Phase diagram of superconductivity in the integer quantum Hall regime.

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

A micromagnetic theory of skyrmion lifetime in ultrathin ferromagnetic films.

We use the continuum micromagnetic framework to derive the formulas for compact skyrmion lifetime due to thermal noise in ultrathin ferromagnetic films with relatively weak interfacial Dzyaloshinskii-Moriya interaction. In the absence of a saddle point connecting the skyrmion solution to the ferromagnetic state, we interpret the skyrmion collapse event as "capture by an absorber" at microscale. This yields an explicit Arrhenius collapse rate with both the barrier height and the prefactor as functions of all the material parameters, as well as the dynamical paths to collapse.

Creation of Room-Temperature Sub-100 nm Antiferromagnetic Skyrmions in an Antiferromagnet IrMn through Interfacial Exchange Coupling.

Antiferromagnetic (AFM) skyrmions are magnetic vortices composed of antiparallell-aligned neighboring spins. In stark contrast to conventional skyrmions based on ferromagnetic order, AFM skyrmions have vanished stray fields, higher response frequencies, and rectified translational motion driven by an external force. Therefore, AFM skyrmions promise highly efficient spintronics devices with high bit mobility and density. Nevertheless, the experimental realization of intrinsic AFM skyrmions remains elusive. Here, we show that AFM skyrmions can be nucleated via interfacial exchange coupling at the surface of a room-temperature AFM material, IrMn, exploiting the particular response from uncompensated moments to the thermal annealing and imprinting effects. Further systematic magnetic characterizations validate the existence of such an AFM order at the IrMn/CoFeB interfaces. Such AFM skyrmions have a typical size of 100 nm, which presents pronounced robustness against field and temperature. Our work opens new pathways for magnetic topological devices based on AFM skyrmions.

Electrical Detection and Nucleation of a Magnetic Skyrmion in a Magnetic Tunnel Junction Observed via Operando Magnetic Microscopy.

Magnetic skyrmions are topological spin textures which are envisioned as nanometer scale information carriers in magnetic memory and logic devices. The recent demonstrations of room temperature skyrmions and their current induced manipulation in ultrathin films were first steps toward the realization of such devices. However, important challenges remain regarding the electrical detection and the low-power nucleation of skyrmions, which are required for the read and write operations. Here, we demonstrate, using operando magnetic microscopy experiments, the electrical detection of a single magnetic skyrmion in a magnetic tunnel junction (MTJ) and its nucleation and annihilation by gate voltage via voltage control of magnetic anisotropy. The nucleated skyrmion can be manipulated by both gate voltages and external magnetic fields, leading to tunable intermediate resistance states. Our results unambiguously demonstrate the readout and voltage controlled write operations in a single MTJ device, which is a major milestone for low power skyrmion based technologies.

Tuning Topology Phases by Controlling Effective Screening and Depolarization in Oxide Superlattices.

Polar topological phases in oxide superlattices attracted significant attention due to their unique properties. Previous work revealed that a polar vortex and polar skyrmions exist in (PTO)/(STO) superlattices under different elastic constraints, i.e., on different substrates. Here, our phase-field simulation demonstrates that manipulating the PTO and STO layers' thickness can control the effective screening provided by STO and the depolarization degree in PTO, thus switching the system among the polar skyrmions, vortex labyrinth, or paraelectric phase without changing elastic constraints. Additionally, reducing the STO thickness creates interlayer coupling among PTO layers, generating the long-range order of topological phases within superlattices. Furthermore, we construct a PTO-STO thickness topological phase diagram. These findings offer insights into the polar topological phases' formation in oxide superlattices, elucidating the roles of ferroelectric and paraelectric layers in their formation.

Demonstration of Controlled Skyrmion Injection Across a Thickness Step.

Spintronic devices incorporating magnetic skyrmions have attracted significant interest recently. Such devices traditionally focus on controlling magnetic textures in 2D thin films. However, enhanced performance of spintronic properties through the exploitation of higher dimensionalities motivates the investigation of variable-thickness skyrmion devices. We report the demonstration of a skyrmion injection mechanism that utilizes charge currents to drive skyrmions across a thickness step and, consequently, a metastability barrier. Our measurements show that under certain temperature and field conditions skyrmions can be reversibly injected from a thin region of an FeGe lamella, where they exist as an equilibrium state, into a thicker region, where they can only persist as a metastable state. This injection is achieved with a current density of 3 × 108 A m-2, nearly 3 orders of magnitude lower than required to move magnetic domain walls. This highlights the possibility to use such an element as a skyrmion source/drain within future spintronic devices.

Spontaneous Atomic-Scale Polar Skyrmions and Merons on a SrTiO3 (001) Surface: Defect Engineering for Emerging Topological Orders.

The emergence of nontrivial topological order in condensed matter has been attracting a great deal of attention owing to its promising technological applications in novel functional nanodevices. In ferroelectrics, the realization of polar topological order at an ultimately small scale is extremely challenging due to the lack of chiral interaction and the critical size of the ferroelectricity. Here, we break through these limitations and demonstrate that the ultimate atomic-scale polar skyrmion and meron (∼2 nm) can be induced by engineering oxygen vacancies on the SrTiO3 (001) surface based on first-principles calculations. The paraelectric-to-antiferrodistortive phase transition leads to a novel topological transition from skyrmion to meron, indicating phase-topology correlations. We also discuss accumulating and driving polar skyrmions based on the oxygen divacancy model; these results and the recent discovery of defect engineering techniques suggest the possibility of arithmetic operations on topological numbers through the natural self-organization and diffusion features of oxygen vacancies.

Nonvolatile Multistate Manipulation of Topological Magnetism in Monolayer CrI3 through Quadruple-Well Ferroelectric Materials.

Nonvolatile multistate manipulation of two-dimensional (2D) magnetic materials holds promise for low dissipation, highly integrated, and versatile spintronic devices. Here, utilizing density functional theory calculations and Monte Carlo simulations, we report the realization of nonvolatile and multistate control of topological magnetism in monolayer CrI3 by constructing multiferroic heterojunctions with quadruple-well ferroelectric (FE) materials. The Pt2Sn2Te6/CrI3 heterojunction exhibits multiple magnetic phases upon modulating FE polarization states of FE layers and interlayer sliding. These magnetic phases include Bloch-type skyrmions and ferromagnetism, as well as a newly discovered topological magnetic structure. We reveal that the Dzyaloshinskii-Moriya interaction (DMI) induced by interfacial coupling plays a crucial role in magnetic skyrmion manipulation, which aligns with the Fert-Levy mechanism. Moreover, a regular magnetic skyrmion lattice survives when removing a magnetic field, demonstrating its robustness. The work sheds light on an effective approach to nonvolatile and multistate control of 2D magnetic materials.

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.

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.

Observation by SANS and PNR of pure Néel-type domain wall profiles and skyrmion suppression below room temperature in magnetic [Pt/CoFeB/Ru]10 multilayers.

We report investigations of the magnetic textures in periodic multilayers [Pt(1 nm)/(CoFeB(0.8 nm)/Ru(1.4 nm)]10 using polarised neutron reflectometry (PNR) and small-angle neutron scattering (SANS). The multilayers are known to host skyrmions stabilized by Dzyaloshinskii-Moriya interactions induced by broken inversion symmetry and spin-orbit coupling at the asymmetric interfaces. From depth-dependent PNR measurements, we observed well-defined structural features and obtained the layer-resolved magnetization profiles. The in-plane magnetization of the CoFeB layers calculated from fitting of the PNR profiles is found to be in excellent agreement with magnetometry data. Using SANS as a bulk probe of the entire multilayer, we observe long-period magnetic stripe domains and skyrmion ensembles with full orientational disorder at room temperature. No sign of skyrmions is found below 250 K, which we suggest is due to an increase of an effective magnetic anisotropy in the CoFeB layer on cooling that suppresses skyrmion stability. Using polarised SANS at room temperature, we prove the existence of pure Néel-type windings in both stripe domain and skyrmion regimes. No Bloch-type winding admixture, i.e. an indication for hybrid windings, is detected within the measurement sensitivity, in good agreement with expectations according to our micromagnetic modelling of the multilayers. Our findings using neutron techniques provide valuable microscopic insights into the rich magnetic behavior of skyrmion-hosting multilayers, which are essential for the advancement of future skyrmion-based spintronic devices.

The study presents a unique investigation of [Pt/CoFeB/Ru]₁₀ multilayers, revealing suppressed skyrmion phases, intricate magnetic domain structures, and Néel-type domain walls, providing crucial insights for spintronic applications.

Correlation of Interface Interdiffusion and Skyrmionic Phases.

Magnetic skyrmions are prime candidates for the next generation of spintronic devices. Skyrmions and other topological magnetic structures are known to be stabilized by the Dzyaloshinskii-Moriya interaction (DMI) that occurs when the inversion symmetry is broken in thin films. Here, we show by first-principles calculations and atomistic spin dynamics simulations that metastable skyrmionic states can also be found in nominally symmetric multilayered systems. We demonstrate that this is correlated with the large enhancement of the DMI strength due to the presence of local defects. In particular, we find that metastable skyrmions can occur in Pd/Co/Pd multilayers without external magnetic fields and can be stable even near room temperature conditions. Our theoretical findings corroborate with magnetic force microscopy images and X-ray magnetic circular dichroism measurements and highlight the possibility of tuning the intensity of DMI by using interdiffusion at thin film interfaces.

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.

Solid-State Lithium Ion Supercapacitor for Voltage Control of Skyrmions.

Ionic control of magnetism gives rise to high magnetoelectric coupling efficiencies at low voltages, which is essential for low-power magnetism-based nonconventional computing technologies. However, for on-chip applications, magnetoionic devices typically suffer from slow kinetics, poor cyclability, impractical liquid architectures, or strong ambient effects. As a route to overcoming these problems, we demonstrate a LiPON-based solid-state ionic supercapacitor with a magnetic Pt/Co40Fe40B20/Pt thin-film electrode which enables voltage control of a magnetic skyrmion state. Skyrmion nucleation and annihilation are caused by Li ion accumulation and depletion at the magnetic interface under an applied voltage. The skyrmion density can be controlled through dc applied voltages or through voltage pulses. The skyrmions are nucleated by single 60 µs voltage pulses, and devices are cycled 750000 times without loss of electrical performance. Our results demonstrate a simple and robust approach to ionic control of magnetism in spin-based devices.

Direct Observation of Magnetic Skyrmions and Their Current-Induced Dynamics in Epitaxial Single-Crystal Oxide Films.

Magnetic skyrmions are scarcely investigated for single-crystal quality films, for which skyrmions may have a remarkable performance. Even in the limited studies in this aspect, the skyrmions are usually probed by the topological Hall effect, missing important information on dynamic properties. Here, we present a comprehensive investigation on the generation/manipulation of magnetic skyrmions in La0.67Ba0.33MnO3 single-crystal films. Using the technique of magnetic force microscopy, the current-driven skyrmion dynamics are directly observed. Unlike isolated skyrmions produced by magnetic field alone, closely packed skyrmions can be generated by electric pulses in a magnetic background, with a high density (∼60/µm2) and a small size (dozens of nanometers). The threshold current moving skyrmions is ∼2.3 × 104 A/cm2, 2-3 orders of magnitude lower than that required by metallic multilayers or van der Waals ferromagnetic heterostructures. Our work demonstrates the great potential of single-crystal oxide films in developing skyrmion-based devices.

Hysteretic Responses of Skyrmion Lattices to Electric Fields in Magnetoelectric Cu2OSeO3.

Electric field control of topologically nontrivial magnetic textures, such as skyrmions, provides a paradigm shift for future spintronics beyond the current silicon-based technology. While significant progress has been made by X-ray and neutron scattering studies, direct observation of such nanoscale spin structures and their dynamics driven by external electric fields remains a challenge in understanding the underlying mechanisms and harness functionalities. Here, using Lorentz transmission electron microscopy combined with in situ electric and magnetic fields at liquid helium temperatures, we report the crystallographic orientation-dependent skyrmion responses to electric fields in thin slabs of magnetoelectric Cu2OSeO3. We show that electric fields not only stabilize the hexagonally packed skyrmion lattices in the entire sample in a hysteretic manner but also induce the rotation of their reciprocal vector discretely by 30°. The nonvolatile and energy-efficient skyrmion lattice control by electric fields demonstrated in this work provides an important foundation for designing skyrmion-based qubits and memory devices.

Room-Temperature Zero-Field kπ-Skyrmions and Their Field-Driven Evolutions in Chiral Nanodisks.

Target skyrmion, characterized by a central skyrmion surrounded by a series of concentric cylinder domains known as kπ-skyrmions (k ≥ 2), holds promise as a novel storage state in next-generation memories. However, target skyrmions comprising one or more concentric cylindrical domains have not been observed in chiral magnets, particularly at room temperature. In this study, we experimentally achieved kπ-skyrmions (k = 2, 3, and 4) with diameters of ∼220, 320, and 410 nm, respectively, and room-temperature stability under zero magnetic field by tightly confining these topological spin textures in ß-Mn-type Co8Zn10Mn2 nanodisks. The magnetic configurations and their field-driven evolutions were simultaneously investigated by using in situ off-axis electron holography. In combination with numerical simulations, we further investigated the dependence of kmax on the nanodisk diameter. These findings highlight the potential of kπ-skyrmions as information carriers and offer insights into manipulation of kπ-skyrmions in the future.

Evidence of Strong Dzyaloshinskii-Moriya Interaction at the Cobalt/Hexagonal Boron Nitride Interface.

The Dzyaloshinskii-Moriya interaction (DMI) and perpendicular magnetic anisotropy (PMA) were measured on four series of Co films (1-2.2 nm thick) grown on Pt or Au and covered with h-BN or Cu. Clean h-BN/Co interfaces were obtained by exfoliating h-BN and transferring it onto the Co film in situ in the ultra-high-vacuum evaporation chamber. By comparing h-BN and Cu-covered samples, the DMI induced by the Co/h-BN interface was extracted and found to be comparable in strength to that of the Pt/Co interface, one of the largest known values. The strong observed DMI despite the weak spin-orbit interaction in h-BN supports a Rashba-like origin in agreement with recent theoretical results. Upon combination of it with Pt/Co in Pt/Co/h-BN heterostructures, even stronger PMA and DMI are found which stabilizes skyrmions at room temperature and a low magnetic field.

Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moiré Superlattices.

The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating |C| = 2 dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity match. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is bosonic, characterized by electronic charge Q = 2e, which is even in units of electron charge e. The skyrmion coupling strength triggering the topological phase transition is realistic, with its lower bound estimated as 4 meV. The Hofstadter butterfly spectrum results in an unexpected quantum Hall conductance sequence ±2e2h,±4e2h,... for TBG with the skyrmion order.

Manipulation of Skyrmion by Magnetic Field Gradients: A Stern-Gerlach-Like Experiment.

Magnetic skyrmions are real-space topological spin textures, which have attracted increasing attention from the nanospintronics community. Toward functional skyrmionics, the efficient manipulation of skyrmions is a prerequisite, which has been successfully demonstrated through electrical, thermal, optical, and other means. Here, through integrating an interfacially asymmetric Ta/CoFeB/MgO multilayer with an on-chip wire that induces Oersted fields and their gradients, we show experimentally the generation and topology-dependent motion of Néel type skyrmions at room temperature. In particular, an opposite longitudinal motion for skyrmions with opposite topological charges along the gradient direction is observed. Through comparing with the well-known Stern-Gerlach experiment, in which the splitting of atomic spins under magnetic field gradients was observed, our work identifies another interesting aspect of the topological character of skyrmions. The present study could also be implemented for designing novel on-chip skyrmionic devices in which the manipulation of skyrmions cannot be done by electrical means.