Disordered skyrmion phase stabilized by magnetic frustration in a chiral magnet

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.

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.

Real-space determination of the isolated magnetic skyrmion deformation under electric current flow

The manipulation and control of electron spins, the fundamental building blocks of magnetic domains and spin textures, are at the core of spintronics. Of particular interest is the effect of the electric current on topological magnetic skyrmions, such as the current-induced deformation of isolated skyrmions. The deformation has consequences ranging from perturbed dynamics to modified packing configurations. In this study, we measured the current-driven real-space deformation of isolated, pinned skyrmions within Co₁₀Zn₁₀ at room temperature. We observed that the skyrmions are surprisingly soft, readily deforming during electric current application into an elliptical shape with a well-defined deformation axis (semimajor axis). We found that this axis rotates unidirectionally toward the current direction irrespective of electric current polarity and that the elliptical deformation reverses back upon current termination. We quantified the average distortion δ, which increased by ∼90% during the largest applied current density |j| = 8.46 ×10⁹ A/m² when compared with the skyrmion's intrinsic shape ([Formula: see text]). Additionally, we demonstrated an approximately 120% average skyrmion core size expansion during current application, highlighting the skyrmions' inherent topological protection. This evaluation of in situ electric current-induced skyrmion deformation paints a clearer picture of spin-polarized electron-skyrmion interactions and may prove essential in designing spintronic devices.

History-dependent domain and skyrmion formation in 2D van der Waals magnet Fe3GeTe2

The discovery of two-dimensional magnets has initiated a new field of research, exploring both fundamental low-dimensional magnetism, and prospective spintronic applications. Recently, observations of magnetic skyrmions in the 2D ferromagnet Fe₃GeTe₂ (FGT) have been reported, introducing further application possibilities. However, controlling the exhibited magnetic state requires systematic knowledge of the history-dependence of the spin textures, which remains largely unexplored in 2D magnets. In this work, we utilise real-space imaging, and complementary simulations, to determine and explain the thickness-dependent magnetic phase diagrams of an exfoliated FGT flake, revealing a complex, history-dependent emergence of the uniformly magnetised, stripe domain and skyrmion states. The results show that the interplay of the dominant dipolar interaction and strongly temperature dependent out-of-plane anisotropy energy terms enables the selective stabilisation of all three states at zero field, and at a single temperature, while the Dzyaloshinksii-Moriya interaction must be present to realise the observed Néel-type domain walls. The findings open perspectives for 2D devices incorporating topological spin textures.

Fe₃GeTe₂, known as FGT, is a van der Waals magnetic material that was recently shown to host magnetic skyrmions. Here, Birch et al using both X-ray and electron microscopy to study the stability of skyrmions in FGT, revealing how the sample history can influence skyrmion formation

Direct Visualisation of Skyrmion Lattice Defect Alignment at Grain Boundaries

We present a method to directly visualise a statistical analysis of skyrmion defect alignment at grain boundaries in the skyrmion host [Formula: see text]OSeO3. Using Lorentz transmission electron microscopy, we collected large data sets with several hundreds of frames containing skyrmion lattices with grain boundaries in them. To address the behaviour of strings of dislocations in these grain boundaries, we developed an algorithm to automatically extract and classify strings of dislocations separating the grains. This way we circumvent the problem of having to create configurations with well-defined relative grain orientations by performing a statistical analysis on a dynamically rearranging image sequence. With this statistical method, we are able to experimentally extract the relationship between grain boundary alignment and defect spacing and find an agreement with geometric expectations. The algorithms used can be extended to other types of lattices such as Abrikosov lattices or colloidal systems in optical microscopy.

Giant Topological Hall Effect in van der Waals Heterostructures of CrTe2/Bi2Te3

Discoveries of the interfacial topological Hall effect (THE) provide an ideal platform for exploring the physics arising from the interplay between topology and magnetism. The interfacial topological Hall effect is closely related to the Dzyaloshinskii-Moriya interaction (DMI) at an interface and topological spin textures. However, it is difficult to achieve a sizable THE in heterostructures due to the stringent constraints on the constituents of THE heterostructures, such as strong spin-orbit coupling (SOC). Here, we report the observation of a giant THE signal of 1.39 μΩ·cm in the van der Waals heterostructures of CrTe₂/Bi₂Te₃ fabricated by molecular beam epitaxy, a prototype of two-dimensional (2D) ferromagnet (FM)/topological insulator (TI). This large magnitude of THE is attributed to an optimized combination of 2D ferromagnetism in CrTe₂, strong SOC in Bi₂Te₃, and an atomically sharp interface. Our work reveals CrTe₂/Bi₂Te₃ as a convenient platform for achieving large interfacial THE in hybrid systems, which could be utilized to develop quantum science and high-density information storage devices.

Topological spin crystals by itinerant frustration

Spin textures with nontrivial topology, such as vortices and skyrmions, have attracted attention as a source of unconventional magnetic, transport, and optical phenomena. Recently, a new generation of topological spin textures has been extensively studied in itinerant magnets; in contrast to the conventional ones induced, e.g., by the Dzyaloshinskii-Moriya interaction in noncentrosymmetric systems, they are characterized by extremely short magnetic periods and stable even in centrosymmetric systems. Here we review such new types of topological spin textures with particular emphasis on their stabilization mechanism. Focusing on the interplay between charge and spin degrees of freedom in itinerant electron systems, we show that itinerant frustration, which is the competition among electron-mediated interactions, plays a central role in stabilizing a variety of topological spin crystals including a skyrmion crystal with unconventional high skyrmion number, meron crystals, and hedgehog crystals. We also show that the essential ingredients in the itinerant frustration are represented by bilinear and biquadratic spin interactions in momentum space. This perspective not only provides a unified understanding of the unconventional topological spin crystals but also stimulates further exploration of exotic topological phenomena in itinerant magnets.

Characterization of a Disordered above Room Temperature Skyrmion Material Co8Zn8Mn4

Topologically nontrivial spin textures host great promise for future spintronic applications. Skyrmions in particular are of burgeoning interest owing to their nanometric size, topological protection, and high mobility via ultra-low current densities. It has been previously reported through magnetic susceptibility, microscopy, and scattering techniques that Co8Zn8Mn4 forms an above room temperature triangular skyrmion lattice. Here, we report the synthesis procedure and characterization of a polycrystalline Co8Zn8Mn4 disordered bulk sample. We employ powder X-ray diffraction and backscatter Laue diffraction as characterization tools of the crystallinity of the samples, while magnetic susceptibility and Small Angle Neutron Scattering (SANS) measurements are performed to study the skyrmion phase. Magnetic susceptibility measurements show a dip anomaly in the magnetization curves, which persists over a range of approximately 305 K-315 K. SANS measurements reveal a rotationally disordered polydomain skyrmion lattice. Applying a symmetry-breaking magnetic field sequence, we were able to orient and order the previously jammed state to yield the prototypical hexagonal diffraction patterns with secondary diffraction rings. This emergence of the skyrmion order serves as a unique demonstration of the fundamental interplay of structural disorder and anisotropy in stabilizing the thermal equilibrium phase.

Directional locking and the influence of obstacle density on skyrmion dynamics in triangular and honeycomb arrays

We numerically examine the dynamics of a single skyrmion driven over triangular and honeycomb obstacle arrays at zero temperature. The skyrmion Hall angleθ_sk, defined as the angle between the applied external drive and the direction of the skyrmion motion, increases in quantized steps or continuously as a function of the applied drive. For the obstacle arrays studied in this work, the skyrmion exhibits two main directional locking angles ofθ_sk= -30° and -60°. We show that these directions are privileged due to the obstacle landscape symmetry, and coincide with channels along which the skyrmion may move with few or no obstacle collisions. Here we investigate how changes in the obstacle density can modify the skyrmion Hall angles and cause some dynamic phases to appear or grow while other phases vanish. This interesting behavior can be used to guide skyrmions along designated trajectories via regions with different obstacle densities. For fixed obstacle densities, we investigate the evolution of the lockedθ_sk= -30° and -60° phases as a function of the Magnus force, and discuss possibilities for switching between these phases using topological selection.

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.

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.

Theory of an electron asymmetric scattering on skyrmion textures in two-dimensional systems

We discuss in detail the electron scattering pattern on skyrmion-like magnetic textures in two-dimensional geometry. The special attention is focused on analyzing the scattering asymmetry, which is a precursor of the topological Hall effect. We present analytical results valid in the limiting regimes of strong and weak coupling, we analyze analytically the conditions when the transverse response acquires a quantized character determined by the topological charge of a magnetic texture, we also derive the numerical scheme that gives access to the exact solution of the scattering problem. We describe how the electron scattering asymmetry is modified due to an additional short-range impurity located inside a magnetic skyrmion. Based on the numerical computations we investigate the properties of the asymmetric scattering for an arbitrary magnitude of the interaction strength and the topology of a magnetic texture, we also account for the presence or absence of a scalar impurity.

Mechanisms of Skyrmion and Skyrmion Crystal Formation from the Conical Phase

Real-space topological magnetic structures such as skyrmions and merons are promising candidates for information storage and transport. However, the microscopic mechanisms that control their formation and evolution are still unclear. Here, using in situ Lorentz transmission electron microscopy, we demonstrate that skyrmion crystals (SkXs) can nucleate, grow, and evolve from the conical phase in the same ways that real nanocrystals form from vapors or solutions. More intriguingly, individual skyrmions can also "reproduce" by division in a mitosis-like process that allows them to annihilate SkX lattice imperfections, which is not available to crystals made of mass-conserving particles. Combined string method and micromagnetic calculations show that competition between repulsive and attractive interactions between skyrmions governs particle-like SkX growth, but nonconservative SkX growth appears to be defect mediated. Our results provide insights toward manipulating magnetic topological states by applying established crystal growth theory, adapted to account for the new process of skyrmion mitosis.

Ferromagnetic Resonance with Magnetic Phase Selectivity by Means of Resonant Elastic X-Ray Scattering on a Chiral Magnet

Cubic chiral magnets, such as Cu_{2}OSeO_{3}, exhibit a variety of noncollinear spin textures, including a trigonal lattice of spin whirls, the so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at gigahertz frequencies, we probe the ferromagnetic resonance (FMR) modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS FMR, is carried out at distinct positions in reciprocal space, it allows us to distinguish contributions originating from different magnetic states, providing information on the precise character, weight, and mode mixing as a prerequisite of tailored excitations for applications.

Smectic Liquid-Crystalline Structure of Skyrmions in Chiral Magnet Co_{8.5}Zn_{7.5}Mn_{4}(110) Thin Film

The organizing of magnetic skyrmions shows several forms similar to atomic arrays of solid states. Using Lorentz transmission electron microscopy, we report the first direct observation of a stable liquid-crystalline structure of skyrmions in chiral magnet Co_{8.5}Zn_{7.5}Mn_{4}(110) thin film, caused by magnetic anisotropy and chiral surface twist. Elongated skyrmions are oriented and periodically arranged only in the ⟨110⟩ directions, whereas they exhibit short-range order along the ⟨001⟩ directions, indicating a smectic skyrmion state. In addition, skyrmions possess anisotropic interaction with an opposite sign depending on the crystal orientation, in contrast to existing isotropic interaction.

Oriented 3D Magnetic Biskyrmions in MnNiGa Bulk Crystals

A biskyrmion consists of two bound, topologically stable, skyrmion spin textures. These coffee-bean-shaped objects are observed in real space in thin plates using Lorentz transmission electron microscopy (LTEM). From LTEM imaging alone, it is not clear whether biskyrmions are surface-confined objects, or, analogous to skyrmions in noncentrosymmetric helimagnets, 3D tube-like structures in a bulk sample. Here, the biskyrmion form factor is investigated in single- and polycrystalline-MnNiGa samples using small-angle neutron scattering. It is found that biskyrmions are not long-range ordered, not even in single crystals. Surprisingly all of the disordered biskyrmions have their in-plane symmetry axis aligned along certain directions, governed by the magnetocrystalline anisotropy. This anisotropic nature of biskyrmions may be further exploited to encode information.

Disordering, clustering, and laning transitions in particle systems with dispersion in the Magnus term

We numerically examine a two-dimensional system of repulsively interacting particles with dynamics that are governed by both a damping term and a Magnus term. The magnitude of the Magnus term has one value for half of the particles and a different value for the other half of the particles. In the absence of a driving force, the particles form a triangular lattice, while when a driving force is applied, we find that there is a critical drive above which a Magnus-induced disordering transition can occur even if the difference in the Magnus term between the two particle species is as small as one percent. The transition arises due to the different Hall angles of the two species, which causes their motion to decouple at the critical drive. At higher drives, the disordered state can undergo both species and density phase separation into a density-modulated stripe that is oriented perpendicular to the driving direction. We observe several additional phases that occur as a function of drive and Magnus force disparity, including a variety of density-modulated diagonal-laned phases. In general, we find a much richer variety of states compared to systems of oppositely driven overdamped Yukawa particles. We discuss the implications of our work for skyrmion systems, where we predict that even for small skyrmion dispersities, a drive-induced disordering transition can occur along with clustering phases and pattern-forming states.