Chiral magnetic soliton lattice on a chiral helimagnet

Direct visualization of stacking-selective self-intercalation in epitaxial Nb1+xSe2 films

Two-dimensional (2D) van der Waals (vdW) materials offer rich tuning opportunities generated by different stacking configurations or by introducing intercalants into the vdW gaps. Current knowledge of the interplay between stacking polytypes and intercalation often relies on macroscopically averaged probes, which fail to pinpoint the exact atomic position and chemical state of the intercalants in real space. Here, by using atomic-resolution electron energy-loss spectroscopy in a scanning transmission electron microscope, we visualize a stacking-selective self-intercalation phenomenon in thin films of the transition-metal dichalcogenide (TMDC) Nb1+xSe2. We observe robust contrasts between 180°-stacked layers with large amounts of Nb intercalants inside their vdW gaps and 0°-stacked layers with little detectable intercalants inside their vdW gaps, coexisting on the atomic scale. First-principles calculations suggest that the films lie at the boundary of a phase transition from 0° to 180° stacking when the intercalant concentration x exceeds ~0.25, which we could attain in our films due to specific kinetic pathways. Our results offer not only renewed mechanistic insights into stacking and intercalation, but also open up prospects for engineering the functionality of TMDCs via stacking-selective self-intercalation.

Chirality-Induced Selectivity of Phonon Angular Momenta in Chiral Quartz Crystals

A generation, propagation, and transfer of phonon angular momenta are examined on thermal transport in chiral insulative and diamagnetic crystals of α-quartz. We found that thermally driven phonons carry chirality-dependent angular momenta in the quartz crystals and they could be extracted from the quartz as a spin signal. Namely, chirality-induced selectivity of phonon angular momenta is realized in the chiral quartz. We argue that chiral phonons available in chiral materials could be a key element in triggering or enhancing chirality-induced spin selectivity with robust spin polarization and long-range spin transport found in various chiral materials.

Spontaneous Vortex-Antivortex Pairs and Their Topological Transitions in a Chiral-Lattice Magnet

The spontaneous formation and topological transitions of vortex-antivortex pairs have implications for a broad range of emergent phenomena, for example, from superconductivity to quantum computing. Unlike magnets exhibiting collinear spin textures, helimagnets with noncollinear spin textures provide unique opportunities to manipulate topological forms such as (anti)merons and (anti)skyrmions. However, it is challenging to achieve multiple topological states and their interconversion in a single helimagnet due to the topological protection for each state. Here, the on-demand creation of multiple topological states in a helimagnet Fe0.5 Co0.5 Ge, including a spontaneous vortex pair of meron with topological charge N = -1/2 and antimeron with N = 1/2, and a vortex-antivortex bundle, that is, a bimeron (meron pair) with N = -1 is reported. The mutual transformation between skyrmions and bimerons with respect to the competitive effects of magnetic field and magnetic shape anisotropy is demonstrated. It is shown that electric currents drive the individual bimerons to form their connecting assembly and then into a skyrmion lattice. These findings signify the feasibility of designing topological states and offer new insights into the manipulation of noncollinear spin textures for potential applications in various fields.

Fe Site Order and Magnetic Properties of Fe1/4NbS2

Transition-metal dichalcogenides (TMDs) have long been attractive to researchers for their diverse properties and high degree of tunability. Most recently, interest in magnetically intercalated TMDs has resurged due to their potential applications in spintronic devices. While certain compositions featuring the absence of inversion symmetry such as Fe1/3NbS2 and Cr1/3NbS2 have garnered the most attention, the diverse compositional space afforded through the host matrix composition as well as intercalant identity and concentration is large and remains relatively underexplored. Here, we report the magnetic ground state of Fe1/4NbS2 that was determined from low-temperature neutron powder diffraction as an A-type antiferromagnet. Despite the presence of overall inversion symmetry, the pristine compound manifests spin polarization induced by the antiferromagnetic order at generic k points, based on density functional theory band-structure calculations. Furthermore, by combining synchrotron diffraction, pair distribution function, and magnetic susceptibility measurements, we find that the magnetic properties of Fe1/4NbS2 are sensitive to the Fe site order, which can be tuned via electrochemical lithiation and thermal history.

Discovery of Charge Order in the Transition Metal Dichalcogenide Fe_{x}NbS_{2}

The Fe intercalated transition metal dichalcogenide (TMD), Fe_{1/3}NbS_{2}, exhibits remarkable resistance switching properties and highly tunable spin ordering phases due to magnetic defects. We conduct synchrotron x-ray scattering measurements on both underintercalated (x=0.32) and overintercalated (x=0.35) samples. We discover a new charge order phase in the overintercalated sample, where the excess Fe atoms lead to a zigzag antiferromagnetic order. The agreement between the charge and magnetic ordering temperatures, as well as their intensity relationship, suggests a strong magnetoelastic coupling as the mechanism for the charge ordering. Our results reveal the first example of a charge order phase among the intercalated TMD family and demonstrate the ability to stabilize charge modulation by introducing electronic correlations, where the charge order is absent in bulk 2H-NbS_{2} compared to other pristine TMDs.

Observation and Characterization of Multiple Resonance Modes in a Chiral Helimagnet CrNb3S6

The chiral helimagnet CrNb3S6 hosts various temperature- and magnetic-field-stabilized chiral soliton lattices (CSLs) and corresponding exotic collective spin resonance modes, which make it an ideal candidate for future magnetic storage/memory and magnon-based information processing. While most studies have focused on characterizing various static spin textures in this chiral helimagnet, its corresponding collective dynamics have rarely been explored. This study systematically investigates the temperature- and magnetic-field-dependent magnetic dynamics of a single crystal of CrNb3S6 using broadband microwave spectroscopy. We observe an optical mode with a temperature-independent mode number in addition to Kittel-like ferromagnetic resonance (FMR) modes in the CSL phase, consistent with the temperature-independent normalized CSL period L(H)/L(0) based on the 1D chiral sine-Gordon model. Furthermore, combining theoretical model fitting and micromagnetic simulation, we provide a detailed phase diagram and temporal-spatial resolution of dynamic modes, which may help to develop high-frequency exchange-coupling-based spintronic devices.

Consequences and Control of Multiscale Order/Disorder in Chiral Magnetic Textures

Transition metal intercalated transition metal dichalcogenides (TMDs) are promising platforms for next-generation spintronic devices based on their wide range of electronic and magnetic phases, which can be tuned by varying the host lattice or intercalant's identity, stoichiometry, or spatial order. Some of these compounds host a chiral magnetic phase in which the helical winding of magnetic moments propagates along a high-symmetry crystalline axis. Previous studies have demonstrated that variation in intercalant concentrations can have a dramatic effect on the formation of chiral domains and ensemble magnetic properties. However, a systematic and comprehensive study of how atomic-scale order and disorder impact these chiral magnetic textures is so far lacking. Here, we leverage a combination of imaging modes in the (scanning) transmission electron microscope (S/TEM) to directly probe (dis)order across multiple length scales and show how subtle changes in the atomic lattice can tune the mesoscale spin textures and bulk magnetic response in Cr1/3NbS2, with direct implications for the fundamental understanding and technological implementation of such compounds.

Comparative Electronic Structures of the Chiral Helimagnets Cr1/3NbS2 and Cr1/3TaS2

Magnetic materials with noncollinear spin textures are promising for spintronic applications. To realize practical devices, control over the length and energy scales of such spin textures is imperative. The chiral helimagnets Cr1/3NbS2 and Cr1/3TaS2 exhibit analogous magnetic-phase diagrams with different real-space periodicities and field dependence, positioning them as model systems for studying the relative strengths of the microscopic mechanisms giving rise to exotic spin textures. Although the electronic structure of the Nb analogue has been experimentally investigated, the Ta analogue has received far less attention. Here, we present a comprehensive suite of electronic structure studies on both Cr1/3NbS2 and Cr1/3TaS2 using angle-resolved photoemission spectroscopy and density functional theory. We show that bands in Cr1/3TaS2 are more dispersive than their counterparts in Cr1/3NbS2, resulting in markedly different Fermi wavevectors. The fact that their qualitative magnetic phase diagrams are nevertheless identical shows that hybridization between the intercalant and host lattice mediates the magnetic exchange interactions in both of these materials. We ultimately find that ferromagnetic coupling is stronger in Cr1/3TaS2, but larger spin-orbit coupling (and a stronger Dzyaloshinskii-Moriya interaction) from the heavier host lattice ultimately gives rise to shorter spin textures.

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

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

Resonant Elastic X-Ray Scattering of Antiferromagnetic Superstructures in EuPtSi_{3}

We report resonant elastic x-ray scattering of long-range magnetic order in EuPtSi_{3}, combining different scattering geometries with full linear polarization analysis to unambiguously identify magnetic scattering contributions. At low temperatures, EuPtSi_{3} stabilizes type A antiferromagnetism featuring various long-wavelength modulations. For magnetic fields applied in the hard magnetic basal plane, well-defined regimes of cycloidal, conical, and fanlike superstructures may be distinguished that encompass a pocket of commensurate type A order without superstructure. For magnetic field applied along the easy axis, the phase diagram comprises the cycloidal and conical superstructures only. Highlighting the power of polarized resonant elastic x-ray scattering, our results reveal a combination of magnetic phases that suggest a highly unusual competition between antiferromagnetic exchange interactions with Dzyaloshinsky-Moriya spin-orbit coupling of similar strength.

Realization and Current-Driven Dynamics of Fractional Hopfions and Their Ensembles in a Helimagnet FeGe

3D topological spin textures-hopfions-are predicted in helimagnetic systems but are not experimentally confirmed thus far. By utilizing an external magnetic field and electric current in the present study, 3D topological spin textures are realized, including fractional hopfions with nonzero topological index, in a skyrmion-hosting helimagnet FeGe. Microsecond current pulses are employed to control the dynamics of the expansion and contraction of a bundle composed of a skyrmion and a fractional hopfion, as well as its current-driven Hall motion. This research approach has demonstrated the novel electromagnetic properties of fractional hopfions and their ensembles in helimagnetic systems.

Giant valley-Zeeman coupling in the surface layer of an intercalated transition metal dichalcogenide

Spin-valley locking is ubiquitous among transition metal dichalcogenides with local or global inversion asymmetry, in turn stabilizing properties such as Ising superconductivity, and opening routes towards 'valleytronics'. The underlying valley-spin splitting is set by spin-orbit coupling but can be tuned via the application of external magnetic fields or through proximity coupling. However, only modest changes have been realized to date. Here, we investigate the electronic structure of the V-intercalated transition metal dichalcogenide V_1/3NbS₂ using microscopic-area spatially resolved and angle-resolved photoemission spectroscopy. Our measurements and corresponding density functional theory calculations reveal that the bulk magnetic order induces a giant valley-selective Ising coupling exceeding 50 meV in the surface NbS₂ layer, equivalent to application of a ~250 T magnetic field. This energy scale is of comparable magnitude to the intrinsic spin-orbit splittings, and indicates how coupling of local magnetic moments to itinerant states of a transition metal dichalcogenide monolayer provides a powerful route to controlling their valley-spin splittings.

Transformation from Magnetic Soliton to Skyrmion in a Monoaxial Chiral Magnet

Topological spin textures are of great interest for both fundamental physics and applications in spintronics. The Dzyaloshinskii-Moriya interaction underpins the formation of single-twisted magnetic solitons or multi-twisted magnetic skyrmions in magnetic materials with different crystallographic symmetries. However, topological transitions between these two kinds of topological objects have not been verified experimentally. Here, the direct observation of transformations from a chiral soliton lattice (CSL) to magnetic skyrmions in a nanostripe of the monoaxial chiral magnet CrNb₃ S₆  using Lorentz transmission electron microscopy is reported. In the presence of an external magnetic field, helical spin structures first transform into CSLs and then evolve into isolated elongated magnetic skyrmions. The detailed spin textures of the elongated magnetic skyrmions are resolved using off-axis electron holography and are shown to comprise two merons, which enclose their ends and have unit total topological charge. Magnetic dipolar interactions are shown to play a key role in the magnetic soliton-skyrmion transformation, which depends sensitively on nanostripe width. The findings here, which are consistent with micromagnetic simulations, enrich the family of topological magnetic states and their transitions and promise to further stimulate the exploration of their emergent electromagnetic properties.

Widely Tunable Berry Curvature in the Magnetic Semimetal Cr1+ δ Te2

Magnetic semimetals have increasingly emerged as lucrative platforms hosting spin-based topological phenomena in real and momentum spaces. Cr_{1+ δ} Te₂ is a self-intercalated magnetic transition metal dichalcogenide (TMD), which exhibits topological magnetism and tunable electron filling. While recent studies have explored real-space Berry curvature effects, similar considerations of momentum-space Berry curvature are lacking. Here, the electronic structure and transport properties of epitaxial Cr_{1+ δ} Te₂ thin films are systematically investigated over a range of doping, δ (0.33 - 0.71). Spectroscopic experiments reveal the presence of a characteristic semi-metallic band region, which shows a rigid like energy shift with δ. Transport experiments show that the intrinsic component of the anomalous Hall effect (AHE) is sizable and undergoes a sign flip across δ. Finally, density functional theory calculations establish a link between the doping evolution of the band structure and AHE: the AHE sign flip is shown to emerge from the sign change of the Berry curvature, as the semi-metallic band region crosses the Fermi energy. These findings underscore the increasing relevance of momentum-space Berry curvature in magnetic TMDs and provide a unique platform for intertwining topological physics in real and momentum spaces.

Integrated Memory Devices Based on 2D Materials

With the advent of the Internet of Things and big data, massive data must be rapidly processed and stored within a short timeframe. This imposes stringent requirements on memory hardware implementation in terms of operation speed, energy consumption, and integration density. To fulfill these demands, 2D materials, which are excellent electronic building blocks, provide numerous possibilities for developing advanced memory device arrays with high performance, smart computing architectures, and desirable downscaling. Over the past few years, 2D-material-based memory-device arrays with different working mechanisms, including defects, filaments, charges, ferroelectricity, and spins, have been increasingly developed. These arrays can be used to implement brain-inspired computing or sensing with extraordinary performance, architectures, and functionalities. Here, recent research into integrated, state-of-the-art memory devices made from 2D materials, as well as their implications for brain-inspired computing are surveyed. The existing challenges at the array level are discussed, and the scope for future research is presented.

Observation of Collective Resonance Modes in a Chiral Spin Soliton Lattice with Tunable Magnon Dispersion

A chiral spin soliton lattice (CSL), one of the representative systems of a magnetic superstructure, exhibits reconfigurability in periodicity over a macroscopic length scale. Such coherent and tunable characteristics of the CSL lead to an emergence of elementary excitation of the CSL as phononlike modes due to translational symmetry breaking and bring a controllability of the dispersion relation of the CSL phonon. Using a broadband microwave spectroscopy technique, we directly found that higher-order magnetic resonance modes appear in the CSL phase of a chiral helimagnet CrNb_{3}S_{6}, which is ascribed to the CSL phonon response. The resonance frequency of the CSL phonon can be tuned between 16 and 40 GHz in the vicinity of the critical field, where the CSL period alters rapidly. The frequency range of the CSL phonon is expected to extend over 100 GHz as extrapolated on the basis of the theoretical model. The present results indicate that chiral helimagnets could work as materials useful for broadband signal processing in the millimeter-wave band.

Structure and Magnetism of Iron- and Chromium-Intercalated Niobium and Tantalum Disulfides

Transition metal dichalcogenides (TMDs) intercalated with spin-bearing transition metal centers are a diverse class of magnetic materials where the spin density and ordering behavior can be varied by the choice of host lattice, intercalant identity, level of intercalation, and intercalant disorder. Each of these degrees of freedom alters the interplay between several key magnetic interactions to produce disparate collective electronic and magnetic phases. The array of magnetic and electronic behavior typified by these systems renders them distinctive platforms for realizing tunable magnetism in solid-state materials and promising candidates for spin-based electronic devices. This Perspective provides an overview of the rich magnetism displayed by transition metal-intercalated TMDs by considering Fe- and Cr-intercalated NbS₂ and TaS₂. These four exemplars of this large family of materials exhibit a wide range of magnetic properties, including sharp switching of magnetic states, current-driven magnetic switching, and chiral spin textures. An understanding of the fundamental origins of the resultant magnetic/electronic phases in these materials is discussed in the context of composition, bonding, electronic structure, and magnetic anisotropy in each case study.

Tunable Single-Atomic Charges on a Cleaved Intercalated Transition Metal Dichalcogenide

Control of a single ionic charge state by altering the number of bound electrons has been considered as an ultimate testbed for atomic charge-induced interactions and manipulations, and such subject has been studied in artificially deposited objects on thin insulating layers. We demonstrate that an entire layer of controllable atomic charges on a periodic lattice can be obtained by cleaving metallic Co_1/3NbS₂, an intercalated transition metal dichalcogenide. We identified a metastable charge state of Co with a different valence and manipulated atomic charges to form a linear chain of the metastable charge state. Density functional theory investigation reveals that the charge state is stable due to a modified crystal field at the surface despite the coupling between NbS₂ and Co via a_1g orbitals. The idea can be generalized to other combinations of intercalants and base matrices, suggesting that they can be a new platform to explore single-atom-operational 2D electronics/spintronics.

Surface anchoring as a control parameter for shaping skyrmion or toron properties in thin layers of chiral nematic liquid crystals and noncentrosymmetric magnets

Existence of topological localized states (skyrmions and torons) and the mechanism of their condensation into modulated states are the ruling principles of condensed matter systems, such as chiral nematic liquid crystals (CLCs) and chiral magnets (ChM). In bulk helimagnets, skyrmions are rendered into thermodynamically stable hexagonal skyrmion lattice due to the combined effect of a magnetic field and, e.g., small anisotropic contributions. In thin glass cells of CLCs, skyrmions are formed in response to the geometrical frustration and field coupling effects. By numerical modeling, I undertake a systematic study of skyrmion or toron properties in thin layers of CLCs and ChMs with competing surface-induced and bulk anisotropies. The conical phase with a variable polar angle serves as a suitable background, which shapes skyrmion internal structure, guides the nucleation processes, and substantializes the skyrmion-skyrmion interaction. I show that the hexagonal lattice of torons can be stabilized in a vast region of the constructed phase diagram for both easy-axis bulk and surface anisotropies. A topologically trivial droplet is shown to form as a domain boundary between two cone states with different rotational fashion, which underpins its stability. The findings provide a recipe for controllably creating skyrmions and torons, possessing the features on demand for potential applications.

Topological spin/structure couplings in layered chiral magnet Cr1/3TaS2: The discovery of spiral magnetic superstructure

Chiral magnets have recently emerged as hosts for topological spin textures and related transport phenomena, which can find use in next-generation spintronic devices. The coupling between structural chirality and noncollinear magnetism is crucial for the stabilization of complex spin structures such as magnetic skyrmions. Most studies have been focused on the physical properties in homochiral states favored by crystal growth and the absence of long-ranged interactions between domains of opposite chirality. Therefore, effects of the high density of chiral domains and domain boundaries on magnetic states have been rarely explored so far. Herein, we report layered heterochiral Cr_1/3TaS₂, exhibiting numerous chiral domains forming topological defects and a nanometer-scale helimagnetic order interlocked with the structural chirality. Tuning the chiral domain density, we discovered a macroscopic topological magnetic texture inside each chiral domain that has an appearance of a spiral magnetic superstructure composed of quasiperiodic Néel domain walls. The spirality of this object can have either sign and is decoupled from the structural chirality. In weak, in-plane magnetic fields, it transforms into a nonspiral array of concentric ring domains. Numerical simulations suggest that this magnetic superstructure is stabilized by strains in the heterochiral state favoring noncollinear spins. Our results unveil topological structure/spin couplings in a wide range of different length scales and highly tunable spin textures in heterochiral magnets.

Chirality-Induced Spin Polarization over Macroscopic Distances in Chiral Disilicide Crystals

A spin-polarized state is examined under charge current at room temperature without magnetic fields in chiral disilicide crystals NbSi_{2} and TaSi_{2}. We found that a long-range spin transport occurs over ten micrometers in these inorganic crystals. A distribution of crystalline grains of different handedness is obtained via location-sensitive electrical transport measurements. The sum rule holds in the conversion coefficient in the current-voltage characteristics. A diamagnetic nature of the crystals supports that the spin polarization is not due to localized electron spins but due to itinerant electron spins. A large difference in the strength of antisymmetric spin-orbit interaction associated with 4d electrons in Nb and 5d ones in Ta is oppositely correlated with that of the spin polarization. A robust protection of the spin polarization occurs over long distances in chiral crystals.

Field-tunable toroidal moment in a chiral-lattice magnet

Ferrotoroidal order, which represents a spontaneous arrangement of toroidal moments, has recently been found in a few linear magnetoelectric materials. However, tuning toroidal moments in these materials is challenging. Here, we report switching between ferritoroidal and ferrotoroidal phases by a small magnetic field, in a chiral triangular-lattice magnet BaCoSiO₄ with tri-spin vortices. Upon applying a magnetic field, we observe multi-stair metamagnetic transitions, characterized by equidistant steps in the net magnetic and toroidal moments. This highly unusual ferri-ferroic order appears to come as a result of an unusual hierarchy of frustrated isotropic exchange couplings revealed by first principle calculations, and the antisymmetric exchange interactions driven by the structural chirality. In contrast to the previously known toroidal materials identified via a linear magnetoelectric effect, BaCoSiO₄ is a qualitatively new multiferroic with an unusual coupling between several different orders, and opens up new avenues for realizing easily tunable toroidal orders.

Toroidal moments arise from vortex like spin arrangements. These moments can then interact, giving rise to ferri- or ferro-toroidal order, though controlling such order is difficult. Here, the authors demonstrate a ferri-toroidal state in BaCoSiO₄, which under an applied magnetic field exhibits multiple toroidal and metamagnetic transitions.

Chiral Helimagnetism and One-Dimensional Magnetic Solitons in a Cr-Intercalated Transition Metal Dichalcogenide

Chiral magnets endowed with topological spin textures are expected to have promising applications in next-generation magnetic memories. In contrast to the well-studied 2D or 3D magnetic skyrmions, the authors report the discovery of 1D nontrivial magnetic solitons in a transition metal dichalcogenide 2H-TaS₂ via precise intercalation of Cr elements. In the synthetic Cr_1/3 TaS₂ (CTS) single crystal, the coupling of the strong spin-orbit interaction from TaS₂ and the chiral arrangement of the magnetic Cr ions evoke a robust Dzyaloshinskii-Moriya interaction. A magnetic helix having a short spatial period of ≈25 nm is observed in CTS via Lorentz transmission electron microscopy. In a magnetic field perpendicular to the helical axis, the helical spin structure transforms into a chiral soliton lattice (CSL) with the spin structure evolution being consistent with the chiral sine-Gordon theory, which opens promising perspectives for the application of CSL to fast-speed nonvolatile magnetic memories. This work introduces a new paradigm to soliton physics and provides an effective strategy for seeking novel 2D magnets.

Tailoring Dzyaloshinskii-Moriya interaction in a transition metal dichalcogenide by dual-intercalation

Dzyaloshinskii-Moriya interaction (DMI) is vital to form various chiral spin textures, novel behaviors of magnons and permits their potential applications in energy-efficient spintronic devices. Here, we realize a sizable bulk DMI in a transition metal dichalcogenide (TMD) 2H-TaS₂ by intercalating Fe atoms, which form the chiral supercells with broken spatial inversion symmetry and also act as the source of magnetic orderings. Using a newly developed protonic gate technology, gate-controlled protons intercalation could further change the carrier density and intensely tune DMI via the Ruderman-Kittel-Kasuya-Yosida mechanism. The resultant giant topological Hall resistivity [Formula: see text] of [Formula: see text] at [Formula: see text] (about [Formula: see text] larger than the zero-bias value) is larger than most known chiral magnets. Theoretical analysis indicates that such a large topological Hall effect originates from the two-dimensional Bloch-type chiral spin textures stabilized by DMI, while the large anomalous Hall effect comes from the gapped Dirac nodal lines by spin-orbit interaction. Dual-intercalation in 2H-TaS₂ provides a model system to reveal the nature of DMI in the large family of TMDs and a promising way of gate tuning of DMI, which further enables an electrical control of the chiral spin textures and related electromagnetic phenomena.

Chirality Memory Stored in Magnetic Domain Walls in the Ferromagnetic State of MnP

Chirality in a helimagnetic structure is determined by the sense of magnetic moment rotation. We found that the chiral information did not disappear even after the phase transition to the high-temperature ferromagnetic phase in a helimagnet MnP. The 2nd harmonic resistivity ρ^{2f}, which reflects the breaking down of mirror symmetry, was found to be almost unchanged after heating the sample above the ferromagnetic transition temperature and cooling it back to the helimagnetic state. The application of a magnetic field along the easy axis in the ferromagnetic state quenched the chirality-induced ρ^{2f}. This indicates that the chirality memory effect originated from the ferromagnetic domain walls.

Recent Advances in 2D Group VB Transition Metal Chalcogenides

2D materials have received considerable research interest owing to their abundant material systems and remarkable properties. Among them, 2D group VB transition metal chalcogenides (GVTMCs) stand out as emerging 2D metallic materials and significantly broaden the research scope of 2D materials. 2D GVTMCs have great advantages in electrical transport, 2D magnetism, charge density wave, sensing, catalysis, and charge storage, making them attractive in the fields of functional devices and energy chemistry. In this review, the recent progress of 2D GVTMCs is summarized systematically from fundamental properties, growth methodologies to potential applications. The challenges and prospects are also discussed for future research in this field.

Annihilation and Control of Chiral Domain Walls with Magnetic Fields

The control of domain walls is central to nearly all magnetic technologies, particularly for information storage and spintronics. Creative attempts to increase storage density need to overcome volatility due to thermal fluctuations of nanoscopic domains and heating limitations. Topological defects, such as solitons, skyrmions, and merons, may be much less susceptible to fluctuations, owing to topological constraints, while also being controllable with low current densities. Here, we present the first evidence for soliton/soliton and soliton/antisoliton domain walls in the hexagonal chiral magnet Mn_1/3NbS₂ that respond asymmetrically to magnetic fields and exhibit pair-annihilation. This is important because it suggests the possibility of controlling the occurrence of soliton pairs and the use of small fields or small currents to control nanoscopic magnetic domains. Specifically, our data suggest that either soliton/soliton or soliton/antisoliton pairs can be stabilized by tuning the balance between intrinsic exchange interactions and long-range magnetostatics in restricted geometries.

Recent advances in small-angle electron diffraction and Lorentz microscopy

We describe small-angle electron diffraction (SmAED) and Lorentz microscopy using a conventional transmission electron microscope. In SmAED, electron diffraction patterns with a wide-angular range on the order of 1 × 10-2 rad to 1 × 10-7 rad can be obtained. It is demonstrated that magnetic information of nanoscale magnetic microstructures can be obtained by Fresnel imaging, Foucault imaging and SmAED. In particular, we report magnetic microstructures associated with magnetic stripes and magnetic skyrmions revealed by Lorentz microscopy with SmAED. SmAED can be applied to the analysis of microstructures in functional materials such as dielectric, ferromagnetic and multiferroic materials.

Excitations of Intercalated Metal Monolayers in Transition Metal Dichalcogenides

We combine Raman scattering spectroscopy and lattice dynamics calculations to reveal the fundamental excitations of the intercalated metal monolayers in the Fe_xTaS₂ (x = 1/4, 1/3) family of materials. Both in- and out-of-plane modes are identified, each of which has trends that depend upon the metal-metal distance, the size of the van der Waals gap, and the metal-to-chalcogenide slab mass ratio. We test these trends against the response of similar systems, including Cr-intercalated NbS₂ and RbFe(SO₄)₂, and demonstrate that the metal monolayer excitations are both coherent and tunable. We discuss the consequences of intercalated metal monolayer excitations for material properties and developing applications.

Multicritical Deconfined Quantum Criticality and Lifshitz Point of a Helical Valence-Bond Phase

The S=1/2 square-lattice J-Q model hosts a deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states. We here study two deformations of this model-a term projecting staggered singlets, as well as a modulation of the J terms forming alternating "staircases" of strong and weak couplings. The first deformation preserves all lattice symmetries. Using quantum Monte Carlo simulations, we show that it nevertheless introduces a second relevant field, likely by producing topological defects. The second deformation induces helical valence-bond order. Thus, we identify the deconfined quantum critical point as a multicritical Lifshitz point-the end point of the helical phase and also the end point of a line of first-order transitions. The helical-antiferromagnetic transitions form a line of generic deconfined quantum-critical points. These findings extend the scope of deconfined quantum criticality and resolve a previously inconsistent critical-exponent bound from the conformal-bootstrap method.

Dynamics of chiral solitons driven by polarized currents in monoaxial helimagnets

Chiral solitons are one dimensional localized magnetic structures that are metastable in some ferromagnetic systems with Dzyaloshinskii–Moriya interactions and/or uniaxial magnetic anisotropy. Though topological textures in general provide a very interesting playground for new spintronics phenomena, how to properly create and control single chiral solitons is still unclear. We show here that chiral solitons in monoaxial helimagnets, characterized by a uniaxial Dzyaloshinskii–Moriya interaction, can be stabilized with external magnetic fields. Once created, the soliton moves steadily in response to a polarized electric current, provided the induced spin-transfer torque has a dissipative (nonadiabatic) component. The structure of the soliton depends on the applied current density in such a way that steady motion exists only if the applied current density is lower than a critical value, beyond which the soliton is no longer stable.

Topological metastability supported by thermal fluctuation upon formation of chiral soliton lattice in [Formula: see text]

Topological magnetic structure possesses topological stability characteristics that make it robust against disturbances which are a big advantage for data processing or storage devices of spintronics; nonetheless, such characteristics have been rarely clarified. This paper focused on the formation of chiral soliton lattice (CSL), a one-dimensional topological magnetic structure, and provides a discussion of its topological stability and influence of thermal fluctuation. Herein, CSL responses against change of temperature and applied magnetic field were investigated via small-angle resonant soft X-ray scattering in chromium niobium sulfide ([Formula: see text]). CSL transformation relative to the applied magnetic field demonstrated a clear agreement with the theoretical prediction of the sine-Gordon model. Further, there were apparent differences in the process of chiral soliton creation and annihilation, discussed from the viewpoint of competing between thermal fluctuation and the topological metastability.

Scaling of the magnetic entropy change in chiral helimagnetic YbNi3Al9

Generally, magnetic anisotropy is a common feature of a layered magnetic material, the exploration of which plays a key role in understanding the intrinsic magnetic couplings. In this work, we have studied the field-induced magnetic transitions for layered YbNi₃Al₉ as the external magnetic field is applied perpendicularly ([Formula: see text]) and parallel (H//c) to the c-axis. We find that two independent universal curves of magnetic entropy change [[Formula: see text]] can be fitted out for [Formula: see text] and H//c, respectively. According to the universality principle of scaling, the extra magnetic entropy changes ([Formula: see text] and [Formula: see text]) caused by the field-induced magnetic phase transitions can be obtained for [Formula: see text] and H//c. The two-dimensional [Formula: see text] plots as functions of field and temperature are constructed, which clearly reveal the evolutions of the magnetic entropy changes resulted from the two different field-induced magnetic phase transitions. It is suggested that the [Formula: see text] for [Formula: see text] with the maximum at (3.2 K, 4.1 kOe) originates from a field-modulated helicoidal spin-texture. However, the [Formula: see text] for H//c with the maximum at (3.4 K, 13.8 kOe) stems from a field-induced canted antiferromagnetic state.

Chirality-Induced Spin-Polarized State of a Chiral Crystal CrNb_{3}S_{6}

Chirality-induced spin transport phenomena are investigated at room temperature without magnetic fields in a monoaxial chiral dichalcogenide CrNb_{3}S_{6}. We found that spin polarization occurs in these chiral bulk crystals under a charge current flowing along the principal c axis. Such phenomena are detected as an inverse spin Hall signal which is induced on the detection electrode that absorbs polarized spin from the chiral crystal. The inverse response is observed when applying the charge current into the detection electrode. The signal sign reverses in the device with the opposite chirality. Furthermore, the spin signals are found over micrometer length scales in a nonlocal configuration. Such a robust generation and protection of the spin-polarized state is discussed based on a one-dimensional model with an antisymmetric spin-orbit coupling.

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.

Electrical switching in a magnetically intercalated transition metal dichalcogenide

Advances in controlling the correlated behaviour of transition metal dichalcogenides have opened a new frontier of many-body physics in two dimensions. A field where these materials have yet to make a deep impact is antiferromagnetic spintronics-a relatively new research direction promising technologies with fast switching times, insensitivity to magnetic perturbations and reduced cross-talk^1-3. Here, we present measurements on the intercalated transition metal dichalcogenide Fe_1/3NbS₂ that exhibits antiferromagnetic ordering below 42 K (refs. ^4,5). We find that remarkably low current densities of the order of 10⁴ A cm^-2 can reorient the magnetic order, which can be detected through changes in the sample resistance, demonstrating its use as an electronically accessible antiferromagnetic switch. Fe_1/3NbS₂ is part of a larger family of magnetically intercalated transition metal dichalcogenides, some of which may exhibit switching at room temperature, forming a platform from which to build tuneable antiferromagnetic spintronic devices^6,7.

MnSnTeO6: A Chiral Antiferromagnet Prepared by a Two-Step Topotactic Transformation

MnSnTeO₆, a new chiral antiferromagnet, was prepared both by topotactic transformation of the metastable rosiaite-type polymorph and by direct synthesis from coprecipitated hydroxides. Its structure and its static and dynamic magnetic properties were studied comprehensively both experimentally (through X-ray and neutron powder diffraction, magnetization, specific heat, dielectric permittivity, and ESR techniques) and theoretically (by means of ab initio density functional theory (DFT) calculations within the spin-polarized generalized gradient approximation). MnSnTeO₆ is isostructural with MnSb₂O₆ (space group P321) and does not show any structural transition between 3 and 300 K. The magnetic susceptibility and specific heat exhibit an antiferromagnetic ordering at T_N ≈ 9.8 K, which is confirmed by low-temperature neutron data. At the same time, the thermodynamic parameters demonstrate an additional anomaly on the temperature dependences of magnetic susceptibility χ(T), specific heat C_p(T) and dielectric permittivity ε(T) at T* ≈ 4.9 K, which is characterized by significant temperature hysteresis. Clear enhancement of the dielectric permittivity at T* is most likely to reflect the coupling of dielectric and magnetic subsystems leading to development of electric polarization. It was established that the ground state of MnSnTeO₆ is stabilized by seven exchange parameters, and neutron diffraction revealed incommensurate magnetic structure with propagation vector k = (0, 0, 0.183) analogous to that of MnSb₂O₆. Ab initio DFT calculations demonstrate that the strongest exchange coupling occurs between planes along diagonals. All exchange parameters are antiferromagnetic and reveal moderate frustration.

Recent Advances in Two-Dimensional Magnets: Physics and Devices towards Spintronic Applications

The emergence of low-dimensional nanomaterials has brought revolutionized development of magnetism, as the size effect can significantly influence the spin arrangement. Since the first demonstration of truly two-dimensional magnetic materials (2DMMs) in 2017, a wide variety of magnetic phases and associated properties have been exhibited in these 2DMMs, which offer a new opportunity to manipulate the spin-based devices efficiently in the future. Herein, we focus on the recent progress of 2DMMs and heterostructures in the aspects of their structural characteristics, physical properties, and spintronic applications. Firstly, the microscopy characterization of the spatial arrangement of spins in 2D lattices is reviewed. Afterwards, the optical probes in the light-matter-spin interactions at the 2D scale are discussed. Then, particularly, we systematically summarize the recent work on the electronic and spintronic devices of 2DMMs. In the section of electronic properties, we raise several exciting phenomena in 2DMMs, i.e., long-distance magnon transport, field-effect transistors, varying magnetoresistance behavior, and (quantum) anomalous Hall effect. In the section of spintronic applications, we highlight spintronic devices based on 2DMMs, e.g., spin valves, spin-orbit torque, spin field-effect transistors, spin tunneling field-effect transistors, and spin-filter magnetic tunnel junctions. At last, we also provide our perspectives on the current challenges and future expectations in this field, which may be a helpful guide for theorists and experimentalists who are exploring the optical, electronic, and spintronic properties of 2DMMs.

Programmable and robust static topological solitons in mechanical metamaterials

Solitary, persistent wave packets called solitons hold potential to transfer information and energy across a wide range of spatial and temporal scales in physical, chemical, and biological systems. Mechanical solitons characteristically emerge either as a single wave packet or uncorrelated propagating topological entities through space and/or time, but these are notoriously difficult to control. Here, we report a theoretical framework for programming static periodic topological solitons into a metamaterial, and demonstrate its implementation in real metamaterials computationally and experimentally. The solitons are excited by deformation localizations under quasi-static compression, and arise from buckling-induced kink-antikink bands that provide domain separation barriers. The soliton number and wavelength demonstrate a previously unreported size-dependence, due to intrinsic length scales. We identify that these unanticipated solitons stem from displacive phase transitions with periodic topological excitations captured by the well-known [Formula: see text] theory. Results reveal pathways for robust regularizations of stochastic responses of metamaterials.

Spiral spin structures and skyrmions in multiferroics

In this article, we focus on (1) type-II multiferroics driven by spiral spin orderings and (2) magnetoelectric couplings in multiferroic skyrmion-hosting materials. We present both phenomenological understanding and microscopic mechanisms for spiral spin state, which is one of the essential starting points for type-II multiferroics and magnetic skyrmions. Two distinct mechanisms of spiral spin states (frustration and Dzyaloshinskii–Moriya [DM] interaction) are discussed in the context of the lattice symmetry. We also discuss the spin-induced ferroelectricity on the basis of the symmetry and microscopic atomic configurations. We compare two well-known microscopic models: the generalized inverse DM mechanism and the metal-ligand d-p hybridization mechanism. As a test for these models, we summarize the multiferroic properties of a family of triangular-lattice antiferromagnets. We also give a brief review of the magnetic skyrmions. Three types of known skyrmion-hosting materials with multiferroicity are discussed from the view point of crystal structure, magnetism, and origins of the magnetoelectric couplings. For exploration of new skyrmion-hosting materials, we also discuss the theoretical models for stabilizing skyrmions by magnetic frustration in centrosymmetric system. Several basic ideas for material design are given, which are successfully demonstrated by the recent experimental evidences for the skyrmion formation in centrosymmetric frustrated magnets.

Critical phenomenon and phase diagram of Mn-intercalated layered MnNb3S6

The magnetization of Mn-intercalated layered MnNb₃S₆ single crystal has been systematically investigated. The angle-dependent magnetization ([Formula: see text], [Formula: see text], and [Formula: see text]) displays that the magnetization of MnNb₃S₆ with [Formula: see text] is much stronger than that with H//c, but no magnetic anisotropy within the ab-plane. In addition, a field-induced magnetic phase transition is found when [Formula: see text]. The investigation of the critical behavior gives the critical exponents [Formula: see text], [Formula: see text], and [Formula: see text] with [Formula: see text] K, which belong to the universality class of three-dimensional Heisenberg model. The critical behavior and exponents indicate that the magnetic coupling in MnNb₃S₆ is of an isotropic short-range type. Based on universality scaling, the H  -  T phase diagram with [Formula: see text] is constructed. The magnetic behaviors and phase diagram of MnNb₃S₆ are analogous to those of CrNb₃S₆ which exhibits a chiral magnetic soliton lattice.

Anomalous Nonreciprocal Electrical Transport on Chiral Magnetic Order

Nonreciprocal flow of conduction electrons is systematically investigated in a monoaxial chiral helimagnet CrNb_{3}S_{6}. We found that such directional dichroism of the electrical transport phenomena, called the electrical magnetochiral (EMC) effect, occurs in a wide range of magnetic fields and temperatures. The EMC signal turns out to be considerably enhanced below the magnetic ordering temperature, suggesting a strong influence of the chiral magnetic order on this anomalous EMC transport property. The EMC coefficients are separately evaluated in terms of crystalline and magnetic contributions in the magnetic phase diagram.

Anomalous Temperature Behavior of the Chiral Spin Helix in CrNb_{3}S_{6} Thin Lamellae

Using Lorentz transmission electron microscopy and small-angle electron scattering techniques, we investigate the temperature-dependent evolution of a magnetic stripe pattern period in thin-film lamellae of the prototype monoaxial chiral helimagnet CrNb_{3}S_{6}. The sinusoidal stripe pattern appears due to formation of a chiral helimagnetic order (CHM) in this material. We found that as the temperature increases, the CHM period is initially independent of temperature and then starts to shrink above the temperature of about 90 K, which is far below the magnetic phase transition temperature for the bulk material T_{c} (123 K). The stripe order disappears at around 140 K, far above T_{c}. We argue that this cascade of transitions reflects a three-stage hierarchical behavior of melting in two dimensions.

Electronic and magnetic properties of the 2H-NbS2 intercalated by 3d transition metal atoms

The electronic structure and magnetic properties of the compound 2H-NbS2 intercalated by 3d elements from Cr to Ni, have been investigated using the Korringa–Kohn–Rostoker electronic structure method. Here, we consider the phases with 33% of intercalation within the ordered phase having a 3 × 3 $\sqrt 3 \times \sqrt 3 $ arrangement of the magnetic atoms. We analyze the relationship of the magnetic and electronic properties on the structural parameters dependent on the intercalant. The exchange coupling parameters calculated from first principles have been used for subsequent Monte Carlo simulations. Within these investigations, the FM order was found for the Cr and Mn intercalated phases as ground state configuration with a Curie temperature being in good agreement with the experiment. According to the Monte Carlo simulation, Fe1/3NbS2 has a complicated noncollinear magnetic structure with a noncompensated total magnetic moment, whereas Co1/3NbS2 and Ni1/3NbS2 are found to be antiferromagnetic, all in line with experimental observations.

A majority gate with chiral magnetic solitons

In magnetic materials, nontrivial spin textures may emerge due to the competition among different types of magnetic interactions. Among such spin textures, chiral magnetic solitons represent topologically protected spin configurations with particle-like properties. Based on atomistic spin dynamics simulations, we demonstrate that these chiral magnetic solitons are ideal to use for logical operations, and we demonstrate the functionality of a three-input majority gate, in which the input states can be controlled by applying an external electromagnetic field or spin-polarized currents. One of the main advantages of the proposed device is that the input and output signals are encoded in the chirality of solitons, that may be moved, allowing to perform logical operations using only minute electric currents. As an example we illustrate how the three input majority gate can be used to perform logical relations, such as Boolean AND and OR.

New magnetic phase of the chiral skyrmion material Cu2OSeO3

The lack of inversion symmetry in the crystal lattice of magnetic materials gives rise to complex noncollinear spin orders through interactions of a relativistic nature, resulting in interesting physical phenomena, such as emergent electromagnetism. Studies of cubic chiral magnets revealed a universal magnetic phase diagram composed of helical spiral, conical spiral, and skyrmion crystal phases. We report a remarkable deviation from this universal behavior. By combining neutron diffraction with magnetization measurements, we observe a new multidomain state in Cu2OSeO3. Just below the upper critical field at which the conical spiral state disappears, the spiral wave vector rotates away from the magnetic field direction. This transition gives rise to large magnetic fluctuations. We clarify the physical origin of the new state and discuss its multiferroic properties.