Room-Temperature Skyrmion Shift Device for Memory Application

Room-Temperature Magnetic Antiskyrmions in Canted Ferrimagnetic CoHo Alloy Films

Magnetic antiskyrmions, the anti-quasiparticles of magnetic skyrmions, possess alternating Bloch- and Néel-type spin spirals, rendering them promising for advanced spintronics-based information storage. To date, antiskyrmions are demonstrated in a few bulk materials featuring anisotropic Dzyaloshinskii-Moriya interactions and a limited number of artificial multilayers. Identifying novel film materials capable of hosting isolated antiskyrmions is critical for memory applications in topological spintronics. Herein, the formation of room-temperature antiskyrmions in single ferrimagnetic CoHo rare-metal alloy films of varying thicknesses, observed using Lorentz transmission electron microscopy is reported. Furthermore, rotating magnetic fields (H) are proposed to facilitate antiskyrmion nucleation and enhance their areal density by an order of magnitude compared to that in the same area under individual vertical H. In addition, experimental and phenomenological analysis confirm that antiskyrmion nucleation can be attributed to spin reorientation involving spontaneous canted magnetism, as evidenced by polarized neutron reflectometry. Micromagnetic simulations further show that the antiskyrmion density significantly depends on the magnitude of the rotating field. These findings expand the family of known antiskyrmion-hosting materials and provide insights into their formation mechanisms, thus serving as a basis for their application in topological spintronics.

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 transformation of synthetic ferromagnetic skyrmions: thermal assisted switching of helicity by spin-orbit torque

This study demonstrates the controllable switching of skyrmion helicity using spin-orbit torque, enhanced by thermal effects. Electric current pulses applied to a [Pt/Co]3/Ru/[Co/Pt]3 multilayer stripe drive skyrmions in a direction opposite to the current flow. Continuous pulsing results in an unexpected reversal of skyrmion motion. Micromagnetic simulations reveal that skyrmions in the upper and lower ferromagnetic layers exhibit distinct helicities, forming a hybrid synthetic skyrmion. The helicity switch of this hybrid structure accounts for the motion reversal. This study introduces innovative helicity control methods, advancing spintronic device applications, including data storage and quantum computing based on skyrmion helicity.

Fundamental theory of current-induced motion of magnetic skyrmions

Magnetic skyrmions are topological spin textures that appear in magnets with broken spatial inversion symmetry as a consequence of competition between the (anti)ferromagnetic exchange interactions and the Dzyaloshinskii-Moriya interactions in a magnetic field. In the research of spintronics, the current-driven dynamics of skyrmions has been extensively studied aiming at their applications to next-generation spintronic devices. However, current-induced skyrmion motion exhibits diverse behaviors depending on various factors and conditions such as the type of skyrmion, driving mechanism, system geometry, direction of applied current, and type of the magnet. While this variety attracts enormous research interest of fundamental science and enriches their possibilities of technical applications, it is, at the same time, a source of difficulty and complexity that hinders their comprehensive understandings. In this article, we discuss fundamental and systematic theoretical descriptions of current-induced motion of skyrmions driven by the spin-transfer torque and the spin-orbit torque. Specifically, we theoretically describe the behaviors of current-driven skyrmions depending on the factors and conditions mentioned above by means of analyses using the Thiele equation. Furthermore, the results of the analytical theory are visually demonstrated and quantitatively confirmed by micromagnetic simulations using the Landau-Lifshitz-Gilbert-Slonczewski equation. In particular, we discuss dependence of the direction and velocity of motion on the type of skyrmion (Bloch type and Néel type) and its helicity, the system geometry (thin plate and nanotrack), the direction of applied current (length and width direction of the nanotrack) and its spin-polarization orientation, and the type of magnet (ferromagnet and antiferromagnet). The comprehensive theory provided by this article is expected to contribute significantly to research on the manipulation and control of magnetic skyrmions by electric currents for future spintronics applications.

Realization of skyrmion shift register

The big data explosion demands novel data storage technology. Among many different approaches, solitonic racetrack memory devices hold great promise for accommodating nonvolatile and low-power functionalities. As representative topological solitons, magnetic skyrmions are envisioned as potential information carriers for efficient information processing. While their advantages as memory and logic elements have been vastly exploited from theoretical perspectives, the corresponding experimental efforts are rather limited. These challenges, which are key to versatile skyrmionic devices, will be studied in this work. Through patterning concaved surface topography with designed arrays of indentations on standard Si/SiO2 substrates, we demonstrate that the resultant non-flat energy landscape could lead to the formation of hexagonal and square skyrmion lattices in Ta/CoFeB/MgO multilayers. Based on these films, one-dimensional racetrack devices are subsequently fabricated, in which a long-distance deterministic shifting of skyrmions between neighboring indentations is achieved at room temperature. Through separating the word line and the bit line, a prototype shift register device, which can sequentially generate and precisely shift complex skyrmionic data strings, is presented. The deterministic writing and long-distance shifting of skyrmionic bits can find potential applications in transformative skyrmionic memory, logic as well as the in-memory computing devices.

Experimental observation of current-driven antiskyrmion sliding in stripe domains

Magnetic skyrmions are promising as next-generation information units. Their antiparticle-the antiskyrmion-has also been discovered in chiral magnets. Here we experimentally demonstrate antiskyrmion sliding in response to a pulsed electric current at room temperature without the requirement of an external magnetic field. This is realized by embedding antiskyrmions in helical stripe domains, which naturally provide one-dimensional straight tracks along which antiskyrmion sliding can be easily launched with low current density and without transverse deflection from the antiskyrmion Hall effect. The higher mobility of the antiskyrmions in the background of helical stripes in contrast to the typical ferromagnetic state is a result of intrinsic material parameters and elastic energy of the stripe domain, thereby smearing out the random pinning potential, as supported by micromagnetic simulations. The demonstration and comprehensive understanding of antiskyrmion movement along naturally straight tracks offers a new perspective for (anti)skyrmion application in spintronics.

Influence of the Hall-bar geometry on texture-induced topological spin transport in two-dimensional Rashba spin-orbit ferromagnets

While the recent prediction and observation of magnetic skyrmions bears inspiring promise for next-generation spintronic devices, how to detect and track their position becomes an important issue. In this work, we investigate the spin transport in a two-dimensional magnetic nanoribbon with the Hall-bar geometry in the presence of Rashba spin-orbit coupling and magnetic skyrmions. We employ the Kwant tight-binding code to compute the Hall conductance and local spin-polarized current density. We consider two versions of the model: One with single skyrmion and one with two separate skyrmions. It is found that the size and position of the skyrmions strongly modulate the Hall conductance near the Hall-bar position. The geometry of the Hall bar also has a strong influence on the Hall conductance of the system. With the decreasing of the width of Hall leads, the peak of Hall conductance becomes sharper. We also show the spatial distribution of the spin-polarized current density around a skyrmion located at different positions. We extend this study toward two separate skyrmions, where the Hall conductance also reveals a sizable dependence on the position of the skyrmions and their distance. Our numerical analysis offers the possibility of electrically detecting the skyrmion position, which could have potential applications in ultrahigh-density storage design.

Steady motion of 80-nm-size skyrmions in a 100-nm-wide track

The current-driven movement of magnetic skyrmions along a nanostripe is essential for the advancement and functionality of a new category of spintronic devices resembling racetracks. Despite extensive research into skyrmion dynamics, experimental verification of current-induced motion of ultra-small skyrmions within an ultrathin nanostripe is still pending. Here, we unveil the motion of individual 80 nm-size skyrmions in an FeGe track with an ultrathin width of 100 nm. The skyrmions can move steadily along the track over a broad range of current densities by using controlled pulse durations of as low as 2 ns. The potential landscape, arising from the magnetic edge twists in such a geometrically confined system, introduces skyrmion inertia and ensures efficient motion with a vanishing skyrmion Hall angle. Our results showcase the steady motion of skyrmions in an ultrathin track, offering a practical pathway for implementing skyrmion-based spintronic devices.

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.

Voltage-controlled magnetic anisotropy gradient-driven skyrmion-based half-adder and full-adder

Spintronic devices have revolutionized the way we process or store information compared to dissipative charge-based electronics. Among various spin-based technologies, skyrmions - topologically protected nano-size spin textures - have emerged as the most promising alternative for future data processing. Here, we have proposed binary adder circuits - central to most digital logic circuits - based on skyrmions. Using micromagnetic simulations, we have demonstrated half-adder and full-adder logic functionalities by precisely driving the skyrmions through voltage-controlled magnetic anisotropy gradient, besides taking advantage of the physical effects such as the skyrmion Hall effect, skyrmion-skyrmion topological repulsion and skyrmion-edge repulsions. The proposed voltage-control-based method of driving the skyrmions is energy efficient compared to the electrical current-driven approach, and it also overcomes the issue of Joule heating. A reliable operation in a wide range of Dzyaloshinskii-Moriya interaction strengths, magnetic anisotropy gradient, and dimensional parameters has been shown, which offers robustness to the device design. The results pave the way for the skyrmion-based computational architecture, which is significant for next-generation non-volatile data processing.

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.

Néel-type optical target skyrmions inherited from evanescent electromagnetic fields with rotational symmetry

Optical skyrmions have recently attracted growing interest due to their potential applications in deep-subwavelength imaging and nanometrology. While optical skyrmions have been successfully demonstrated using different field vectors, the study of their generation and control, as well as their general correlation with electromagnetic (EM) fields, is still in its infancy. Here, we theoretically propose that evanescent transverse-magnetic-polarized (TM-polarized) EM fields with rotational symmetry are actually Néel-type optical target skyrmions of the electric field vectors. Such optical target skyrmions are independent of the operation frequency and medium. Our proposal was verified by numerical simulations and real-space nano-imaging experiments performed on a graphene monolayer, where the target skyrmions could be as small as ∼100 nm in diameter. The results can therefore not only further our understanding of the formation mechanisms of EM topological textures, but also provide guidelines for the facile construction of EM skyrmions that may impact future information technologies.

Reversible conversion between skyrmions and skyrmioniums

Skyrmions and skyrmioniums are topologically non-trivial spin textures found in chiral magnetic systems. Understanding the dynamics of these particle-like excitations is crucial for leveraging their diverse functionalities in spintronic devices. This study investigates the dynamics and evolution of chiral spin textures in [Pt/Co]₃/Ru/[Co/Pt]₃ multilayers with ferromagnetic interlayer exchange coupling. By precisely controlling the excitation and relaxation processes through combined magnetic field and electric current manipulation, reversible conversion between skyrmions and skyrmioniums is achieved. Additionally, we observe the topological conversion from a skyrmionium to a skyrmion, characterized by the sudden emergence of the skyrmion Hall effect. The experimental realization of reversible conversion between distinct magnetic topological spin textures represents a significant development that promises to expedite the advancement of the next generation of spintronic devices.

Systematic Control of Ferrimagnetic Skyrmions via Composition Modulation in Pt/Fe1-xTbx/Ta Multilayers

Magnetic skyrmions are topological spin textures that can be used as memory and logic components for advancing the next generation spintronics. In this regard, control of nanoscale skyrmions, including their sizes and densities, is of particular importance for enhancing the storage capacity of skyrmionic devices. Here, we propose a viable route for engineering ferrimagnetic skyrmions via tuning the magnetic properties of the involved ferrimagnets Fe_1-xTb_x. Via tuning the composition of Fe_1-xTb_x that alters the magnetic anisotropy and the saturation magnetization, the size of the ferrimagnetic skyrmion (d_s) and the average density (η_s) can be effectively tailored in [Pt/Fe_1-xTb_x/Ta]₁₀ multilayers. In particular, a stabilization of sub-50 nm skyrmions with a high density is demonstrated at room temperature. Our work provides an effective approach for designing ferrimagnetic skyrmions with the desired size and density, which could be useful for enabling high-density ferrimagnetic skyrmionics.

Electric field manipulation of spin chirality and skyrmion dynamic

The Dzyaloshinskii-Moriya interaction (DMI) is an antisymmetric exchange interaction that stabilizes spin chirality. One scientific and technological challenge is understanding and controlling the interaction between spin chirality and electric field. In this study, we investigate an unconventional electric field effect on interfacial DMI, skyrmion helicity, and skyrmion dynamics in a system with broken inversion symmetry. We design heterostructures with a 3d-5d atomic orbital interface to demonstrate the gate bias control of the DMI energy and thus transform the DMI between opposite chiralities. Furthermore, we use this voltage-controlled DMI (VCDMI) to manipulate the skyrmion spin texture. As a result, a type of intermediate skyrmion with a unique helicity is created, and its motion can be controlled and made to go straight. Our work shows the effective control of spin chirality, skyrmion helicity, and skyrmion dynamics by VCDMI. It promotes the emerging field of voltage-controlled chiral interactions and voltage-controlled skyrmionics.

Experimental Realization of a Skyrmion Circulator

Magnetic skyrmions are mobile topological spin textures that can be manipulated by different means. Their applications have been frequently discussed in the context of information carriers for racetrack memory devices, which on the other hand, exhibit a skyrmion Hall effect as a result of the nontrivial real-space topology. While the skyrmion Hall effect is believed to be detrimental for constructing racetrack devices, we show here that it can be implemented for realizing a three-terminal skyrmion circulator. In analogy to the microwave circulator, nonreciprocal transportation and circulation of skyrmions are studied both numerically and experimentally. In particular, successful control of the circulating direction of being either clockwise or counterclockwise is demonstrated, simply by changing the sign of the topological charge. Our studies suggest that the topological property of skyrmions can be incorporated for enabling novel spintronic functionalities; the skyrmion circulator is just one example.

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.

Distinguishing the Two-Component Anomalous Hall Effect from the Topological Hall Effect

In transport, the topological Hall effect (THE) presents itself as nonmonotonic features (or humps and dips) in the Hall signal and is widely interpreted as a sign of chiral spin textures, like magnetic skyrmions. However, when the anomalous Hall effect (AHE) is also present, the coexistence of two AHEs could give rise to similar artifacts, making it difficult to distinguish between genuine THE with AHE and two-component AHE. Here, we confirm genuine THE with AHE by means of transport and magneto-optical Kerr effect (MOKE) microscopy, in which magnetic skyrmions are directly observed, and find that genuine THE occurs in the transition region of the AHE. In sharp contrast, the artifact "THE" or two-component AHE occurs well beyond the saturation of the "AHE component" (under the false assumption of THE + AHE). Furthermore, we distinguish artifact "THE" from genuine THE by three methods: (1) minor loops, (2) temperature dependence, and (3) gate dependence. Minor loops of genuine THE with AHE are always within the full loop, while minor loops of the artifact "THE" may reveal a single loop that cannot fit into the "AHE component". In addition, the temperature or gate dependence of the artifact "THE" may also be accompanied by a polarity change of the "AHE component", as the nonmonotonic features vanish, while the temperature dependence of genuine THE with AHE reveals no such change. Our work may help future researchers to exercise caution and use these methods for careful examination in order to ascertain the genuine THE.

Spin-hedgehog-derived electromagnetic effects in itinerant magnets

In itinerant magnets, the indirect exchange coupling of Ruderman-Kittel-Kasuya-Yosida type is known to stabilize incommensurate spin spirals, whereas an account of higher order spin interactions favors the formation of a noncoplanar magnetic texture. This is manifested by the finite Berry phase the conduction electrons accumulate when their spins follow this texture, leading thus to the topological Hall effect. We herein utilize the effective spin model with bilinear-biquadratic exchange interactions for studying the formation of the magnetic hedgehog lattice, that represents a periodic array of magnetic anti- and monopoles and has been recently observed in the B20-type compounds, in a three-dimensional itinerant magnet. As opposed to widely used Monte Carlo simulations, we employ a neural-network-based approach for exploring the ground state spin configuration in a noncentrosymmetric crystal structure. Further, we address the topological Hall conductivity, associated with nonzero scalar spin chirality, in the itinerant magnet due to the coupling to the spin hedgehog lattice, and provide the evidence of a magneto-optic Kerr effect.

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.

Magnetic order and disorder environments in superantiferromagnetic [Formula: see text] nanoparticles

Magnetic nanoparticles exhibit two different local symmetry environments, one ascribed to the core and one corresponding to the nanoparticle surface. This implies the existence of a dual spin dynamics, leading to the presence of two different magnetic arrangements governed by different correlation lengths. In this work, two ensembles of [Formula: see text] nanoparticles with mean sizes of 18 nm and 13 nm have been produced to unravel the magnetic couplings established among the magnetic moments located within the core and at the nanoparticle surface. To this end, we have combined neutron diffraction measurements, appropriate to investigate magnetically-ordered spin arrangements, with time-dependent macroscopic AC susceptibility measurements to reveal memory and aging effects. The observation of the latter phenomena are indicative of magnetically-frustrated states. The obtained results indicate that, while the [Formula: see text] magnetic moments located within the nanoparticle core keep the bulk antiferromagnetic commensurate structure in the whole magnetic state, the correlations among the surface spins give rise to a collective frustrated spin-glass phase. The interpretation of the magnetic structure of the nanoparticles is complemented by specific-heat measurements, which further support the lack of incommensurability in the nanoparticle state.

Slowdown of photoexcited spin dynamics in the non-collinear spin-ordered phases in skyrmion host GaV4S8

Formation of magnetic order alters the character of spin excitations, which then affects transport properties. We investigate the photoexcited ultrafast spin dynamics in different magnetic phases in Néel-type skyrmion host GaV₄S₈ with time-resolved magneto-optical Kerr effect experiments. The coherent spin precession, whose amplitude is enhanced in the skyrmion-lattice phase, shows a signature of phase coexistence across the magnetic phase transitions. The incoherent spin relaxation dynamics slows down by a factor of two in the skyrmion-lattice/cycloid phases, indicating significant decrease in thermal conductivity triggered by a small change of magnetic field. The slow heat diffusion in the skyrmion-lattice/cycloid phases is attributed to the stronger magnon scattering off the domain walls formed in abundance in the skyrmion-lattice/cycloid phase. These results highlight the impact of spatial spin structure on the ultrafast heat transport in spin systems, providing a useful insight for the step toward ultrafast photocontrol of the magnets with novel spin orders.

Skyrmions are a topological magnetic texture that have garnered considerable interest for various technological applications. Here, Sekiguchi et al. investigate the ultrafast optical response of GaV4S6, and find a significant reduction in the thermal conductivity in the skyrmion phase.

Comprehensive Study of the Current-Induced Spin-Orbit Torque Perpendicular Effective Field in Asymmetric Multilayers

The spin–orbit torques (SOTs) in the heavy metal (HM)/ferromagnetic metal (FM) structure hold promise for next-generation low-power and high-density spintronic memory and logic applications. For the SOT switching of a perpendicular magnetization, an external magnetic field is inevitable for breaking the mirror symmetry, which is not practical for high-density nanoelectronics applications. In this work, we study the current-induced field-free SOT switching and SOT perpendicular effective field (Hzeff) in a variety of laterally asymmetric multilayers, where the asymmetry is introduced by growing the FM layer in a wedge shape. We show that the design of structural asymmetry by wedging the FM layer is a universal scheme for realizing field-free SOT switching. Moreover, by comparing the FM layer thickness dependence of (Hzeff) in different samples, we show that the efficiency (β =Hzeff/J, J is the current density) is sensitive to the HM/FM interface and the FM layer thickness. The sign of β for thin FM thicknesses is related to the spin Hall angle (θ_SH) of the HM layer attached to the FM layer. β changes its sign with the thickness of the FM layer increasing, which may be caused by the thickness dependence of the work function of FM. These results show the possibility of engineering the deterministic field-free switching by combining the symmetry breaking and the materials design of the HM/FM interface.

Deterministic Generation and Guided Motion of Magnetic Skyrmions by Focused He+-Ion Irradiation

Magnetic skyrmions are quasiparticles with nontrivial topology, envisioned to play a key role in next-generation data technology while simultaneously attracting fundamental research interest due to their emerging topological charge. In chiral magnetic multilayers, current-generated spin-orbit torques or ultrafast laser excitation can be used to nucleate isolated skyrmions on a picosecond time scale. Both methods, however, produce randomly arranged skyrmions, which inherently limits the precision on the location at which the skyrmions are nucleated. Here, we show that nanopatterning of the anisotropy landscape with a He⁺-ion beam creates well-defined skyrmion nucleation sites, thereby transforming the skyrmion localization into a deterministic process. This approach allows control of individual skyrmion nucleation as well as guided skyrmion motion with nanometer-scale precision, which is pivotal for both future fundamental studies of skyrmion dynamics and applications.

Topological Hall effect in SrRuO3thin films and heterostructures

Transition metal oxides hold a wide spectrum of fascinating properties endowed by the strong electron correlations. In 4dand 5doxides, exotic phases can be realized with the involvement of strong spin-orbit coupling (SOC), such as unconventional magnetism and topological superconductivity. Recently, topological Hall effects (THEs) and magnetic skyrmions have been uncovered in SrRuO₃thin films and heterostructures, where the presence of SOC and inversion symmetry breaking at the interface are believed to play a key role. Realization of magnetic skyrmions in oxides not only offers a platform to study topological physics with correlated electrons, but also opens up new possibilities for magnetic oxides using in the low-power spintronic devices. In this review, we discuss recent observations of THE and skyrmions in the SRO film interfaced with various materials, with a focus on the electric tuning of THE. We conclude with a discussion on the directions of future research in this field.

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.

Enhanced Spin-Orbit Torque and Low Critical Current Density in Pt100-xRux/[CoNi]/Ru Multilayer for Spintronic Devices

Using a heavy-metal (HM) alloy layer in spin-orbit torque (SOT)-based devices is an effective method for obtaining a high current-spin conversion efficiency θ_SH. In this work, SOT-based spintronic devices with a Pt_100-xRu_x-alloyed HM layer are studied by applying harmonic Hall measurements and magneto-optical Kerr effect microscopy to detect the θ_SH and to observe the process of current-induced magnetization switching. Both the highest θ_SH of 0.132 and the lowest critical current density (J_c) of 8 × 10⁵ A/cm² are realized in a device with x = 20, which satisfies the high SOT efficiency and low energy consumption simultaneously. The interfacial Dzyaloshinskii-Moriya interaction can be overcome by increasing the in-plane assist field. Meanwhile, the minimum in-plane field required for current-induced complete switching can be reduced to ±60 Oe. Our study reveals that using the Pt-Ru alloyed HM layer is an effective route for SOT application with enhanced performance.

Electrical Generation and Deletion of Magnetic Skyrmion-Bubbles via Vertical Current Injection

The magnetic skyrmion is a topologically protected spin texture that has attracted much attention as a promising information carrier because of its distinct features of suitability for high-density storage, low power consumption, and stability. One of the skyrmion devices proposed so far is the skyrmion racetrack memory, which is the skyrmion version of the domain-wall racetrack memory. For application in devices, skyrmion racetrack memory requires electrical generation, deletion, and displacement of isolated skyrmions. Despite the progress in experimental demonstrations of skyrmion generation, deletion, and displacement, these three operations have yet to be realized in one device. Here, a route for generating and deleting isolated skyrmion-bubbles through vertical current injection with an explanation of its microscopic origin is presented. By combining the proposed skyrmion-bubble generation/deletion method with the spin-orbit-torque-driven skyrmion shift, a proof-of-concept experimental demonstration of the skyrmion racetrack memory operation in a three-terminal device structure is provided.

Isolated skyrmion, skyrmion lattice and antiskyrmion lattice creation through magnetization reversal in Co/Pd nanostructure

Skyrmion and antiskyrmion spin textures are axisymmetric inhomogeneous localized objects with distinct chirality in magnetic systems. These spin textures are potential candidates for the next generation energy-efficient spintronic applications due to their unique topological properties. Controlled and effective creation of the spin textures is required to use in conventional and neuromorphic computing applications. Here we show by micromagnetic simulations creating an isolated skyrmion, skyrmion lattice and antiskyrmion lattice through the magnetization reversal in Co/Pd multilayer nanostructure using spin-polarized current. The spin textures' stability depends on the spin-polarized current density, current pulse width, and Dzyaloshinskii-Moriya interaction (DMI). Antiskyrmions are evolved during the formation of a single skyrmion and skyrmion lattice. Skyrmion and antiskyrmion lattices together are observed for lower pulse width, 0.05 ns. Our micromagnetic studies suggest that the two distinct lattice phases' evolution could help to design the topological spin textures-based devices.

Microdynamic Study of Spin-Lattice Coupling Effects on Skyrmion Transport

Skyrmion transport fundamentally determines the speed, energy consumption, and functionality of skyrmion-based spintronic devices, attracting considerable attention. Recent experimental studies found there is a migration barrier for the thermal activated transport of a skyrmion, which is speculated to be induced by the pinning effects of crystalline defects. In this Letter, we propose an alternative source of migration barrier for skyrmion transport, i.e., a local lattice distortion field due to spin-lattice coupling, which can lead to the same Arrhenius diffusion behavior in defect-free skyrmion materials. By performing spin-lattice dynamics simulations, we study the microdynamic insight into the influence of local lattice distortion field, which refreshes the mechanistic understanding on skyrmion transport.

Topological structures, spontaneous symmetry breaking and energy spectra in dipole hexagonal lattices

The interplay between the special triangular/hexagonal two dimensional lattice and the long range dipole-dipole interaction gives rise to topological defects, specifically the vortex, formed by a particular arrangement of the interacting classic dipoles. The nature of such vortices has been traditionally explained on the basis of numerical evidence. Here we propose the emerging formation of vortices as the natural minimum energy configuration of interacting (in-plane) two-dimensional dipoles based on the mechanism of spontaneous symmetry breaking. As opposed to the quantal case, where spin textures such as skyrmions or bimerons occur due to non-linearities in their Hamiltonian, it is still possible to witness classic topological structures due only to the nature of the dipole-dipole force. We shall present other (new) topological structures for the in-plane honeycomb lattice, as well as for two-dimensional out-of-plane dipoles. These structures will prove to be essential in the minimum energy configurations for three-dimensional simple hexagonal and hexagonal-closed-packed structures, whose energies in the bulk are obtained for the first time.

Skyrmion ratchet propagation: utilizing the skyrmion Hall effect in AC racetrack storage devices

Magnetic skyrmions are whirl-like nano-objects with topological protection. When driven by direct currents, skyrmions move but experience a transverse deflection. This so-called skyrmion Hall effect is often regarded a drawback for memory applications. Herein, we show that this unique effect can also be favorable for spintronic applications: We show that in a racetrack with a broken inversion symmetry, the skyrmion Hall effect allows to translate an alternating current into a directed motion along the track, like in a ratchet. We analyze several modes of the ratchet mechanism and show that it is unique for topological magnetic whirls. We elaborate on the fundamental differences compared to the motion of topologically trivial magnetic objects, as well as classical particles driven by periodic forces. Depending on the exact racetrack geometry, the ratchet mechanism can be soft or strict. In the latter case, the skyrmion propagates close to the efficiency maximum.

Recent Progress on Topological Structures in Ferroic Thin Films and Heterostructures

Topological spin/polarization structures in ferroic materials continue to draw great attention as a result of their fascinating physical behaviors and promising applications in the field of high-density nonvolatile memories as well as future energy-efficient nanoelectronic and spintronic devices. Such developments have been made, in part, based on recent advances in theoretical calculations, the synthesis of high-quality thin films, and the characterization of their emergent phenomena and exotic phases. Herein, progress over the last decade in the study of topological structures in ferroic thin films and heterostructures is explored, including the observation of topological structures and control of their structures and emergent physical phenomena through epitaxial strain, layer thickness, electric, magnetic fields, etc. First, the evolution of topological spin structures (e.g., magnetic skyrmions) and associated functionalities (e.g., topological Hall effect) in magnetic thin films and heterostructures is discussed. Then, the exotic polar topologies (e.g., domain walls, closure domains, polar vortices, bubble domains, and polar skyrmions) and their emergent physical properties in ferroelectric oxide films and heterostructures are explored. Finally, a brief overview and prospectus of how the field may evolve in the coming years is provided.

Roadmap of spin-orbit torques

Spin-orbit torque (SOT) is an emerging technology that enables the efficient manipulation of spintronic devices. The initial processes of interest in SOTs involved electric fields, spin-orbit coupling, conduction electron spins and magnetization. More recently interest has grown to include a variety of other processes that include phonons, magnons, or heat. Over the past decade, many materials have been explored to achieve a larger SOT efficiency. Recently, holistic design to maximize the performance of SOT devices has extended material research from a nonmagnetic layer to a magnetic layer. The rapid development of SOT has spurred a variety of SOT-based applications. In this Roadmap paper, we first review the theories of SOTs by introducing the various mechanisms thought to generate or control SOTs, such as the spin Hall effect, the Rashba-Edelstein effect, the orbital Hall effect, thermal gradients, magnons, and strain effects. Then, we discuss the materials that enable these effects, including metals, metallic alloys, topological insulators, two-dimensional materials, and complex oxides. We also discuss the important roles in SOT devices of different types of magnetic layers, such as magnetic insulators, antiferromagnets, and ferrimagnets. Afterward, we discuss device applications utilizing SOTs. We discuss and compare three-terminal and two-terminal SOT-magnetoresistive random-access memories (MRAMs); we mention various schemes to eliminate the need for an external field. We provide technological application considerations for SOT-MRAM and give perspectives on SOT-based neuromorphic devices and circuits. In addition to SOT-MRAM, we present SOT-based spintronic terahertz generators, nano-oscillators, and domain wall and skyrmion racetrack memories. This paper aims to achieve a comprehensive review of SOT theory, materials, and applications, guiding future SOT development in both the academic and industrial sectors.

Coexistence of distinct skyrmion phases observed in hybrid ferromagnetic/ferrimagnetic multilayers

Materials hosting magnetic skyrmions at room temperature could enable compact and energetically-efficient storage such as racetrack memories, where information is coded by the presence/absence of skyrmions forming a moving chain through the device. The skyrmion Hall effect leading to their annihilation at the racetrack edges can be suppressed, for example, by antiferromagnetically-coupled skyrmions. However, avoiding modifications of the inter-skyrmion distances remains challenging. As a solution, a chain of bits could also be encoded by two different solitons, such as a skyrmion and a chiral bobber, with the limitation that it has solely been realized in B20-type materials at low temperatures. Here, we demonstrate that a hybrid ferro/ferri/ferromagnetic multilayer system can host two distinct skyrmion phases at room temperature, namely tubular and partial skyrmions. Furthermore, the tubular skyrmion can be converted into a partial skyrmion. Such systems may serve as a platform for designing memory applications using distinct skyrmion types.

Topological spin textures are of technological interest due to their potential as a store of information. Here the authors experimentally demonstrate two distinct topological spin textures, tubular and incomplete skyrmions, and their mutual conversion in a ferromagnetic/ferromagnetic heterostructure.

Magnetic Direct-Write Skyrmion Nanolithography

Magnetic skyrmions are stable spin textures with quasi-particle behavior and attract significant interest in fundamental and applied physics. The metastability of magnetic skyrmions at zero magnetic field is particularly important to enable, for instance, a skyrmion racetrack memory. Here, the results of the nucleation of stable skyrmions and formation of ordered skyrmion lattices by magnetic force microscopy in (Pt/CoFeSiB/W)_n multilayers, exploiting the additive effect of the interfacial Dzyaloshinskii-Moriya interaction, are presented. The appropriate conditions under which skyrmion lattices are confined with a dense two-dimensional liquid phase are identified. A crucial parameter to control the skyrmion lattice characteristics and the number of scans resulting in the complete formation of a skyrmion lattice is the distance between two adjacent scanning lines of a magnetic force microscopy probe. The creation of skyrmion patterns with complex geometry is demonstrated, and the physical mechanism of direct magnetic writing of skyrmions is comprehended by micromagnetic simulations. This study shows a potential of a direct-write (maskless) skyrmion (topological) nanolithography with sub-100 nm resolution, where each skyrmion acts as a pixel in the final topological image.

Minimum and maximum energy for crystals of magnetic dipoles

Properties of many magnetic materials consisting of dipoles depend crucially on the nature of the dipole-dipole interaction. In the present work, we study systems of magnetic dipoles where the dipoles are arranged on various types of one-dimensional, two-dimensional and three-dimensional lattices. It is assumed that we are in the regime of strong dipole moments where a classical treatment is possible. We combine a new classical numerical approach in conjuncture with an ansatz for an energy decomposition method to study the energy stability of various magnetic configurations at zero temperature for systems of dipoles ranging from small to an infinite number of particles. A careful analysis of the data in the bulk limit allows us to identify very accurate minimum and maximum energy bounds as well as ground state configurations corresponding to various types of lattices. The results suggest stabilization of a particularly interesting ground state configuration consisting of three embedded spirals for the case of a two-dimensional hexagonal lattice.

Linear chains of nanomagnets: engineering the effective magnetic anisotropy

This paper investigates the control of effective magnetic anisotropy in Permalloy linear chain arrays, achieved by tuning the symmetry arrangement of the ellipsoidal nanomagnets and the film thickness. When the ellipsoidal nanomagnets are coupled along their easy axis, stronger effective magnetic anisotropy is achieved compared to when the nanomagnets are coupled along their hard axis. A clear transition from a single domain state to a combination of complex flux closure states such as a vortex or double vortices is observed at different applied field angles when the film thickness is varied in the range from 20 nm to 100 nm. Tunable microwave absorption spectra, obtained by ferromagnetic resonance spectroscopy, established the complex interplay between the shape anisotropy and magnetostatic interactions, which becomes more intriguing at different film thicknesses and applied field angles. The micromagnetic simulations are in good agreement with the experimental results. Our results demonstrate possible ways of manipulating the effective magnetic anisotropy in arrays of nanomagnets for magnonic and microwave applications.

Half-hedgehog spin textures in sub-100 nm soft magnetic nanodots

Topologically non-trivial structures such as magnetic skyrmions are nanometric spin textures of outstanding potential for spintronic applications due to their unique features. It is well known that Néel skyrmions of definite chirality are stabilized by the Dzyaloshinskii-Moriya exchange interaction (DMI) in bulk non-centrosymmetric materials or ultrathin films with strong spin-orbit coupling at the interface. In this work, we show that soft magnetic (permalloy) hemispherical nanodots are able to host three-dimensional chiral structures (half-hedgehog spin textures) with non-zero tropological charge. They are observed at room temperature, in absence of DMI interaction and they can be further stabilized by the magnetic field arising from the Magnetic Force Microscopy probe. Micromagnetic simulations corroborate the experimental data. Our work implies the existence of a new degree of freedom to create and manipulate complex 3D spin-textures in soft magnetic nanodots and opens up future possibilities to explore their magnetization dynamics.

Sub-nanoscale atom-by-atom crafting of skyrmion-defect interaction profiles

Magnetic skyrmions are prime candidates as information carriers for spintronic devices due to their topological nature and nanometric size. However, unavoidable inhomogeneities inherent to any material leads to pinning or repulsion of skyrmions that, in analogy to biology concepts, define the phenotype of the skyrmion-defect interaction, generating complexity in their motion and challenging their application as future bits of information. Here, we demonstrate that atom-by-atom manufacturing of multi-atomic defects, being antiferromagnetic or ferromagnetic, permits the breeding of their energy profiles, for which we build schematically a Punnet-square. As established from first-principles for skyrmions generated in PdFe bilayer on Ir(111) surface, the resulting interaction phenotype is rich. It can be opposite to the original one and eventually be of dual pinning-repulsive nature yielding energy landscapes hosting multi-domains. This is dictated by the stacking site, geometry, size and chemical nature of the adsorbed defects, which control the involved magnetic interactions. This work provides new insights towards the development of disruptive device architectures incorporating defects into their design aiming to control and guide skyrmions.

Ferrimagnetic Skyrmions in Topological Insulator/Ferrimagnet Heterostructures

Magnetic skyrmions are topologically nontrivial chiral spin textures that have potential applications in next-generation energy-efficient and high-density spintronic devices. In general, the chiral spins of skyrmions are stabilized by the noncollinear Dzyaloshinskii-Moriya interaction (DMI), originating from the inversion symmetry breaking combined with the strong spin-orbit coupling (SOC). Here, the strong SOC from topological insulators (TIs) is utilized to provide a large interfacial DMI in TI/ferrimagnet heterostructures at room temperature, resulting in small-size (radius ≈ 100 nm) skyrmions in the adjacent ferrimagnet. Antiferromagnetically coupled skyrmion sublattices are observed in the ferrimagnet by element-resolved scanning transmission X-ray microscopy, showing the potential of a vanishing skyrmion Hall effect and ultrafast skyrmion dynamics. The line-scan spin profile of the single skyrmion shows a Néel-type domain wall structure and a 120 nm size of the 180° domain wall. This work demonstrates the sizable DMI and small skyrmions in TI-based heterostructures with great promise for low-energy spintronic devices.

Skyrmion-skyrmion interaction in a magnetic film

Interaction of two skyrmions stabilized by the ferromagnetic exchange, Dzyaloshinskii-Moriya interaction (DMI), and external magnetic field has been studied numerically on a 2D lattice of size large compared to the separation,d, between the skyrmions. We show that two skyrmions of the same chirality (determined by the symmetry of the crystal) repel. In accordance with earlier analytical results, their long-range pair interaction falls out with the separation as exp(-d/δH), whereδHis the magnetic screening length, independent of the DMI. The prefactor in this expression depends on the DMI that drives the repulsion. The latter results in the spiral motion of the two skyrmions around each other, with the separation between them growing logarithmically with time. When two skyrmions of the total topological chargeQ= 2 are pushed close to each other, the discreteness of the atomic lattice makes them collapse into one skyrmion of chargeQ= 1 below a critical separation. Experiment is proposed that would allow one to measure the interaction between two skyrmions by holding them in positions with two magnetic tips. Our findings should be of value for designing topologically protected magnetic memory based upon skyrmions.

Topology-Dependent Brownian Gyromotion of a Single Skyrmion

Noninteracting particles exhibiting Brownian motion have been observed in many occasions of sciences, such as molecules suspended in liquids, optically trapped microbeads, and spin textures in magnetic materials. In particular, a detailed examination of Brownian motion of spin textures is important for designing thermally stable spintronic devices, which motivates the present study. In this Letter, through using temporally and spatially resolved polar magneto-optic Kerr effect microscopy, we have experimentally observed the thermal fluctuation-induced random walk of a single isolated Néel-type magnetic skyrmion in an interfacially asymmetric Ta/CoFeB/TaO_{x} multilayer. An intriguing topology-dependent Brownian gyromotion behavior of skyrmions has been identified. The onset of Brownian gyromotion of a single skyrmion induced by thermal effects, including a nonlinear temperature-dependent diffusion coefficient and topology-dependent gyromotion are further formulated based on the stochastic Thiele equation. The experimental and numerical demonstration of topology-dependent Brownian gyromotion of skyrmions can be useful for understanding the nonequilibrium magnetization dynamics and implementing spintronic devices.

Tuning the Properties of Zero-Field Room Temperature Ferromagnetic Skyrmions by Interlayer Exchange Coupling

Magnetic materials offer an opportunity to overcome the scalability and energy consumption limits affecting the semiconductor industry. New computational device architectures, such as low-power solid state magnetic logic and memory-in-logic devices, have been proposed which rely on the unique properties of magnetic materials. Magnetic skyrmions, topologically protected quasi-particles, are at the core of many of the newly proposed spintronic devices. Many different materials systems have been shown hosting ferromagnetic skyrmions at room temperature. However, a magnetic field is a key ingredient to stabilize skyrmions, and this is not desirable for applications, due to the poor scalability of active components generating magnetic fields. Here we report the observation of ferromagnetic skyrmions at room temperature and zero magnetic field, stabilized through interlayer exchange coupling (IEC) between a reference magnet and a free magnet. Most importantly, by tuning the strength of the IEC, we are able to tune the skyrmion size and areal density. Our findings are relevant to the development of skyrmion-based spintronic devices suitable for general-use applications which go beyond modern nanoelectronics.

Influence of rare earth metal Ho on the interfacial Dzyaloshinskii-Moriya interaction and spin torque efficiency in Pt/Co/Ho multilayers

Owing to the large spin-orbit coupling and tunable magnetization, heavy rare-earth metals Gd and Tb have great effects on the enhancement of spin-orbit torque (SOT) and fast domain wall (DW) motion. However, the reports on the heavy rare-earth metal Ho with more 4f electrons in the research of spintronics are limited. In this work, we found that the interfacial Dzyaloshinskii-Moriya interaction (DMI) and SOT in Pt/Co/Ho multilayers can be strongly influenced by changing the thickness of the Ho (tHo) layer. At tHo = 2.4 nm, DMI exchange constant |D| and spin torque efficiency ξDL reach maximum values of 1.24 mJ m-2 and 0.137 respectively, which are comparable with those in other Pt/Co/nonmagnetic (NM) layer structures. Deterministic current-induced magnetization switching with a low critical current density of 106 A cm-2 can be realized when tHo is less than 5 nm. The Néel-type DW with left-handed chirality and positive sign D can be determined by observing the current-induced asymmetric DW motion. Our results are helpful to prompt the application of heavy rare-earth elements in the fields of the DMI, SOT and chiral DW dynamics.

Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications

The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last decades. In this topical review, we mainly review and discuss key results and findings in skyrmion research since the first experimental observation of magnetic skyrmions in 2009. We particularly focus on the theoretical, computational and experimental findings and advances that are directly relevant to the spintronic applications based on magnetic skyrmions, i.e. their writing, deleting, reading and processing driven by magnetic field, electric current and thermal energy. We then review several potential applications including information storage, logic computing gates and non-conventional devices such as neuromorphic computing devices. Finally, we discuss possible future research directions on magnetic skyrmions, which also cover rich topics on other topological textures such as antiskyrmions and bimerons in antiferromagnets and frustrated magnets.

Determining Surface Terminations and Chirality of Noncentrosymmetric FeGe Thin Films via Scanning Tunneling Microscopy

Scanning tunneling microscopy was used to study the surfaces of 20-100 nm thick FeGe films grown by molecular beam epitaxy. An average surface lattice constant of ∼6.8 Å, in agreement with the bulk value, was observed via scanning tunneling microscopy, low energy electron diffraction, and reflection high energy electron diffraction. Each of the four possible chemical terminations in the FeGe films were identified by comparing atomic-resolution images, showing distinct contrast with simulations from density functional theory calculations. A detailed study of the atomic layering order and registry across step edges allows us to uniquely determine the grain orientation and chirality in these noncentrosymmetric films.

Creating zero-field skyrmions in exchange-biased multilayers through X-ray illumination

Skyrmions, magnetic textures with topological stability, hold promises for high-density and energy-efficient information storage devices owing to their small size and low driving-current density. Precise creation of a single nanoscale skyrmion is a prerequisite to further understand the skyrmion physics and tailor skyrmion-based applications. Here, we demonstrate the creation of individual skyrmions at zero-field in an exchange-biased magnetic multilayer with exposure to soft X-rays. In particular, a single skyrmion with 100-nm size can be created at the desired position using a focused X-ray spot of sub-50-nm size. This single skyrmion creation is driven by the X-ray-induced modification of the antiferromagnetic order and the corresponding exchange bias. Furthermore, artificial skyrmion lattices with various arrangements can be patterned using X-ray. These results demonstrate the potential of accurate optical control of single skyrmion at sub-100 nm scale. We envision that X-ray could serve as a versatile tool for local manipulation of magnetic orders.

Skyrmions are objects with whirled magnetization protected by their topology that can be created by different means, however, without control of their position. Here, the authors present a method exploiting x-rays to create skyrmions at the beam position allowing for creation of artificial skyrmion lattices.