microscopy (Lorentz 4D-STEM). We find strong nanometer-scale variations in the hybrid angle and domain wall width within structurally and chemically homogeneous FeGd ferrimagnetic films. These variations fluctuate during different magnetization circles, revealing intrinsic local magnetization inhomogeneities. Furthermore, hybrid skyrmions can also be nucleated in FeGd films. These analyses demonstrate that the Lorentz 4D-STEM is a quantitative tool for exploring complex spin textures.

Dynamical Control of Topology in Polar Skyrmions via Twisted Light

Twisted light carries a nonzero orbital angular momentum, that can be transferred from light to electrons and particles ranging from nanometers to micrometers. Up to now, the interplay between twisted light with dipolar systems has scarcely been explored, though the latter bear abundant forms of topologies such as skyrmions and embrace strong light-matter coupling. Here, using first-principles-based simulations, we show that twisted light can excite and drive dynamical polar skyrmions and transfer its nonzero winding number to ferroelectric ultrathin films. The skyrmion is successively created and annihilated alternately at the two interfaces, and experiences a periodic transition from a markedly "Bloch" to "Néel" character, accompanied with the emergence of a "Bloch point" topological defect with vanishing polarization. The dynamical evolution of skyrmions is connected to a constant jump of topological number between "0" and "1" over time. These intriguing phenomena are found to have an electrostatic origin. Our study thus demonstrates that, and explains why this unique light-matter interaction can be very powerful in creating and manipulating topological solitons in functional materials.

Chiral Skyrmions Interacting with Chiral Flowers

The chiral nature of active matter plays an important role in the dynamics of active matter interacting with chiral structures. Skyrmions are chiral objects, and their interactions with chiral nanostructures can lead to intriguing phenomena. Here, we explore the random-walk dynamics of a thermally activated chiral skyrmion interacting with a chiral flower-like obstacle in a ferromagnetic layer, which could create topology-dependent outcomes. It is a spontaneous mesoscopic order-from-disorder phenomenon driven by the thermal fluctuations and topological nature of skyrmions that exists only in ferromagnetic and ferrimagnetic systems. The interactions between the skyrmions and chiral flowers at finite temperatures can be utilized to control the skyrmion position and distribution without applying any external driving force or temperature gradient. The phenomenon that thermally activated skyrmions are dynamically coupled to chiral flowers may provide a new way to design topological sorting 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.

All-Electrical 9-Bit Skyrmion-Based Racetrack Memory Designed with Laser Irradiation

Racetrack memories with magnetic skyrmions have recently been proposed as a promising storage technology. To be appealing, several challenges must still be faced for the deterministic generation of skyrmions, their high-fidelity transfer, and accurate reading. Here, we realize the first proof-of-concept of a 9-bit skyrmion racetrack memory with all-electrical controllable functionalities implemented in the same device. The key ingredient is the generation of a tailored nonuniform distribution of magnetic anisotropy via laser irradiation in order to (i) create a well-defined skyrmion nucleation center, (ii) define the memory cells hosting the information coded as the presence/absence of skyrmions, and (iii) improve the signal-to-noise ratio of anomalous Hall resistance measurements. This work introduces a strategy to unify previous findings and predictions for the development of a generation of racetrack memories with robust control of skyrmion nucleation and position, as well as effective skyrmion electrical detection.

Ordered creation and motion of skyrmions with surface acoustic wave

Magnetic skyrmions with a well-defined spin texture have shown unprecedented potential for various spintronic applications owning to their topologically non-trivial and quasiparticle properties. To put skyrmions into practical technology, efficient manipulation, especially the inhibition of skyrmion Hall effect (SkHE) has been intensively pursued. In spite of the recent progress made on reducing SkHE in several substituted systems, such as ferrimagnets and synthetic antiferromagnets, the organized creation and current driven motion of skyrmions with negligible SkHE in ferromagnets remain challenging. Here, by embedding the [Co/Pd] multilayer into a surface acoustic wave (SAW) delay line where the longitudinal leaky SAW is excited to provide both the strain and thermal effect, we experimentally realized the ordered generation of magnetic skyrmions. The resultant current-induced skyrmions movement with negligible SkHE was observed, which can be attributed to the energy redistribution of the system during the excitation of SAW. Our findings open up an unprecedentedly new perspective for manipulating topological solitons, which could possibly trigger the future discoveries in skyrmionics and spin acousto-electronics.

Encoding and Multiplexing Information Signals in Magnetic Multilayers with Fractional Skyrmion Tubes

Tailored magnetic multilayers (MMLs) provide skyrmions with enhanced thermal stability, leading to the possibility of skyrmion-based devices for room-temperature applications. At the same time, the search for additional stable topological spin textures has been under intense research focus. Besides their fundamental importance, such textures may expand the information encoding capability of spintronic devices. However, fractional spin texture states within MMLs in the vertical dimension are yet to be investigated. In this work, we demonstrate numerically fractional skyrmion tubes (FSTs) in a tailored MML system. We subsequently propose to encode sequences of information signals with FSTs as information bits in a tailored MML device. Micromagnetic simulations and theoretical calculations are used to verify the feasibility of hosting distinct FST states within a single device, and their thermal stability is investigated. A multilayer multiplexing device is proposed, where multiple sequences of the information signals can be encoded and transmitted based on the nucleation and propagation of packets of FSTs. Finally, pipelined information transmission and automatic demultiplexing are demonstrated by exploiting the skyrmion Hall effect and introducing voltage-controlled synchronizers and width-based track selectors. The findings indicate that FSTs can be potential candidates as information carriers for future spintronic applications.

Spherical ferroelectric solitons

Spherical ferroelectric domains, such as electrical bubbles, polar skyrmion bubbles and hopfions, share a single and unique feature-their homogeneously polarized cores are surrounded by a vortex ring of polarization whose outer shells form a spherical domain boundary. The resulting polar texture, typical of three-dimensional topological solitons, has an entirely new local symmetry characterized by a high polarization and strain gradients. Consequently, spherical domains represent a different material system of their own with emergent properties drastically different from that of their surrounding medium. Examples of new functionalities inherent to spherical domains include chirality, optical response, negative capacitance and giant electromechanical response. These characteristics, particularly given that the domains naturally have an ultrafine scale, offer new opportunities in high-density and low-energy nanoelectronic technologies. This Perspective gives an insight into the complex polar structure and physical origin of these spherical domains, which facilitates the understanding and development of spherical domains for device applications.

300-Times-Increased Diffusive Skyrmion Dynamics and Effective Pinning Reduction by Periodic Field Excitation

Thermally induced skyrmion dynamics, as well as skyrmion pinning effects, in thin films have attracted significant interest. While pinning poses challenges in deterministic skyrmion devices and slows down skyrmion diffusion, for applications in non-conventional computing, both pinning of an appropriate strength and skyrmion diffusion speed are key. Here, periodic field excitations are employed to realize an increase of the skyrmion diffusion by more than two orders of magnitude. Amplifying the excitation, a drastic reduction of the effective skyrmion pinning, is reported, and a transition from pinning-dominated diffusive hopping to dynamics approaching free diffusion is observed. By tailoring the field oscillation frequency and amplitude, a continuous tuning of the effective pinning and skyrmion dynamics is demonstrated, which is a key asset and enabler for non-conventional computing applications. It is found that the periodic excitations additionally allow stabilization of skyrmions at different sizes for field values that are inaccessible in static systems, opening up new approaches to ultrafast skyrmion motion by transiently exciting moving skyrmions.

Skyrmion based majority logic gate by voltage controlled magnetic anisotropy in a nanomagnetic device

Magnetic skyrmions are topologically protected spin textures and they are suitable for future logic-in-memory applications for energy-efficient, high-speed information processing and computing technologies. In this work, we have demonstrated skyrmion-based 3 bit majority logic gate using micromagnetic simulations. The skyrmion motion is controlled by introducing agatethat works on voltage controlled magnetic anisotropy. Here, the inhomogeneous magnetic anisotropy behaves as a tunable potential barrier/well that modulates the skyrmion trajectory in the structure for the successful implementation of the majority logic gate. In addition, several other effects such as skyrmion-skyrmion topological repulsion, skyrmion-edge repulsion, spin-orbit torque and skyrmion Hall effect have been shown to govern the logic functionalities. We have systematically presented the robust logic operations by varying the current density, magnetic anisotropy, voltage-controlled gate dimension and geometrical parameters of the logic device. The skyrmion Hall angle is monitored to understand the trajectory and stability of the skyrmion as a function of time in the logic device. The results demonstrate a novel method to achieve majority logic by using voltage controlled magnetic anisotropy which further opens up a new route for skyrmion-based low-power and high-speed computing devices.

Universal Quantum Computation Based on Nanoscale Skyrmion Helicity Qubits in Frustrated Magnets

We propose a skyrmion-based universal quantum computer. Skyrmions have the helicity degree of freedom in frustrated magnets, where twofold degenerated Bloch-type skyrmions are energetically favored by the magnetic dipole-dipole interaction. We construct a qubit based on them. A skyrmion must become a quantum-mechanical object when its size is of the order of nanometers. It is shown that the universal quantum computation is possible based on nanoscale skyrmions in a magnetic bilayer system. The one-qubit quantum gates are materialized by controlling the electric field and the spin current. The two-qubit gate is materialized with the use of the Ising-type exchange coupling. The merit of the present mechanism is that external magnetic field is not necessary. Our results may open a possible way toward universal quantum computation based on nanoscale topological spin textures.

Local Manipulation of Skyrmion Nucleation in Microscale Areas of a Thin Film with Nitrogen-Ion Implantation

Precise manipulation of skyrmion nucleation in microscale or nanoscale areas of thin films is a critical issue in developing high-efficient skyrmionic memories and logic devices. Presently, the mainstream controlling strategies focus on the application of external stimuli to tailor the intrinsic attributes of charge, spin, and lattice. This work reports effective skyrmion manipulation by controllably modifying the lattice defect through ion implantation, which is potentially compatible with large-scale integrated circuit technology. By implanting an appropriate dose of nitrogen ions into a Pt/Co/Ta multilayer film, the defect density was effectively enhanced to induce an apparent modulation of magnetic anisotropy, consequently boosting the skyrmion nucleation. Furthermore, the local control of skyrmions in microscale areas of the macroscopic film was realized by combining the ion implantation with micromachining technology, demonstrating a potential application in both binary storage and multistate storage. These findings provide a new approach to advancing the functionalization and application of skyrmionic devices.

Magnetic Skyrmion Transistor Gated with Voltage-Controlled Magnetic Anisotropy

The paradigm shift of information carriers from charge to spin has long been awaited in modern electronics. The invention of the spin-information transistor is expected to be an essential building block for the future development of spintronics. Here, a proof-of-concept experiment of a magnetic skyrmion transistor working at room temperature, which has never been demonstrated experimentally, is introduced. With the spatially uniform control of magnetic anisotropy, the shape and topology of a skyrmion when passing the controlled area can be maintained. The findings will open a new route toward the design and realization of skyrmion-based spintronic devices in the near future.

Magnon scattering modulated by omnidirectional hopfion motion in antiferromagnets for meta-learning

Neuromorphic computing is expected to achieve human-brain performance by reproducing the structure of biological neural systems. However, previous neuromorphic designs based on synapse devices are all unsatisfying for their hardwired network structure and limited connection density, far from their biological counterpart, which has high connection density and the ability of meta-learning. Here, we propose a neural network based on magnon scattering modulated by an omnidirectional mobile hopfion in antiferromagnets. The states of neurons are encoded in the frequency distribution of magnons, and the connections between them are related to the frequency dependence of magnon scattering. Last, by controlling the hopfion's state, we can modulate hyperparameters in our network and realize the first meta-learning device that is verified to be well functioning. It not only breaks the connection density bottleneck but also provides a guideline for future designs of neuromorphic devices.

Skyrmion based 3D low complex runtime reconfigurable architecture design methodology of universal logic gate

In this study, we introduce the area efficient low complex runtime reconfigurable architecture design methodology based on Skyrmion logic for universal logic gate (ULG) i.e. NOR/NAND implementation using micromagnetic simulations. We have modelled the two input 3D device structure using bilayer ferromagnet/heavy metal where the magnetic tunnel junctions inject and detect the input and output skyrmions by exploiting the input reversal mechanism. The implementation of NOR and NAND is performed using this same device where it is reconfigured runtime with enhanced tunability by the ON and OFF state of current passing through a non magnetic metallic gate respectively. This gate acts as a barrier for skyrmion motion (additional control mechanism) to realize the required Skyrmion logic output states. To the best of authors's knowledge the boolean optimizations and the mapping logic have been presented for the first time to demonstrate the functionalities of the NOR/NAND implementation. This proposed architecture design methodology of ULG leads to reduced device footprint with regard to the number of thin film structures proposed, low complexity in terms of fabrication and also providing runtime reconfigurability to reduce the number of physical designs to achieve all truth table entries (∼75% device footprint reduction). The proposed 3D ULG architecture design benefits from the miniaturization resulting in opening up a new perspective for magneto-logic devices.

Skyrmions Under Control-FIB Irradiation as a Versatile Tool for Skyrmion Circuits

Magnetic data storage and processing offer certain advances over conventional technologies, amongst which nonvolatility and low power operation are the most outstanding ones. Skyrmions are a promising candidate as a magnetic data carrier. However, the sputtering of skyrmion films and the control of the skyrmion nucleation, motion, and annihilation remains challenging. This work demonstrates that using optimized focused ion beam irradiation and annealing protocols enables the skyrmion phase in W/CoFeB/MgO thin films to be accessed easily. By analyzing ion-beam-engineered skyrmion hosting wires, excited by sub-100 ns current pulses, possibilities to control skyrmion nucleation, guide their motion, and control their annihilation unfold. Overall, the key elements needed to develop extensive skyrmion networks are presented.

Current-Induced Magnetic Skyrmions with Controllable Polarities in the Helical Phase

We report the current-induced creation of magnetic skyrmions in a chiral magnet FeGe nanostructure by using in situ Lorentz transmission electron microscopy. We show that magnetic skyrmions with controllable polarity can be transferred from the helical ground state simply by controlling the direction of the current flow at zero magnetic fields. The force analysis and symmetry consideration, backed up by micromagnetic simulations, well explain the experimental results, where magnetic skyrmions are created because of the edge instability of the helical state in the presence of spin-transfer torque. The on-demand generation of skyrmions and control of their polarity by electric current without the need for a magnetic field will enable novel purely electric-controlled skyrmion devices.

Magnetic Field Magnitudes Needed for Skyrmion Generation in a General Perpendicularly Magnetized Film

Due to its topological protection, the magnetic skyrmion has been intensively studied for both fundamental aspects and spintronics applications. However, despite recent advancements in skyrmion research, the deterministic creation of isolated skyrmions in a generic perpendicularly magnetized film is still one of the most essential and challenging techniques. Here, we present a method to create magnetic skyrmions in typical perpendicular magnetic anisotropy (PMA) films by applying a magnetic field pulse and a method to determine the magnitude of the required external magnetic fields. Furthermore, to demonstrate the usefulness of this result for future skyrmion research, we also experimentally study the PMA dependence on the minimum size of skyrmions. Although field-driven skyrmion generation is unsuitable for device application, this result can provide an easier approach for obtaining isolated skyrmions, making skyrmion-based research more accessible.

Confinement of Skyrmions in Nanoscale FeGe Device-like Structures

Skyrmion-based devices have been proposed as a promising solution for low-energy data storage. These devices include racetrack or logic structures and require skyrmions to be confined in regions with dimensions comparable to the size of a single skyrmion. Here we examine skyrmions in FeGe device shapes using Lorentz transmission electron microscopy to reveal the consequences of skyrmion confinement in a device-like structure. Dumbbell-shaped elements were created by focused ion beam milling to provide regions where single skyrmions are confined adjacent to areas containing a skyrmion lattice. Simple block shapes of equivalent dimensions were also prepared to allow a direct comparison with skyrmion formation in a less complex, yet still confined, device geometry. The impact of applying a magnetic field and varying the temperature on the formation of skyrmions within the shapes was examined. This revealed that it is not just confinement within a small device structure that controls the position and number of skyrmions but that a complex device geometry changes the skyrmion behavior, including allowing skyrmions to form at lower applied magnetic fields than in simple shapes. The impact of edges in complex shapes is observed to be significant in changing the behavior of the magnetic textures formed. This could allow methods to be developed to control both the position and number of skyrmions within device structures.

Ultrasensitive Sub-monolayer Palladium Induced Chirality Switching and Topological Evolution of Skyrmions

Chiral spin textures are fundamentally interesting, with promise for device applications. Stabilizing chirality is conventionally achieved by introducing Dzyaloshinskii-Moriya interaction (DMI) in asymmetric multilayers, where the thickness of each layer is at least a few monolayers. Here we report an ultrasensitive chirality switching in (Ni/Co)_n multilayer induced by capping with only 0.22 monolayer of Pd. Using spin-polarized low-energy electron microscopy, we monitor the gradual evolution of domain walls from left-handed to right-handed Néel walls and quantify the DMI induced by the Pd capping layer. We also observe the chiral evolution of a skyrmion during the DMI switching, where no significant topological protection is found as the skyrmion winding number varies. This corresponds to a minimum energy cost of <1 attojoule during the skyrmion chirality switching. Our results demonstrate the detailed chirality evolution within skyrmions during the DMI sign switching, which is relevant to practical applications of skyrmionic devices.

Zero-Field Nucleation and Fast Motion of Skyrmions Induced by Nanosecond Current Pulses in a Ferrimagnetic Thin Film

Skyrmion racetrack memories are highly attractive for next-generation data storage technologies. Skyrmions are noncollinear spin textures stabilized by chiral interactions. To achieve a fast-operating memory device, it is critical to move skyrmions at high speeds. The skyrmion dynamics induced by spin-orbit torques (SOTs) in the commonly studied ferromagnetic films is hindered by strong pinning effects and a large skyrmion Hall effect causing deflection of the skyrmion toward the racetrack edge, which can lead to information loss. Here, we investigate the current-induced nucleation and motion of skyrmions in ferrimagnetic Pt/CoGd/(W or Ta) thin films. We first reveal field-free skyrmion nucleation mediated by Joule heating. We then achieve fast skyrmion motion driven by SOTs with velocities as high as 610 m s^-1 and a small skyrmion Hall angle |θ_SkHE| ≲ 3°. Our results show that ferrimagnets are better candidates for fast skyrmion-based memory devices with low risk of information loss.

The skyrmion bags in an anisotropy gradient

Skyrmion bags as spin textures with arbitrary topological charge are expected to be the carriers in racetrack memory. Here, we theoretically and numerically investigated the dynamics of skyrmion bags in an anisotropy gradient. It is found that, without the boundary potential, the dynamics of skyrmion bags are dependent on the spin textures, and the velocity of skyrmionium withQ = 0 is faster than other skyrmion bags. However, when the skyrmion bags move along the boundary, the velocities of all skyrmion bags with differentQare same. In addition, we theoretically derived the dynamics of skyrmion bags in the two cases using the Thiele approach and discussed the scope of Thiele equation. Within a certain range, the simulation results are in good agreement with the analytically calculated results. Our findings provide an alternative way to manipulate the racetrack memory based on the skyrmion bags.

Tuning the Coexistence Regime of Incomplete and Tubular Skyrmions in Ferromagnetic/Ferrimagnetic/Ferromagnetic Trilayers

The development of skyrmionic devices requires a suitable tuning of material parameters to stabilize skyrmions and control their density. It has been demonstrated recently that different skyrmion types can be simultaneously stabilized at room temperature in heterostructures involving ferromagnets, ferrimagnets, and heavy metals, offering a new platform of coding binary information in the type of skyrmion instead of the presence/absence of skyrmions. Here, we tune the energy landscape of the two skyrmion types in such heterostructures by engineering the geometrical and material parameters of the individual layers. We find that a fine adjustment of the ferromagnetic layer thickness, and thus its magnetic anisotropy, allows the trilayer system to support either one of the skyrmion types or the coexistence of both and with varying densities.

Voltage-Controlled Skyrmionic Interconnect with Multiple Magnetic Information Carriers

Magnetic skyrmions have been in the spotlight since they were observed in technologically relevant systems at room temperature. More recently, there has been increasing interest in additional quasiparticles that may exist as stable/metastable spin textures in magnets, such as the skyrmionium and the antiskyrmionite (i.e., a skyrmion bag with two skyrmions inside) that have distinct topological characteristics. The next challenge and opportunity, at the same time, is to investigate the use of multiple magnetic quasiparticles as information carriers in a single device for next-generation nanocomputing. In this paper, we propose a spintronic interconnect device where multiple sequences of information signals are encoded and transmitted simultaneously by skyrmions, skyrmioniums, and antiskyrmionites. The proposed spintronic interconnect device can be pipelined via voltage-controlled magnetic anisotropy (VCMA) gated synchronizers that behave as intermediate registers. We demonstrate theoretically that the interconnect throughput and transmission energy can be effectively tuned by the VCMA gate voltage and appropriate electric current pulses. By carefully adjusting the device structure characteristics, our spintronic interconnect device exhibits comparable energy efficiency with copper interconnects in mainstream CMOS technologies. This study provides fresh insight into the possibilities of skyrmionic devices in future spintronic applications.

Collective skyrmion motion under the influence of an additional interfacial spin-transfer torque

Here we study the effect of an additional interfacial spin-transfer torque, as well as the well-established spin–orbit torque and bulk spin-transfer torque, on skyrmion collections—group of skyrmions dense enough that they are not isolated from one another—in ultrathin heavy metal/ferromagnetic multilayers, by comparing modelling with experimental results. Using a skyrmion collection with a range of skyrmion diameters and landscape disorder, we study the dependence of the skyrmion Hall angle on diameter and velocity, as well as the velocity as a function of diameter. We show that inclusion of the interfacial spin-transfer torque results in reduced skyrmion Hall angles, with values close to experimental results. We also show that for skyrmion collections the velocity is approximately independent of diameter, in marked contrast to the motion of isolated skyrmions, as the group of skyrmions move together at an average group velocity. Moreover, the calculated skyrmion velocities are comparable to those obtained in experiments when the interfacial spin-transfer torque is included. Our results thus show the significance of the interfacial spin-transfer torque in ultrathin magnetic multilayers, which helps to explain the low skyrmion Hall angles and velocities observed in experiment. We conclude that the interfacial spin-transfer torque should be considered in numerical modelling for reproduction of experimental results.

Skyrmion pinning energetics in thin film systems

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. Magnetic microscopy imaging demonstrates that in contrast to findings in previous investigations, for large skyrmions the pinning originates at the skyrmion boundary and not at its core. The boundary pinning is strongly influenced by the very complex pinning energy landscape that goes beyond the conventional effective rigid quasi-particle description. This gives rise to complex skyrmion shape distortions and allows for dynamic switching of pinning sites and flexible tuning of the pinning.

Skyrmions, topological spin textures, can be pinned by defects present in the material that hosts them, influencing their motion. Here, Gruber et al show that the skyrmions are pinned at their boundary where the finite size of the skyrmions governs their pinning, and they demonstrate that certain pinning sites can switched on and off in-situ.

Noise logic with an InGaN/SiNx/Si uniband diode photodetector

Noise logic is introduced by the wavelength dependent photocurrent noise of an InGaN/SiNx/Si uniband diode photodetector. A wavelength versus photocurrent noise discrimination map is constructed from the larger photocurrent noise for red light than that for green light. A minimum measurement time of four seconds is deduced from the standard deviation of the photocurrent noise for a safe wavelength distinction. A logic NOT gate is realized as representative with on or off red or green light as binary 1 or 0 inputs and the photocurrent noise above or below a defined threshold as binary 1 or 0 outputs.

Hilbert Space Structure of the Low Energy Sector of U(N) Quantum Hall Ferromagnets and Their Classical Limit

Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites with the carrier space of irreducible representations of U(N) described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N)/U(M)×U(N−M). We embed this N-component fermion mixture in Fock space through a Schwinger–Jordan (boson and fermion) representation of U(N)-spin operators. We provide different realizations of basis vectors using Young diagrams, Gelfand–Tsetlin patterns and Fock states (for an electron/flux occupation number in the fermionic/bosonic representation). U(N)-spin operator matrix elements in the Gelfand–Tsetlin basis are explicitly given. Coherent state excitations above the ground state are computed and labeled by complex (N−M)×M matrix points Z on the Grassmannian phase space. They adopt the form of a U(N) displaced/rotated highest-weight vector, or a multinomial Bose–Einstein condensate in the flux occupation number representation. Replacing U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy (long wavelength) U(N)-spin-wave coherent excitations (skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.

Electrical manipulation of skyrmions in a chiral magnet

Writing, erasing and computing are three fundamental operations required by any working electronic device. Magnetic skyrmions could be essential bits in promising in emerging topological spintronic devices. In particular, skyrmions in chiral magnets have outstanding properties like compact texture, uniform size, and high mobility. However, creating, deleting, and driving isolated skyrmions, as prototypes of aforementioned basic operations, have been a grand challenge in chiral magnets ever since the discovery of skyrmions, and achieving all these three operations in a single device is even more challenging. Here, by engineering chiral magnet Co₈Zn₁₀Mn₂ into the customized micro-devices for in-situ Lorentz transmission electron microscopy observations, we implement these three operations of skyrmions using nanosecond current pulses with a low current density of about 10¹⁰ A·m⁻² at room temperature. A notched structure can create or delete magnetic skyrmions depending on the direction and magnitude of current pulses. We further show that the magnetic skyrmions can be deterministically shifted step-by-step by current pulses, allowing the establishment of the universal current-velocity relationship. These experimental results have immediate significance towards the skyrmion-based memory or logic devices.

There has been much interest in using skyrmions for new approaches to compution, however, creating, deleting and driving skyrmions remains a challenge. Here, Wang et al demonstrate all three operations for skyrmions in tailored Co8Zn10Mn2 nanodevices using tailored current pulses.

Behavior of Vortex-Like Inhomogeneities Originating in Magnetic Films with Modulated Uniaxial Anisotropy in a Planar Magnetic Field

This paper investigates the processes of magnetization reversal of a uniaxial ferromagnetic disk containing a columnar defect of the potential well type in perpendicular and planar magnetic fields. The characteristic stages of magnetization reversal of the domain structure of the disk and vortex-like inhomogeneities forming on the defect are determined. The critical fields of their existence are found and an explanation is given for the presence of a significant difference in their values for the perpendicular and planar fields of the defect magnetization reversal. The role of chirality in the behavior of a Bloch-type magnetic skyrmion during the magnetization reversal of a defect in a planar field is shown.

Reversible writing/deleting of magnetic skyrmions through hydrogen adsorption/desorption

Magnetic skyrmions are topologically nontrivial spin textures with envisioned applications in energy-efficient magnetic information storage. Toggling the presence of magnetic skyrmions via writing/deleting processes is essential for spintronics applications, which usually require the application of a magnetic field, a gate voltage or an electric current. Here we demonstrate the reversible field-free writing/deleting of skyrmions at room temperature, via hydrogen chemisorption/desorption on the surface of Ni and Co films. Supported by Monte-Carlo simulations, the skyrmion creation/annihilation is attributed to the hydrogen-induced magnetic anisotropy change on ferromagnetic surfaces. We also demonstrate the role of hydrogen and oxygen on magnetic anisotropy and skyrmion deletion on other magnetic surfaces. Our results open up new possibilities for designing skyrmionic and magneto-ionic devices.

To use skyrmions to store information, an effective method for writing and deleting them is required. Here, Chen et al demonstrate the writing and deleting of skyrmions at room temperature by using hydrogen adsorption to change the magnetic anisotropy of the metallic multilayer hosting the skyrmions.

Effect of Chiral Damping on the dynamics of chiral domain walls and skyrmions

Friction plays an essential role in most physical processes that we experience in our everyday life. Examples range from our ability to walk or swim, to setting boundaries of speed and fuel efficiency of moving vehicles. In magnetic systems, the displacement of chiral domain walls (DW) and skyrmions (SK) by Spin Orbit Torques (SOT), is also prone to friction. Chiral damping (α_c), the dissipative counterpart of the Dzyaloshinskii Moriya Interaction (DMI), plays a central role in these dynamics. Despite experimental observation, and numerous theoretical studies confirming its existence, the influence of chiral damping on DW and SK dynamics has remained elusive due to the difficulty of discriminating from DMI. Here we unveil the effect that α_c has on the flow motion of DWs and SKs driven by current and magnetic field. We use a static in-plane field to lift the chiral degeneracy. As the in-plane field is increased, the chiral asymmetry changes sign. When considered separately, neither DMI nor α_c can explain the sign reversal of the asymmetry, which we prove to be the result of their competing effects. Finally, numerical modelling unveils the non-linear nature of chiral dissipation and its critical role for the stabilization of moving SKs.

Chiral damping plays a critical role in the motion of skyrmions and domain walls, but it difficult to distinguish its influence from Dzyaloshinskii Moriya Interaction (DMI). Here, Safeer et al show that competition between chiral damping and the DMI result in a sign change in the chiral asymmetry.

Assembling Diverse Skyrmionic Phases in Fe3 GeTe2 Monolayers

Skyrmionic magnetic states are promising in advanced spintronics. This topic is experiencing recent progress in 2D magnets, with, for example, a near 300 K Curie temperature observed in Fe₃ GeTe₂ . However, despite previous studies reporting skyrmions in Fe₃ GeTe₂ , such a system remains elusive, since it has been reported to host either Néel-type or Bloch-type textures, while a net Dzyaloshinskii-Moriya interaction (DMI) cannot occur in this compound for symmetry reasons. It is thus desirable to develop an accurate model to deeply understand Fe₃ GeTe₂ . Here, a newly developed method adopting spin invariants is applied to build a first-principle-based Hamiltonian, which predicts colorful topological defects assembled from the unit of Bloch lines, and reveals the critical role of specific forms of fourth-order interactions in Fe₃ GeTe₂ . Rather than the DMI, it is the multiple fourth-order interactions, with symmetry and spin-orbit couplings considered, that stabilize both Néel-type and Bloch-type skyrmions, as well as antiskyrmions, without any preference for clockwise versus counterclockwise spin rotation. This study also demonstrates that spin invariants can be used as a general approach to study complex magnetic interactions.

Skyrmions-based logic gates in one single nanotrack completely reconstructed via chirality barrier

Logic gates based on magnetic elements are promising candidates for logic-in-memory applications with non-volatile data retention, near-zero leakage and scalability. In such spin-based logic devices, however, the multi-strip structure and fewer functions are obstacles to improving integration and reducing energy consumption. Here we propose a skyrmions-based single-nanotrack logic family including AND, OR, NOT, NAND, NOR, XOR and XNOR that can be implemented and reconstructed by building and switching the Dzyaloshinskii-Moriya interaction (DMI) chirality barrier on a racetrack memory. Besides the pinning effect of the DMI chirality barrier on skyrmions, the annihilation, fusion and shunting of two skyrmions with opposite chirality are also achieved and demonstrated via local reversal of the DMI, which are necessary for the design of an engineer programmable logic nanotrack, transistor and complementary racetrack memory.

Direct visualization of the three-dimensional shape of skyrmion strings in a noncentrosymmetric magnet

Magnetic skyrmions are topologically stable swirling spin textures that appear as particle-like objects in two-dimensional (2D) systems. Here, utilizing scalar magnetic X-ray tomography under applied magnetic fields, we report the direct visualization of the three-dimensional (3D) shape of individual skyrmion strings in the room-temperature skyrmion-hosting non-centrosymmetric compound Mn_1.4Pt_0.9Pd_0.1Sn. Through the tomographic reconstruction of the 3D distribution of the [001] magnetization component on the basis of transmission images taken at various angles, we identify a skyrmion string running through the entire thickness of the sample, as well as various defect structures, such as the interrupted and Y-shaped strings. The observed point defect may represent the Bloch point serving as an emergent magnetic monopole, as proposed theoretically. Our tomographic approach with a tunable magnetic field paves the way for direct visualization of the structural dynamics of individual skyrmion strings in 3D space, which will contribute to a better understanding of the creation, annihilation and transfer of these topological objects.

Direct Visualisation of Skyrmion Lattice Defect Alignment at Grain Boundaries

We present a method to directly visualise a statistical analysis of skyrmion defect alignment at grain boundaries in the skyrmion host [Formula: see text]OSeO3. Using Lorentz transmission electron microscopy, we collected large data sets with several hundreds of frames containing skyrmion lattices with grain boundaries in them. To address the behaviour of strings of dislocations in these grain boundaries, we developed an algorithm to automatically extract and classify strings of dislocations separating the grains. This way we circumvent the problem of having to create configurations with well-defined relative grain orientations by performing a statistical analysis on a dynamically rearranging image sequence. With this statistical method, we are able to experimentally extract the relationship between grain boundary alignment and defect spacing and find an agreement with geometric expectations. The algorithms used can be extended to other types of lattices such as Abrikosov lattices or colloidal systems in optical microscopy.