Large anisotropic deformation of skyrmions in strained crystal

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

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

Role of isotropic and anisotropic Dzyaloshinskii-Moriya interaction on skyrmions, merons and antiskyrmions in theCnvsymmetric system

The lattice Hamiltonian with the presence of a chiral magnetic isotropic Dzyaloshinskii-Moriya interaction (DMI) in a square and hexagonal lattice is numerically solved to give the full phase diagram consisting of skyrmions and merons in different parameter planes. The phase diagram provides the actual regions of analytically unresolved asymmetric skyrmions and merons, and it is found that these regions are substantially larger than those of symmetric skyrmions and merons. With magnetic field, a change from meron or spin spiral (SS) to skyrmion is seen. The complete phase diagram for theCnvsymmetric system with anisotropic DMI is drawn and it is shown that this DMI helps to change the SS propagation direction. Finally, the well-defined region of a thermodynamically stable antiskyrmion phase in theCnvsymmetric system is shown.

Raman Shifts in Two-Dimensional van der Waals Magnets Reveal Magnetic Texture Evolution

Two-dimensional (2D) van der Waals magnets comprise rich physics that can be exploited for spintronic applications. We investigate the interplay between spin-phonon coupling and spin textures in a 2D van der Waals magnet by combining magneto-Raman spectroscopy with cryogenic Lorentz transmission electron microscopy. We find that when stable skyrmion bubbles are formed in the 2D magnet, a field-dependent Raman shift can be observed, and this shift is absent for the 2D magnet prepared in its ferromagnetic state. Correlating these observations with numerical simulations that take into account field-dependent magnetic textures and spin--phonon coupling in the 2D magnet, we associate the Raman shift to field-induced modulations of the skyrmion bubbles and derive the existence of inhomogeneity in the skyrmion textures over the film thickness.

Strain-Induced Reversible Motion of Skyrmions at Room Temperature

Magnetic skyrmions are topologically protected swirling spin textures with great potential for future spintronic applications. The ability to induce skyrmion motion using mechanical strain not only stimulates the exploration of exotic physics but also affords the opportunity to develop energy-efficient spintronic devices. However, the experimental realization of strain-driven skyrmion motion remains a formidable challenge. Herein, we demonstrate that the inhomogeneous uniaxial compressive strain can induce the movement of isolated skyrmions from regions of high strain to regions of low strain at room temperature, which was directly observed using an in situ Lorentz transmission electron microscope with a specially designed nanoindentation holder. We discover that the uniaxial compressive strain can transform skyrmions into a single domain with in-plane magnetization, resulting in the coexistence of skyrmions with a single domain along the direction of the strain gradient. Through comprehensive micromagnetic simulations, we reveal that the repulsive interactions between skyrmions and the single domain serve as the driving force behind the skyrmion motion. The precise control of skyrmion motion through strain provides exciting opportunities for designing advanced spintronic devices that leverage the intricate interplay between strain and magnetism.

High-density, spontaneous magnetic biskyrmions induced by negative thermal expansion in ferrimagnets

Magnetic skyrmions are topologically protected quasiparticles that are promising for applications in spintronics. However, the low stability of most magnetic skyrmions leads to either a narrow temperature range in which they can exist, a low density of skyrmions, or the need for an external magnetic field, which greatly limits their wide application. In this study, high-density, spontaneous magnetic biskyrmions existing within a wide temperature range and without the need for a magnetic field were formed in ferrimagnets owing to the existence of a negative thermal expansion of the lattice. Moreover, a strong connection between the atomic-scale ferrimagnetic structure and nanoscale magnetic domains in Ho(Co,Fe)3 was revealed via in situ neutron powder diffraction and Lorentz transmission electron microscopy measurements. The critical role of the negative thermal expansion in generating biskyrmions in HoCo3 based on the magnetoelastic coupling effect is further demonstrated by comparing the behavior of HoCo2.8Fe0.2 with a positive thermal expansion.

Strain-Control of Cycloidal Spin Order in a Metallic Van der Waals Magnet

The manipulation of magnetism through strain control is a captivating area of research with potential applications for low-power devices that do not require dissipative currents. Recent investigations of insulating multiferroics have unveiled tunable relationships among polar lattice distortions, Dzyaloshinskii-Moriya interactions (DMI), and cycloidal spin orders that break inversion symmetry. These findings have raised the possibility of utilizing strain or strain gradient to manipulate intricate magnetic states by changing polarization. However, the effectiveness of manipulating cycloidal spin orders in "metallic" materials with screened magnetism-relevant electric polarization remains uncertain. In this study, the reversible strain control of cycloidal spin textures in a metallic van der Waals magnet, Cr1/3 TaS2 , through the modulation of polarization and DMI induced by strain is demonstrated. With thermally-induced biaxial strains and isothermally-applied uniaxial strains, systematic manipulation of the sign and wavelength of the cycloidal spin textures is realized, respectively. Additionally, unprecedented reflectivity reduction under strain and domain modification at a record-low current density are also discovered. These findings establish a connection between polarization and cycloidal spins in metallic materials and present a new avenue for utilizing the remarkable tunability of cycloidal magnetic textures and optical functionality in van der Waals metals with strain.

Stabilization and racetrack application of asymmetric Néel skyrmions in hybrid nanostructures

Magnetic skyrmions, topological quasiparticles, are small stable magnetic textures that possess intriguing properties and potential for data storage applications. Hybrid nanostructures comprised of skyrmions and soft magnetic material can offer additional advantages for developing skyrmion-based spintronic and magnonic devices. We show that a Néel-type skyrmion confined within a nanodot placed on top of a ferromagnetic in-plane magnetized stripe produces a unique and compelling platform for exploring the mutual coupling between magnetization textures. The skyrmion induces an imprint upon the stripe, which, in turn, asymmetrically squeezes the skyrmion in the dot, increasing their size and the range of skyrmion stability at small values of Dzyaloshinskii-Moriya interaction, as well as introducing skyrmion bi-stability. Finally, by exploiting the properties of the skyrmion in a hybrid system, we demonstrate unlimited skyrmion transport along a racetrack, free of the skyrmion Hall effect.

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.

Light-Induced Metastable Hidden Skyrmion Phase in the Mott Insulator Cu2 OSeO3

The discovery of a novel long-lived metastable skyrmion phase in the multiferroic insulator Cu2 OSeO3 visualized with Lorentz transmission electron microscopy for magnetic fields below the equilibrium skyrmion pocket is reported. This phase can be accessed by exciting the sample non-adiabatically with near-infrared femtosecond laser pulses and cannot be reached by any conventional field-cooling protocol, referred as a hidden phase. From the strong wavelength dependence of the photocreation process and via spin-dynamics simulations, the magnetoelastic effect is identified as the most likely photocreation mechanism. This effect results in a transient modification of the magnetic free energy landscape extending the equilibrium skyrmion pocket to lower magnetic fields. The evolution of the photoinduced phase is monitored for over 15 min and no decay is found. Because such a time is much longer than the duration of any transient effect induced by a laser pulse in a material, it is assumed that the newly discovered skyrmion state is stable for practical purposes, thus breaking ground for a novel approach to control magnetic state on demand at ultrafast timescales and drastically reducing heat dissipation relevant for next-generation spintronic devices.

Direct observation of tensile-strain-induced nanoscale magnetic hardening

Magnetoelasticity is the bond between magnetism and mechanics, but the intricate mechanisms via which magnetic states change due to mechanical strain remain poorly understood. Here, we provide direct nanoscale observations of how tensile strain modifies magnetic domains in a ferromagnetic Ni thin plate using in situ Fresnel defocus imaging, off-axis electron holography and a bimetallic deformation device. We present quantitative measurements of magnetic domain wall structure and its transformations as a function of strain. We observe the formation and dissociation of strain-induced periodic 180° magnetic domain walls perpendicular to the strain axis. The magnetization transformation exhibits stress-determined directional sensitivity and is reversible and tunable through the size of the nanostructure. In this work, we provide direct evidence for expressive and deterministic magnetic hardening in ferromagnetic nanostructures, while our experimental approach allows quantifiable local measurements of strain-induced changes in the magnetic states of nanomaterials.

Nonreciprocal Phonon Propagation in a Metallic Chiral Magnet

The phonon magnetochiral effect (MChE) is the nonreciprocal acoustic and thermal transports of phonons caused by the simultaneous breaking of the mirror and time-reversal symmetries. So far, the phonon MChE has been observed only in a ferrimagnetic insulator Cu_{2}OSeO_{3}, where the nonreciprocal response disappears above the Curie temperature of 58 K. Here, we study the nonreciprocal acoustic properties of a room-temperature ferromagnet Co_{9}Zn_{9}Mn_{2} for unveiling the phonon MChE close to room temperature. Surprisingly, the nonreciprocity in this metallic compound is enhanced at higher temperatures and observed up to 250 K. This clear contrast between insulating Cu_{2}OSeO_{3} and metallic Co_{9}Zn_{9}Mn_{2} suggests that metallic magnets have a mechanism to enhance the nonreciprocity at higher temperatures. From the ultrasound and microwave-spectroscopy experiments, we conclude that the magnitude of the phonon MChE of Co_{9}Zn_{9}Mn_{2} mostly depends on the Gilbert damping, which increases at low temperatures and hinders the magnon-phonon hybridization. Our results suggest that the phonon nonreciprocity could be further enhanced by engineering the magnon band of materials.

Lorentz electron ptychography for imaging magnetic textures beyond the diffraction limit

Nanoscale spin textures, especially magnetic skyrmions, have attracted intense interest as candidate high-density and power-efficient information carriers for spintronic devices^1,2. Facilitating a deeper understanding of sub-hundred-nanometre to atomic-scale spin textures requires more advanced magnetic imaging techniques^3-5. Here we demonstrate a Lorentz electron ptychography method that can enable high-resolution, high-sensitivity magnetic field imaging for widely available electron microscopes. The resolution of Lorentz electron ptychography is not limited by the usual diffraction limit of lens optics, but instead is determined by the maximum scattering angle at which a statistically meaningful dose can still be recorded-this can be an improvement of up to 2-6 times depending on the allowable dose. Using FeGe as the model system, we realize a more accurate magnetic field measurement of skyrmions with an improved spatial resolution and sensitivity by also correcting the probe-damping effect from the imaging optics via Lorentz electron ptychography. This allows us to directly resolve subtle internal structures of magnetic skyrmions near the skyrmion cores, boundaries and dislocations in an FeGe single crystal. Our study establishes a quantitative, high-resolution magnetic microscopy technique that can reveal nanoscale spin textures, especially magnetization discontinuities and topological defects in nanomagnets⁶. The technique's high-dose efficiency should also make it well suited for the exploration of magnetic textures in electron radiation-sensitive materials such as organic or molecular magnets⁷.

Confinement of Skyrmions in Nanoscale FeGe Device-like Structures

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

The impacts of molecular adsorption on antiferromagnetic MnPS3 monolayers: enhanced magnetic anisotropy and intralayer Dzyaloshinskii-Moriya interaction

In two-dimensional (2D) magnetic systems, significant magnetic anisotropy is required to protect magnetic ordering against thermal fluctuation. In this paper, we explored the effect of molecular adsorption on the magnetic anisotropy and intralayer Dzyaloshinskii-Moriya interaction (DMI) of monolayer MnPS₃, combining the first-principles calculation and theoretical analysis. We find that molecular adsorption can break the spatial inversion symmetry in a 2D magnet, and results in a significant DMI, which is rare in pristine 2D magnets. For example, in an MPS-NO system, the magnitude of the asymmetric DMI vector increases 9 times, and the magnetocrystalline anisotropy increases 600 times compared with the pristine MPS monolayer. It is found the DMI mainly comes from the structural deformation after adsorption, whereas the increase of magnetocrystalline anisotropy mainly originates from a new 'bridge' super-exchange interaction between Mn ions and NO gas molecules. The calculated Mn-NO-Mn 'bridge' super-exchange coupling strength is much higher than the Mn-S-Mn coupling strength. Our findings offer a new strategy to increase the magnetic anisotropy and induce chiral magnetic structures in 2D magnets.

Emergent elastic fields induced by topological phase transitions: Impact of molecular chirality and steric anisotropy

SignificanceChirality, the property of an object that cannot be superimposed on its mirror image, plays an essential role in condensed matter, such as magnetic, electronic, and liquid crystal systems. Topological phases emerge in such chiral materials, wherein helical and vortex-like structures-called skyrmions-are observed. However, the role of elastic fields in these topological phases remains unexplored. Here, we construct a molecular model of two-dimensional crystals incorporating steric anisotropy and chiral interactions to elucidate this problem. The coupling between the elastic fields and phase transitions between uniform, helical, and half-skyrmion phases can be utilized to switch these topological phases by external forces. Our results provide a fundamental physical principle for designing topological materials using chiral molecular and colloidal crystals.

Atomically sharp domain walls in an antiferromagnet

The interest in understanding scaling limits of magnetic textures such as domain walls spans the entire field of magnetism from its physical fundamentals to applications in information technologies. Here, we explore antiferromagnetic CuMnAs in which imaging by x-ray photoemission reveals the presence of magnetic textures down to nanoscale, reaching the detection limit of this established microscopy in antiferromagnets. We achieve atomic resolution by using differential phase-contrast imaging within aberration-corrected scanning transmission electron microscopy. We identify abrupt domain walls in the antiferromagnetic film corresponding to the Néel order reversal between two neighboring atomic planes. Our work stimulates research of magnetic textures at the ultimate atomic scale and sheds light on electrical and ultrafast optical antiferromagnetic devices with magnetic field-insensitive neuromorphic functionalities.

Giant tunable spin Hall angle in sputtered Bi2Se3 controlled by an electric field

Finding an effective way to greatly tune spin Hall angle in a low power manner is of fundamental importance for tunable and energy-efficient spintronic devices. Recently, topological insulator of Bi₂Se₃, having a large intrinsic spin Hall angle, show great capability to generate strong current-induced spin-orbit torques. Here we demonstrate that the spin Hall angle in Bi₂Se₃ can be effectively tuned asymmetrically and even enhanced about 600% reversibly by applying a bipolar electric field across the piezoelectric substrate. We reveal that the enhancement of spin Hall angle originates from both the charge doping and piezoelectric strain effet on the spin Berry curvature near Fermi level in Bi₂Se₃. Our findings provide a platform for achieving low power consumption and tunable spintronic devices.

Controlling the spin Hall angle is significant to tunable and energy-efficient spintronic devices. Here, the authors demonstrate that the spin Hall angle in Bi₂Se₃ can be tuned and even enhanced about 600% reversibly by the electric field.

Tuning the size of skyrmion by strain at the Co/Pt3 Interfaces

Based on density functional theory calculations, we elucidated the tunability of the atomic structures and magnetic interactions of Co/Pt₃ interface (one layer of hcp(0001) Co and three layers of fcc(111) Pt) and thus the skyrmion sizes using strain. The dispersion relations of the spin spiral in the opposite directions, E(q) and E(-q), were evaluated based on generalized Bloch equations. Effective exchange coupling (EC) and Dzyaloshinsky-Moriya interaction (DMI) parameters between different neighbors J_i and d_i at different lattice constants were derived by fitting the resulting spin spiral dispersion E(q) to EC model with DMI and E(q)-E(-q) formula, respectively. We observed an increase in DMI and a significant decrease in EC with an increase in strain. Hence, the size of Néel-type skyrmions determined by the ratio of EC/DMI can be controlled by applying strain, leading to an effective approach to tailor the formation of skyrmion lattices by inducing slight structural modifications on the magnetic thin films.

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Calculate the EC and DMI of multi-nearest neighbors in the VASP program

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Show detailed changes of multi-nearest neighboring EC and DMI with deformation

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The size of skyrmion does decrease as the lattice constant increases

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Distance between Co and Pt layer determines the size of DMI

Doping Control of Magnetic Anisotropy for Stable Antiskyrmion Formation in Schreibersite (Fe,Ni)3 P with S4 symmetry

Magnetic skyrmions, vortex-like topological spin textures, have attracted much interest in a wide range of research fields from fundamental physics to spintronics applications. Recently, growing attention is also paid to antiskyrmions emerging with opposite topological charge in non-centrosymmetric magnets with D_2d or S₄ symmetry. In these magnets, complex interplay among anisotropic Dzyaloshinskii-Moriya interaction, uniaxial magnetic anisotropy, and magnetic dipolar interactions generates various magnetic textures. However, the precise role of these magnetic interactions in stabilizing antiskyrmions remains to be elucidated. In this work, the uniaxial magnetic anisotropy of schreibersite (Fe,Ni)₃ P with S₄ symmetry is controlled by doping and its impact on the stability of antiskyrmions is investigated. The authors' magnetometry study, supported by ferromagnetic resonance spectroscopy, shows that the variation of the Ni content and slight doping with 4d transition metals considerably change the magnetic anisotropy. In particular, doping with Pd induces easy-axis anisotropy, giving rise to formation of antiskyrmions, while a temperature-induced spin reorientation is observed in an Rh-doped compound. In combination with Lorentz transmission electron microscopy and micromagnetic simulations, the stability of antiskyrmion as functions of uniaxial anisotropy and demagnetization energy is quantitatively analyzed, and demonstrated that subtle balance between them is necessary to stabilize the antiskyrmions.

Strain-Driven Dzyaloshinskii-Moriya Interaction for Room-Temperature Magnetic Skyrmions

Dzyaloshinskii-Moriya interaction in magnets, which is usually derived from inversion symmetry breaking at interfaces or in noncentrosymmetric crystals, plays a vital role in chiral spintronics. Here we report that an emergent Dzyaloshinskii-Moriya interaction can be achieved in a centrosymmetric material, La_{0.67}Sr_{0.33}MnO_{3}, by a graded strain. This strain-driven Dzyaloshinskii-Moriya interaction not only exhibits distinctive two coexisting nonreciprocities of spin-wave propagation in one system, but also brings about a robust room-temperature magnetic skyrmion lattice as well as a spiral lattice at zero magnetic field. Our results demonstrate the feasibility of investigating chiral spintronics in a large category of centrosymmetric magnetic materials.

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.

Nano-to-micro spatiotemporal imaging of magnetic skyrmion's life cycle

Magnetic skyrmions are self-organized topological spin textures that behave like particles. Because of their fast creation and typically long lifetime, experimental verification of skyrmion's creation/annihilation processes has been challenging. Here, we successfully track skyrmion dynamics in defect-introduced Co₉Zn₉Mn₂ by using pump-probe Lorentz transmission electron microscope. Following the nanosecond photothermal excitation, we resolve 160-nm skyrmion's proliferation at <1 ns, contraction at 5 ns, drift from 10 ns to 4 μs, and coalescence at ~5 μs. These motions relay the multiscale arrangement and relaxation of skyrmion clusters in a repeatable cycle of 20 kHz. Such repeatable dynamics of skyrmions, arising from the weakened but still persistent topological protection around defects, enables us to visualize the whole life of the skyrmions and demonstrates the possible high-frequency manipulations of topological charges brought by skyrmions.

Magnetic Skyrmion Materials

Skyrmion, a concept originally proposed in particle physics half a century ago, can now find the most fertile field for its applicability, that is, the magnetic skyrmion realized in helimagnetic materials. The spin swirling vortex-like texture of the magnetic skyrmion can define the particle nature by topology; that is, all the constituent spin moments within the two-dimensional sheet wrap the sphere just one time. Such a topological nature of the magnetic skyrmion can lead to extraordinary metastability via topological protection and the driven motion with low electric-current excitation, which may promise future application to spintronics. The skyrmions in the magnetic materials frequently show up as the crystal lattice form, e.g., hexagonal lattice, but sometimes as isolated or independent particles. These skyrmions in magnets were initially found in acentric magnets, such as chiral, polar, and bilayered magnets endowed with antisymmetric spin exchange interaction, while the skyrmion host materials have been explored in a broader family of compounds including centrosymmetric magnets. This review describes the materials science and materials chemistry of magnetic skyrmions using the classification scheme of the skyrmion forming microscopic mechanisms. The emergent phenomena and functions mediated by skyrmions are described, including the generation of emergent magnetic and electric field by statics and dynamics of skrymions and the inherent magnetoelectric effect. The other important magnetic topological defects in two or three dimensions, such as biskyrmions, antiskyrmions, merons, and hedgehogs, are also reviewed in light of their interplay with the skyrmions.

Néel-Type Elliptical Skyrmions in a Laterally Asymmetric Magnetic Multilayer

Magnetic skyrmions, topological-chiral spin textures, have potential applications in next-generation high-density and energy-efficient spintronic devices for information storage and logic technologies. Tailoring the detailed spin textures of skyrmions is of pivotal importance for tuning skyrmion dynamics, which is one of the key factors for the design of skyrmionic devices. Here, the direct observation of parallel aligned elliptical magnetic skyrmions in Pt/Co/Ta multilayers with an oblique-angle deposited Co layer is reported. Domain wall velocity and spin-orbit-torque-induced out-of-plane effective field analysis demonstrate that the formation of unusual elliptical skyrmions is correlated to the anisotropic effective perpendicular magnetic anisotropy energy density (K^eff _u ) and Dzyaloshinskii-Moriya interaction (DMI) in the film plane. Structural analysis and first-principles calculations further show that the anisotropic K^eff _u and DMI originate from the interfacial anisotropic strain introduced by the oblique-angle deposition. The work provides a method to tune the spin textures of skyrmions in magnetic multilayers and, thereby, a new degree of freedom for the design of skyrmionic devices.

Electric-field control of skyrmions in multiferroic heterostructure via magnetoelectric coupling

Room-temperature skyrmions in magnetic multilayers are considered to be promising candidates for the next-generation spintronic devices. Several approaches have been developed to control skyrmions, but they either cause significant heat dissipation or require ultrahigh electric fields near the breakdown threshold. Here, we demonstrate electric-field control of skyrmions through strain-mediated magnetoelectric coupling in ferromagnetic/ferroelectric multiferroic heterostructures. We show the process of non-volatile creation of multiple skyrmions, reversible deformation and annihilation of a single skyrmion by performing magnetic force microscopy with in situ electric fields. Strain-induced changes in perpendicular magnetic anisotropy and interfacial Dzyaloshinskii–Moriya interaction strength are characterized experimentally. These experimental results, together with micromagnetic simulations, demonstrate that strain-mediated magnetoelectric coupling (via strain-induced changes in both the perpendicular magnetic anisotropy and interfacial Dzyaloshinskii–Moriya interaction is responsible for the observed electric-field control of skyrmions. Our work provides a platform to investigate electric-field control of skyrmions in multiferroic heterostructures and paves the way towards more energy-efficient skyrmion-based spintronics.

The common approaches to control of skymions cause significant heat dissipation or require high electric fields near the breakdown threshold. Here, the authors demonstrate electric-field control of skyrmions through strain-mediated magnetoelectric coupling in multiferroic heterostructures.

Spin waves in skyrmionic structures with various topological charges

Equilibrium properties and localized magnon excitations are investigated in topologically distinct skyrmionic textures. The observed shape of the structures and their orientation on the lattice is explained based on their vorticities and the symmetry of the crystal. The transformation between different textures and their annihilation as a function of magnetic field is understood based on the energy differences between them. The angular momentum spin-wave eigenmodes characteristic of cylindrically symmetric structures are combined in the distorted spin configurations, leading to avoided crossings in the magnon spectrum. The susceptibility of the skyrmionic textures to homogeneous external fields is calculated, revealing that a high number of modes become detectable due to the hybridization between the angular momentum eigenmodes. These findings should contribute to the observation of spin waves in distorted skyrmionic structures via experiments and numerical simulations, widening the range of their possible applications in magnonic devices.

Deterministic reversal of single magnetic vortex circulation by an electric field

The ability to control magnetic vortex is critical for their potential applications in spintronic devices. Traditional methods including magnetic field, spin-polarized current etc. have been used to flip the core and/or reverse circulation of vortex. However, it is challenging for deterministic electric-field control of the single magnetic vortex textures with time-reversal broken symmetry and no planar magnetic anisotropy. Here it is reported that a deterministic reversal of single magnetic vortex circulation can be driven back and forth by a space-varying strain in multiferroic heterostructures, which is controlled by using a bi-axial pulsed electric field. Phase-field simulation reveals the mechanism of the emerging magnetoelastic energy with the space variation and visualizes the reversal pathway of the vortex. This deterministic electric-field control of the single magnetic vortex textures demonstrates a new approach to integrate the low-dimensional spin texture into the magnetoelectric thin film devices with low energy consumption.

Electric-field-driven non-volatile multi-state switching of individual skyrmions in a multiferroic heterostructure

Electrical manipulation of skyrmions attracts considerable attention for its rich physics and promising applications. To date, such a manipulation is realized mainly via spin-polarized current based on spin-transfer torque or spin-orbital torque effect. However, this scheme is energy consuming and may produce massive Joule heating. To reduce energy dissipation and risk of heightened temperatures of skyrmion-based devices, an effective solution is to use electric field instead of current as stimulus. Here, we realize an electric-field manipulation of skyrmions in a nanostructured ferromagnetic/ferroelectrical heterostructure at room temperature via an inverse magneto-mechanical effect. Intriguingly, such a manipulation is non-volatile and exhibits a multistate feature. Numerical simulations indicate that the electric-field manipulation of skyrmions originates from strain-mediated modification of effective magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Our results open a direction for constructing low-energy-dissipation, non-volatile, and multistate skyrmion-based spintronic devices.

Electric-Field Control of Spin-Orbit Torques in Perpendicularly Magnetized W/CoFeB/MgO Films

Controlling magnetism by electric fields offers a highly attractive perspective for designing future generations of energy-efficient information technologies. Here, we demonstrate that the magnitude of current-induced spin-orbit torques in thin perpendicularly magnetized CoFeB films can be tuned and even increased by electric-field generated piezoelectric strain. Using theoretical calculations, we uncover that the subtle interplay of spin-orbit coupling, crystal symmetry, and orbital polarization is at the core of the observed strain dependence of spin-orbit torques. Our results open a path to integrating two energy efficient spin manipulation approaches, the electric-field-induced strain and the current-induced magnetization switching, thereby enabling novel device concepts.

Manipulation of the Dzyaloshinskii-Moriya Interaction in Co/Pt Multilayers with Strain

Interfacial Dzyaloshinskii-Moriya interaction (DMI) is experimentally investigated in Pt/Co/Pt multilayer films under strain. A strong variation (from 0.1 to 0.8  mJ/m^{2}) of the DMI constant is demonstrated at ±0.1% in-plane uniaxial deformation of the films. The anisotropic strain induces strong DMI anisotropy. The DMI constant perpendicular to the strain direction changes sign, while the constant along the strain direction does not. Estimates show that the DMI can be controlled with an electric field in hybrid ferroelectric-ferromagnetic systems. So, the observed effect opens the way to control the DMI and eventually skyrmions with a voltage via a strain-mediated magnetoelectric coupling.

Elliptical Bloch skyrmion chiral twins in an antiskyrmion system

Skyrmions and antiskyrmions are distinct topological chiral spin textures that have been observed in various material systems depending on the symmetry of the crystal structure. Here we show, using Lorentz transmission electron microscopy, that arrays of skyrmions can be stabilized in a tetragonal inverse Heusler with D_2d symmetry whose Dzyaloshinskii-Moriya interaction (DMI) otherwise supports antiskyrmions. These skyrmions can be distinguished from those previously found in several B20 systems which have only one chirality and are circular in shape. We find Bloch-type elliptical skyrmions with opposite chiralities whose major axis is oriented along two specific crystal directions: [010] and [100]. These structures are metastable over a wide temperature range and we show that they are stabilized by long-range dipole-dipole interactions. The possibility of forming two distinct chiral spin textures with opposite topological charges of ±1 in one material makes the family of D_2d materials exceptional.

Skyrmions and anti-skyrmions often exist in distinct material systems. Here, the authors observe elliptical skyrmions and anti-skyrmions with opposite topological charges in one tetragonal Heusler compound Mn_1.4Pt_0.9Pd_0.1Sn with D_2d symmetry.

Phonon Magnetochiral Effect

The magnetochiral effect (MCE) of phonons, a nonreciprocal acoustic propagation arising due to symmetry principles, is demonstrated in the chiral-lattice ferrimagnet Cu_{2}OSeO_{3}. Our high-resolution ultrasound experiments reveal that the sound velocity differs for parallel and antiparallel propagation with respect to the external magnetic field. The sign of the nonreciprocity depends on the chirality of the crystal in accordance with the selection rule of the MCE. The nonreciprocity is enhanced below the magnetic ordering temperature and at higher ultrasound frequencies, which is quantitatively explained by a proposed magnon-phonon hybridization mechanism.

An achiral ferromagnetic/chiral antiferromagnetic bilayer system leading to controllable size and density of skyrmions

Magnetic skyrmions are topologically protected domain structures related to the Dzyaloshinskii-Moriya interaction (DMI). To understand how magnetic skyrmions occur under different circumstances, we propose a model for skyrmion formation in a bilayer system of ferromagnetic/antiferromagnetic (FM/AFM) films, in which the bulk DMI is only present in the AFM film. Micromagnetic simulations reveal that skyrmions are formed in this system due to the competition between the DMI and demagnetization energies. A critical interfacial exchange energy (A_i = 6.5 mJ/m²) is determined, above which the competition occurs at its full extent. More skyrmions are formed with increasing external magnetic field till a critical value above which the external field is too large and thus leading to the annihilation of skyrmions. The spacing between two skyrmions can be as small as 45 nm. Our results may give technological implications for future skyrmion applications.

Response of the Skyrmion Lattice in MnSi to Cubic Magnetocrystalline Anisotropies

We report high-precision small-angle neutron scattering of the orientation of the Skyrmion lattice in a spherical sample of MnSi under systematic changes of the magnetic field direction. For all field directions the Skyrmion lattice may be accurately described as a triple-Q[over →] state, where the modulus |Q[over →]| is constant and the wave vectors enclose rigid angles of 120°. Along a great circle across ⟨100⟩, ⟨110⟩, and ⟨111⟩ the normal to the Skyrmion-lattice plane varies systematically by ±3° with respect to the field direction, while the in-plane alignment displays a reorientation by 15° for magnetic field along ⟨100⟩. Our observations are qualitatively and quantitatively in excellent agreement with an effective potential, which is determined by the symmetries of the tetrahedral point group T and includes contributions up to sixth order in spin-orbit coupling, providing a full account of the effect of cubic magnetocrystalline anisotropies on the Skyrmion lattice in MnSi.

Tunable surface configuration of skyrmion lattices in cubic helimagnets

In bulk helimagnets, the presence of magnetic skyrmion lattices is always accompanied by a periodic stress field due to the intrinsic magnetoelastic coupling. The release of this nontrivial stress field at the surface causes a periodic displacement field, which characterizes a novel particle-like property of skyrmion: its surface configuration. Here, we derive the analytical solution of this displacement field for semi-infinite cubic helimagnet with the skyrmion magnetization approximated by the triple-Q representation. For MnSi, we show that the skyrmion lattices have a bumpy surface configuration characterized by periodically arranged peaks with a characteristic height of about 10^-13 m. The pattern of the peaks can be controlled by varying the strength of the applied magnetic field. Moreover, we prove that the surface configuration varies together with the motion and deformation of the skyrmion lattices. As a result, the surface configuration can be tuned by application of electric current, mechanical loads, as well as any other effective external fields for skyrmion lattices.

Creation of Single Chain of Nanoscale Skyrmion Bubbles with Record-High Temperature Stability in a Geometrically Confined Nanostripe

Nanoscale topologically nontrivial spin textures, such as magnetic skyrmions, have been identified as promising candidates for the transport and storage of information for spintronic applications, notably magnetic racetrack memory devices. The design and realization of a single skyrmion chain at room temperature (RT) and above in the low-dimensional nanostructures are of great importance for future practical applications. Here, we report the creation of a single skyrmion bubble chain in a geometrically confined Fe₃Sn₂ nanostripe with a width comparable to the featured size of a skyrmion bubble. Systematic investigations on the thermal stability have revealed that the single chain of skyrmion bubbles can keep stable at temperatures varying from RT up to a record-high temperature of 630 K. This extreme stability can be ascribed to the weak temperature-dependent magnetic anisotropy and the formation of edge states at the boundaries of the nanostripes. The realization of the highly stable skyrmion bubble chain in a geometrically confined nanostructure is a very important step toward the application of skyrmion-based spintronic devices.

Current-Driven Motion of Domain Boundaries between Skyrmion Lattice and Helical Magnetic Structure

To utilize magnetic skyrmions, nanoscale vortex-like magnetic structures, experimental elucidation of their dynamics against current application in various circumstances such as in confined structure and mixture of different magnetic phases is indispensable. Here, we investigate the current-induced dynamics of the coexistence state of magnetic skyrmions and helical magnetic structure in a thin plate of B20-type helimagnet FeGe in terms of in situ real-space observation using Lorentz transmission electron microscopy. Current pulses with various heights and widths were applied, and the change of the magnetic domain distribution was analyzed using a machine-learning technique. The observed average driving direction of the two-magnetic-state domain boundary is opposite to the applied electric current, indicating ferromagnetic s-d exchange coupling in the spin-transfer torque mechanism. The evaluated driving distance tends to increase with increasing the pulse duration time, current density (>1 × 10⁹ A/m²), and sample temperature, providing valuable information about hitherto unknown current-induced dynamics of the skyrmion-lattice ensemble.

Endotaxial growth of FexGe single-crystals on Ge(001) substrates

Through a 3D diffraction method combined with HRTEM images, we have successfully determined the specific phase of each Fe_xGe island grown on the Ge substrate.

Helimagnon Resonances in an Intrinsic Chiral Magnonic Crystal

We experimentally study magnetic resonances in the helical and conical magnetic phases of the chiral magnetic insulator Cu_{2}OSeO_{3} at the temperature T=5  K. Using a broadband microwave spectroscopy technique based on vector network analysis, we identify three distinct sets of helimagnon resonances in the frequency range 2  GHz≤f≤20  GHz with low magnetic damping α≤0.003. The extracted resonance frequencies are in accordance with calculations of the helimagnon band structure found in an intrinsic chiral magnonic crystal. The periodic modulation of the equilibrium spin direction that leads to the formation of the magnonic crystal is a direct consequence of the chiral magnetic ordering caused by the Dzyaloshinskii-Moriya interaction. The mode coupling in the magnonic crystal allows excitation of helimagnons with wave vectors that are multiples of the spiral wave vector.

Equilibrium Skyrmion Lattice Ground State in a Polar Easy-plane Magnet

The skyrmion lattice state (SkL), a crystal built of mesoscopic spin vortices, gains its stability via thermal fluctuations in all bulk skyrmion host materials known to date. Therefore, its existence is limited to a narrow temperature region below the paramagnetic state. This stability range can drastically increase in systems with restricted geometries, such as thin films, interfaces and nanowires. Thermal quenching can also promote the SkL as a metastable state over extended temperature ranges. Here, we demonstrate more generally that a proper choice of material parameters alone guarantees the thermodynamic stability of the SkL over the full temperature range below the paramagnetic state down to zero kelvin. We found that GaV₄Se₈, a polar magnet with easy-plane anisotropy, hosts a robust Néel-type SkL even in its ground state. Our supporting theory confirms that polar magnets with weak uniaxial anisotropy are ideal candidates to realize SkLs with wide stability ranges.

Helical and skyrmion lattice phases in three-dimensional chiral magnets: Effect of anisotropic interactions

In this work, we study the magnetic orders of a classical spin model with anisotropic exchanges and Dzyaloshinskii-Moriya interactions in order to understand the uniaxial stress effect in chiral magnets such as MnSi. Variational zero temperature calculations demonstrate that various helical orders can be developed depending on the interaction anisotropy magnitude, consistent with experimental observations at low temperatures. Furthermore, the uniaxial stress induced creation and annihilation of skyrmions can be also qualitatively reproduced in our Monte Carlo simulations. Our work suggests that the interaction anisotropy tuned by applied uniaxial stress may play an essential role in modulating the magnetic orders in strained chiral magnets.

Control of morphology and formation of highly geometrically confined magnetic skyrmions

The ability to controllably manipulate magnetic skyrmions, small magnetic whirls with particle-like properties, in nanostructured elements is a prerequisite for incorporating them into spintronic devices. Here, we use state-of-the-art electron holographic imaging to directly visualize the morphology and nucleation of magnetic skyrmions in a wedge-shaped FeGe nanostripe that has a width in the range of 45–150 nm. We find that geometrically-confined skyrmions are able to adopt a wide range of sizes and ellipticities in a nanostripe that are absent in both thin films and bulk materials and can be created from a helical magnetic state with a distorted edge twist in a simple and efficient manner. We perform a theoretical analysis based on a three-dimensional general model of isotropic chiral magnets to confirm our experimental results. The flexibility and ease of formation of geometrically confined magnetic skyrmions may help to optimize the design of skyrmion-based memory devices.

Proposals for skyrmion-based high-density memory devices require an understanding of the formation and shape of skyrmions in confined geometries. Here, the authors use electron holography to image magnetic textures in FeGe nanostripes and explore the parameters governing skyrmion morphology.

Dynamical Defects in Rotating Magnetic Skyrmion Lattices

The chiral magnet Cu_{2}OSeO_{3} hosts a Skyrmion lattice that may be equivalently described as a superposition of plane waves or a lattice of particlelike topological objects. A thermal gradient may break up the Skyrmion lattice and induce rotating domains, raising the question of which of these scenarios better describes the violent dynamics at the domain boundaries. Here, we show that in an inhomogeneous temperature gradient caused by illumination in a Lorentz transmission electron microscope different parts of the Skyrmion lattice can be set into motion with different angular velocities. Tracking the time dependence, we show that the constant rearrangement of domain walls is governed by dynamic 5-7 defects arranging into lines. An analysis of the associated defect density is described by Frank's equation and agrees well with classical 2D Monte Carlo simulations. Fluctuations of boundaries show a surgelike rearrangement of Skyrmion clusters driven by defect rearrangement consistent with simulations treating Skyrmions as point particles. Our findings underline the particle character of the Skyrmion.

Dynamical and Reversible Control of Topological Spin Textures

Recent observations of topological spin textures brought spintronics one step closer to new magnetic memories. Nevertheless, the existence of Skyrmions, as well as their stabilization, require very specific intrinsic magnetic properties which are usually fixed in magnets. Here we address the possibility to dynamically control their intrinsic magnetic interactions by varying the strength of a high-frequency laser field. It is shown that drastic changes can be induced in the antiferromagnetic exchange interactions and the latter can even be reversed to become ferromagnetic, provided the direct exchange is already non-negligible in equilibrium as predicted, for example, in Si doped with C, Sn, or Pb adatoms. In the presence of Dzyaloshinskii-Moriya interactions, this enables us to tune features of ferromagnetic Skyrmions such as their radius, making them easier to stabilize. Alternatively, such topological spin textures can occur in frustrated triangular lattices. Then, we demonstrate that a high-frequency laser field can induce dynamical frustration in antiferromagnets, where the degree of frustration can subsequently be tuned suitably to drive the material toward a Skyrmionic phase.

Observation of stable Néel skyrmions in cobalt/palladium multilayers with Lorentz transmission electron microscopy

Néel skyrmions are of high interest due to their potential applications in a variety of spintronic devices, currently accessible in ultrathin heavy metal/ferromagnetic bilayers and multilayers with a strong Dzyaloshinskii–Moriya interaction. Here we report on the direct imaging of chiral spin structures including skyrmions in an exchange-coupled cobalt/palladium multilayer at room temperature with Lorentz transmission electron microscopy, a high-resolution technique previously suggested to exhibit no Néel skyrmion contrast. Phase retrieval methods allow us to map the internal spin structure of the skyrmion core, identifying a 25 nm central region of uniform magnetization followed by a larger region characterized by rotation from in- to out-of-plane. The formation and resolution of the internal spin structure of room temperature skyrmions without a stabilizing out-of-plane field in thick magnetic multilayers opens up a new set of tools and materials to study the physics and device applications associated with chiral ordering and skyrmions.

Néel skyrmions are spin textures with a magnetization that rotates from in- to out-of-plane with distance from its centre. Here, the authors show that Lorentz transmission electron microscopy can be used to directly image Néel skyrmions with high resolution in thick exchange-coupled magnetic multilayers.

Deformation of Topologically-Protected Supercooled Skyrmions in a Thin Plate of Chiral Magnet Co8Zn8Mn4

Magnetic skyrmions in Co₈Zn₈Mn₄ thin plates are observed to deform in a metastable state prepared in a magnetic-field-cooling process by way of the thermal-equilibrium skyrmion phase. In cooling, the disk-shape skyrmions change to bar- or L-shaped elongated form, whereas the skyrmion density is nearly conserved. The deformation of the skyrmions in the supercooled metastable phase is observed irrespective of the crystallographic orientation of the thin plate, whereas the elongation direction nearly aligns along the magnetic easy axis. It is proposed that the deformation should be induced by a large increase in magnetic modulation wavenumber when decreasing the temperature, whereas the topological protection of the skyrmions keeps the averaged skyrmion density constant.