Magnetic skyrmions for unconventional computing

Switching Intrinsic Magnetic Skyrmions with Controllable Magnetic Anisotropy in van der Waals Multiferroic Heterostructures

Magnetic skyrmions, topologically nontrivial whirling spin textures at nanometer scales, have emerged as potential information carriers for spintronic devices. The ability to efficiently create and erase magnetic skyrmions is vital yet challenging for such applications. Based on first-principles studies, we find that switching between intrinsic magnetic skyrmion and high-temperature ferromagnetic states can be achieved in the two-dimensional van der Waals (vdW) multiferroic heterostructure CrSeI/In2Te3 by reversing the ferroelectric polarization of In2Te3. The core mechanism of this switching is traced to the controllable magnetic anisotropy of CrSeI influenced by the ferroelectric polarization of In2Te3. We propose a useful descriptor linking the presence of magnetic skyrmions to magnetic parameters and validate this connection through studies of a variety of similar vdW multiferroic heterostructures. Our work demonstrates that manipulating magnetic skyrmions via tunable magnetic anisotropies in vdW multiferroic heterostructures represents a highly promising and energy-efficient strategy for the future development of spintronics.

Proposal for All-Electrical Skyrmion Detection in van der Waals Tunnel Junctions

A major challenge for magnetic skyrmions in atomically thin van der Waals (vdW) materials is reliable skyrmion detection. Here, based on rigorous first-principles calculations, we show that all-electrical skyrmion detection is feasible in two-dimensional vdW magnets via scanning tunneling microscopy (STM) and in planar tunnel junctions. We use the nonequilibrium Green's function method for quantum transport in planar junctions, including self-energy due to electrodes and working conditions, going beyond the standard Tersoff-Hamann approximation. We obtain a very large tunneling anisotropic magnetoresistance (TAMR) around the Fermi energy for a graphite/Fe3GeTe2/germanene/graphite vdW tunnel junction. For atomic-scale skyrmions, the noncollinear magnetoresistance (NCMR) reaches giant values. We trace the origin of the NCMR to spin mixing between spin-up and -down states of pz and dz2 character at the surface atoms. Both TAMR and NCMR are drastically enhanced in tunnel junctions with respect to STM geometry due to orbital symmetry matching at the interface.

Handwritten digit recognition by spin waves in a Skyrmion reservoir

By performing numerical simulations for the handwritten digit recognition task, we demonstrate that a magnetic skyrmion lattice confined in a thin-plate magnet possesses high capability of reservoir computing. We obtain a high recognition rate of more than 88%, higher by about 10% than a baseline taken as the echo state network model. We find that this excellent performance arises from enhanced nonlinearity in the transformation which maps the input data onto an information space with higher dimensions, carried by interferences of spin waves in the skyrmion lattice. Because the skyrmions require only application of static magnetic field instead of nanofabrication for their creation in contrast to other spintronics reservoirs, our result consolidates the high potential of skyrmions for application to reservoir computing devices.

Bloch-type magnetic skyrmions in two-dimensional lattices

Magnetic skyrmions in two-dimensional lattices are a prominent topic of condensed matter physics and materials science. Current research efforts in this field are exclusively constrained to Néel-type and antiskyrmions, while Bloch-type magnetic skyrmions are rarely explored. Here, we report the discovery of Bloch-type magnetic skyrmions in a two-dimensional lattice of MnInP2Te6, using first-principles calculations and Monte-Carlo simulations. Arising from the joint effect of broken inversion symmetry and strong spin-orbit coupling, monolayer MnInP2Te6 presents large Dzyaloshinskii-Moriya interaction. This, along with ferromagnetic exchange interaction and out-of-plane magnetic anisotropy, gives rise to skyrmion physics in monolayer MnInP2Te6, in the absence of a magnetic field. Remarkably, different from all previous works on two-dimensional lattices, the resultant magnetic skyrmions feature Bloch-type magnetism, which is protected by D3 symmetry. Furthermore, Bloch-type magnetic bimerons are also identified in monolayer MnTlP2Te6. The phase diagrams of these Bloch-type topological magnetisms under a magnetic field, temperature and strain are mapped out. Our results greatly enrich the research on magnetic skyrmions in two-dimensional lattices.

Emergence of field-induced memory effect in spin ices

Out-of-equilibrium investigation of strongly correlated materials deciphers the hidden equilibrium properties. Herein, we have investigated the out-of-equilibrium magnetic properties of polycrystalline Dy2Ti2O7and Ho2Ti2O7spin ices. Our experimental findings reveal the emergence of magnetic field-induced anomalous hysteresis observed solely in temperature-and magnetic field-dependent AC susceptibility measurements. The observed memory effect (anomalous thermomagnetic hysteresis) exhibits a strong dependence on both thermal and non-thermal driving variables. Owing to the non-collinear spin structure, the applied DC bias magnetic field produces quenched disorder sites in the cooperative Ising spin matrix and suppresses the spin-phonon coupling. These quench disorders create a dynamic spin correlation, having slow spin relaxation and quick decay time, which additionally contribute to AC susceptibility. The initial conditions and measurement protocol decide the magnitude and sign of this dynamical term contributing to AC susceptibility. It is being suggested that such out-of-equilibrium properties arise from the combined influences of geometric frustration, disorder, and the cooperative nature of spin dynamics exhibited by these materials.

Topological magneto-optical effect from skyrmion lattice

The magnetic skyrmion is a spin-swirling topological object characterized by its nontrivial winding number, holding potential for next-generation spintronic devices. While optical readout has become increasingly important towards the high integration and ultrafast operation of those devices, the optical response of skyrmions has remained elusive. Here, we show the magneto-optical Kerr effect (MOKE) induced by the skyrmion formation, i.e., topological MOKE, in Gd2PdSi3. The significantly enhanced optical rotation found in the skyrmion phase demonstrates the emergence of topological MOKE, exemplifying the light-skyrmion interaction arising from the emergent gauge field. This gauge field in momentum space causes a dramatic reconstruction of the electronic band structure, giving rise to magneto-optical activity ranging up to the sub-eV region. The present findings pave a way for photonic technology based on skyrmionics.

Experimental demonstration of a skyrmion-enhanced strain-mediated physical reservoir computing system

Physical reservoirs holding intrinsic nonlinearity, high dimensionality, and memory effects have attracted considerable interest regarding solving complex tasks efficiently. Particularly, spintronic and strain-mediated electronic physical reservoirs are appealing due to their high speed, multi-parameter fusion and low power consumption. Here, we experimentally realize a skyrmion-enhanced strain-mediated physical reservoir in a multiferroic heterostructure of Pt/Co/Gd multilayers on (001)-oriented 0.7PbMg_1/3Nb_2/3O₃-0.3PbTiO₃ (PMN-PT). The enhancement is coming from the fusion of magnetic skyrmions and electro resistivity tuned by strain simultaneously. The functionality of the strain-mediated RC system is successfully achieved via a sequential waveform classification task with the recognition rate of 99.3% for the last waveform, and a Mackey-Glass time series prediction task with normalized root mean square error (NRMSE) of 0.2 for a 20-step prediction. Our work lays the foundations for low-power neuromorphic computing systems with magneto-electro-ferroelastic tunability, representing a further step towards developing future strain-mediated spintronic applications.

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.

Device geometry dependent deterministic skyrmion generation from a skyrmionium

A magnetic skyrmionium can be perceived as an association of two magnetic skyrmions with opposite topological charges. In this work, we have investigated the transformation of skyrmionium into multi-skyrmionic states via domain wall pairs in three different devices with variable geometric configurations. The same device geometries are considered for single ferromagnetic layer and synthetic antiferromagnetic system. It is observed that by tuning the current density, deterministic generation of skyrmions is possible via the spin transfer torque. The proposed device is efficiently adjustable to change the number of skyrmions also at room temperature. The results may lead to development of skyrmion-based devices for neuromorphic and unconventional computing.

Controllable Itinerant Ferromagnetism in Weakly Correlated 5d SrIrO3

The weakly correlated nature of 5d oxide SrIrO₃ determines its rare ferromagnetism, and the control of its magnetic order is even less studied. Tailoring structure distortion is currently a main route to tune the magnetic order of 5d iridates, but only for the spatially confined insulating counterparts. Here, we have realized ferromagnetic order in metallic SrIrO₃ by construction of SrIrO₃/ferromagnetic-insulator (LaCoO₃) superlattices, which reveal a giant coercivity of ∼10 T and saturation field of ∼25 T with strong perpendicular magnetic anisotropy. The Curie temperature of SrIrO₃ can be controlled by engineering interface charge transfer, which is confirmed by Hall effect measurements collaborating with EELS and XAS. Besides, the noncoplanar spin texture is captured, which is caused by interfacial Dzyaloshinskii-Moriya interactions as well. These results indicate controllable itinerant ferromagnetism and an emergent topological magnetic state in strong spin-orbit coupled semimetal SrIrO₃, showing great potential to develop efficient spintronic devices.

Disorder-Induced Topological State Transition in the Optical Skyrmion Family

Skyrmions endowed with topological protection have been extensively investigated in various platforms including magnetics, ferroelectrics, and liquid crystals, stimulating applications such as memories, logic devices, and neuromorphic computing. While the optical counterpart has been proposed and realized recently, the study of optical skyrmions is still in its infancy. Among the unexplored questions, the investigation of the topology induced robustness against disorder is of substantial importance on both fundamental and practical sides but remains elusive. In this Letter, we manage to generate optical skyrmions numerically in real space with different topological features at will, providing a unique platform to investigate the robustness of various optical skyrmions. A disorder-induced topological state transition is observed for the first time in a family of optical skyrmions composed of six classes with different skyrmion numbers. Intriguingly, the optical skyrmions produced from a vectorial hologram are exceptionally robust against scattering from a random medium, shedding light on topological photonic devices for the generation and manipulation of robust states for applications including imaging and communication.

Brownian reservoir computing realized using geometrically confined skyrmion dynamics

Reservoir computing (RC) has been considered as one of the key computational principles beyond von-Neumann computing. Magnetic skyrmions, topological particle-like spin textures in magnetic films are particularly promising for implementing RC, since they respond strongly nonlinearly to external stimuli and feature inherent multiscale dynamics. However, despite several theoretical proposals that exist for skyrmion reservoir computing, experimental realizations have been elusive until now. Here, we propose and experimentally demonstrate a conceptually new approach to skyrmion RC that leverages the thermally activated diffusive motion of skyrmions. By confining the electrically gated and thermal skyrmion motion, we find that already a single skyrmion in a confined geometry suffices to realize nonlinearly separable functions, which we demonstrate for the XOR gate along with all other Boolean logic gate operations. Besides this universality, the reservoir computing concept ensures low training costs and ultra-low power operation with current densities orders of magnitude smaller than those used in existing spintronic reservoir computing demonstrations. Our proposed concept is robust against device imperfections and can be readily extended by linking multiple confined geometries and/or by including more skyrmions in the reservoir, suggesting high potential for scalable and low-energy reservoir computing.

Reversible Transformation between Isolated Skyrmions and Bimerons

Skyrmions and bimerons are versatile topological spin textures that can be used as information bits for both classical and quantum computing. The transformation between isolated skyrmions and bimerons is an essential operation for computing architecture based on multiple different topological bits. Here we report the creation of isolated skyrmions and their subsequent transformation to bimerons by harnessing the electric current-induced Oersted field and temperature-induced perpendicular magnetic anisotropy variation. The transformation between skyrmions and bimerons is reversible, which is controlled by the current amplitude and scanning direction. Both skyrmions and bimerons can be created in the same system through the skyrmion-bimeron transformation and magnetization switching. Deformed skyrmion bubbles and chiral labyrinth domains are found as nontrivial intermediate transition states. Our results may provide a unique way for building advanced information-processing devices using different types of topological spin textures in the same system.

Strain-Driven Zero-Field Near-10 nm Skyrmions in Two-Dimensional van der Waals Heterostructures

Magnetic skyrmions─localized chiral spin structures─show great promise for spintronic applications. The recent discovery of two-dimensional (2D) magnets opened new opportunities for topological spin structures in atomically thin van der Waals (vdW) materials. Despite recent progress in stabilizing metastable skyrmions in 2D magnets, their lifetime, essential for applications, has not been explored yet. Here, using first-principles calculations and atomistic spin simulations, we predict that compressive strain leads to stabilizing zero-field skyrmions with diameters close to 10 nm in a Fe₃GeTe₂/germanene vdW heterostructure. The origin of these unique skyrmions is attributed to the high tunability of Dzyaloshinskii-Moriya interaction and magnetocrystalline anisotropy energy by strain, which generally holds for Fe₃GeTe₂ heterostructures with buckled substrates. Furthermore, we calculate the energy barriers protecting skyrmions against annihilation and their lifetimes using transition-state theory. We show that nanoscale skyrmions in strained Fe₃GeTe₂/germanene can be stable for hours at temperatures up to 20 K.

Skyrmions in synthetic antiferromagnets and their nucleation via electrical current and ultra-fast laser illumination

Magnetic skyrmions are topological spin textures that hold great promise as nanoscale information carriers in non-volatile memory and logic devices. While room-temperature magnetic skyrmions and their current-induced motion were recently demonstrated, the stray field resulting from their finite magnetisation and their topological charge limit their minimum size and reliable motion. Antiferromagnetic skyrmions allow to lift these limitations owing to their vanishing magnetisation and net zero topological charge, promising ultra-small and ultra-fast skyrmions. Here, we report on the observation of isolated skyrmions in compensated synthetic antiferromagnets at zero field and room temperature using X-ray magnetic microscopy. Micromagnetic simulations and an analytical model confirm the chiral antiferromagnetic nature of these skyrmions and allow the identification of the physical mechanisms controlling their size and stability. Finally, we demonstrate the nucleation of synthetic antiferromagnetic skyrmions via local current injection and ultra-fast laser excitation.

Spontaneous Magnetic Skyrmions in Single-Layer CrInX3 (X = Te, Se)

The realization of magnetic skyrmions in nanostructures holds great promise for both fundamental research and device applications. Despite recent progress, intrinsic magnetic skyrmions in two-dimensional lattice are still rarely explored. Here, using first-principles calculations and Monte Carlo simulations, we report the identification of spontaneous magnetic skyrmions in single-layer CrInX₃ (X = Te, Se). Because of the joint effect of broken inversion symmetry and strong spin-orbit coupling, inherent large Dzyaloshinskii-Moriya interaction occurs in both systems, endowing the intriguing Néel-type skyrmions. By further imposing moderate magnetic field, the skyrmion phase can be obtained and is stable within a wide temperature range. Particularly for single-layer CrInTe₃, the size of skyrmions is sub-10 nm and the skyrmion phase can be maintained at an elevated temperature of ∼180 K. In addition, the phase diagrams of their topological spin textures under the variation of magnetic parameters of D, J, and K are mapped out.

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.

Single skyrmion true random number generator using local dynamics and interaction between skyrmions

Magnetic skyrmions are of great interest to both fundamental research and applications in post-von-Neumann computing devices. The successful implementation of skyrmionic devices requires functionalities of skyrmions with effective controls. Here we show that the local dynamics of skyrmions, in contrast to the global dynamics of a skyrmion as a whole, can be introduced to provide effective functionalities for versatile computing. A single skyrmion interacting with local pinning centres under thermal effects can fluctuate in time and switch between a small-skyrmion and a large-skyrmion state, thereby serving as a robust true random number generator for probabilistic computing. Moreover, neighbouring skyrmions exhibit an anti-correlated coupling in their fluctuation dynamics. Both the switching probability and the dynamic coupling strength can be tuned by modifying the applied magnetic field and spin current. Our results could lead to progress in developing magnetic skyrmionic devices with high tunability and efficient controls.

Skyrmions, a kind of topological spin texture, have been considered as having potential for use in spin-based computing. Here, Wang et al. study the local dynamics of skyrmions interacting with pinning sites, demonstrating a skyrmion true random number generator with the magnetic field and spin current as two control parameters.

Surface acoustic wave controlled skyrmion-based synapse devices

Magnetic skyrmions, which are particle-like spin structures, are promising information carriers for neuromorphic computing devices due to their topological stability and nanoscale size. In this work, we propose controlling magnetic skyrmions by electric-field-excited surface acoustic waves in neuromorphic computing device structures. Our micromagnetic simulations show that the number of created skyrmions, which emulates the synaptic weight parameter, increases monotonically with increases in the amplitude of the surface acoustic waves. Additionally, the efficiency of skyrmion creation is investigated systemically with a wide range of magnetic parameters, and the optimal values are presented accordingly. Finally, the functionalities of short-term plasticity and long-term potentiation are demonstrated via skyrmion excitation by a sequence of surface acoustic waves with different intervals. The application of surface acoustic waves in skyrmionic neuromorphic computing devices paves a novel approach to low-power computing systems.

Confinement and Protection of Skyrmions by Patterns of Modified Magnetic Properties

Magnetic skyrmions are versatile topological excitations that can be used as nonvolatile information carriers. The confinement of skyrmions in channels is fundamental for any application based on the accumulation and transport of skyrmions. Here, we report a method that allows effective position control of skyrmions in designed channels by engineered energy barriers and wells, which is realized in a magnetic multilayer film by harnessing the boundaries of patterns with modified magnetic properties. We experimentally and computationally demonstrate that skyrmions can be attracted or repelled by the boundaries of areas with modified perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction. By fabricating square and stripe patterns with modified magnetic properties, we show the possibility of building reliable channels for confinement, accumulation, and transport of skyrmions, which effectively protect skyrmions from being destroyed at the device edges. Our results are useful for the design of spintronic applications using either static or dynamic skyrmions.

Helium Ions Put Magnetic Skyrmions on the Track

Magnetic skyrmions are deemed to be the forerunners of novel spintronic memory and logic devices. While their observation and their current-driven motion at room temperature have been demonstrated, certain issues regarding their nucleation, stability, pinning, and skyrmion Hall effect still need to be overcome to realize functional devices. Here, we demonstrate that focused He⁺-ion-irradiation can be used to create and guide skyrmions in racetracks. We show that the reduction of the perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction in the track defined by ion-irradiation leads to the formation of stable isolated skyrmions. Current-driven skyrmion motion experiments and simulations reveal that the skyrmions move along the irradiated track, resulting in the suppression of the skyrmion Hall effect, and that the maximum skyrmion velocity can be enhanced by tuning the magnetic properties. These results open up a new path to nucleate and guide magnetic skyrmions in racetrack devices.

Friedel Oscillations Induced by Magnetic Skyrmions: From Scattering Properties to All-Electrical Detection

Magnetic skyrmions are spin swirling solitonic defects that can play a major role in information technology. Their future in applications and devices hinges on their efficient manipulation and detection. Here, we explore from ab-initio their nature as magnetic inhomongeities in an otherwise unperturbed magnetic material, Fe layer covered by a thin Pd film and deposited on top of Ir(111) surface. The presence of skyrmions triggers scattering processes, from which Friedel oscillations emerge. The latter mediate interactions among skyrmions or between skyrmions and other potential surrounding defects. In contrast to their wavelengths, the amplitude of the oscillations depends strongly on the size of the skyrmion. The analogy with the scattering-off atomic defects enables the assignment of an effective scattering potential and a phase shift to the skyrmionic particles, which can be useful to predict their behavior on the basis of simple scattering frameworks. The induced charge ripples can be utilized for a noninvasive all-electrical detection of skyrmions located on a surface or even if buried a few nanometers away from the detecting electrode.