Controlled transformation of skyrmions and antiskyrmions in a non-centrosymmetric magnet

Experimental observation of current-driven antiskyrmion sliding in stripe domains

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

Alloying Driven Antiferromagnetic Skyrmions on NiPS3 Monolayer: A First-Principles Calculation

Topological magnetic states are promising information carriers for ultrahigh-density and high-efficiency magnetic storage. Recent advances in two-dimensional (2D) magnets provide powerful platforms for stabilizing various nanometer-size topological spin textures within a wide range of magnetic field and temperature. However, non-centrosymmetric 2D magnets with broken inversion symmetry are scarce in nature, making direct observations of the chiral spin structure difficult, especially for antiferromagnetic (AFM) skyrmions. In this work, it is theoretically predicted that intrinsic AFM skyrmions can be easily triggered in XY-type honeycomb magnet NiPS3 monolayer by alloying of Cr atoms, due to the presence of a sizable Dzyaloshinskii-Moriya interaction. More interestingly, the diameter of the AFM skyrmions in Ni3/4Cr1/4PS3 decreases from 12 to 4.4 nm as the external magnetic field increases and the skyrmion phases remain stable up to an external magnetic field of 4 T. These results highlight an effective strategy to generate and modulate the topological spin texture in 2D magnets by alloying with magnetic element.

Topological Spin Textures: Basic Physics and Devices

In the face of escalating modern data storage demands and the constraints of Moore's Law, exploring spintronic solutions, particularly the devices based on magnetic skyrmions, has emerged as a promising frontier in scientific research. Since the first experimental observation of skyrmions, topological spin textures have been extensively studied for their great potential as efficient information carriers in spintronic devices. However, significant challenges have emerged alongside this progress. This review aims to synthesize recent advances in skyrmion research while addressing the major issues encountered in the field. Additionally, current research on promising topological spin structures in addition to skyrmions is summarized. Beyond 2D structures, exploration also extends to 1D magnetic solitons and 3D spin textures. In addition, a diverse array of emerging magnetic materials is introduced, including antiferromagnets and 2D van der Waals magnets, broadening the scope of potential materials hosting topological spin textures. Through a systematic examination of magnetic principles, topological categorization, and the dynamics of spin textures, a comprehensive overview of experimental and theoretical advances in the research of topological magnetism is provided. Finally, both conventional and unconventional applications are summarized based on spin textures proposed thus far. This review provides an outlook on future development in applied spintronics.

Topological Complex Charge Conservation in Nontrivial Z2 × Z2 Domain Walls

Localized topological modes such as solitons, Majorana Fermions, and skyrmions are attracting great interest as robust information carriers for future devices. Here, a novel conserved quantity for topological domain wall networks of a Z2 × Z2 order generated with spin-polarized current in Sr2VO3FeAs is discovered. Domain walls are mobilized by the scanning tunneling current, which also observes in atomic scale active dynamics of domain wall vertices including merge, bifurcation, pair creation, and annihilation. Within this dynamics, the product of the topological complex charges defined for domain wall vertices is conserved with a novel boundary-charge correspondence rule. These results may open an avenue toward topological electronics based on domain wall vertices in generic Z2 × Z2 systems.

Noncentrosymmetric Triangular Magnet CaMnTeO6: Strong Quantum Fluctuations and Role of s0 versus s2 Electronic States in Competing Exchange Interactions

Noncentrosymmetric triangular magnets offer a unique platform for realizing strong quantum fluctuations. However, designing these quantum materials remains an open challenge attributable to a knowledge gap in the tunability of competing exchange interactions at the atomic level. Here, a new noncentrosymmetric triangular S = 3/2 magnet CaMnTeO6 is created based on careful chemical and physical considerations. The model material displays competing magnetic interactions and features nonlinear optical responses with the capability of generating coherent photons. The incommensurate magnetic ground state of CaMnTeO6 with an unusually large spin rotation angle of 127°(1) indicates that the anisotropic interlayer exchange is strong and competing with the isotropic interlayer Heisenberg interaction. The moment of 1.39(1) µB, extracted from low-temperature heat capacity and neutron diffraction measurements, is only 46% of the expected value of the static moment 3 µB. This reduction indicates the presence of strong quantum fluctuations in the half-integer spin S = 3/2 CaMnTeO6 magnet, which is rare. By comparing the spin-polarized band structure, chemical bonding, and physical properties of AMnTeO6 (A = Ca, Sr, Pb), how quantum-chemical interpretation can illuminate insights into the fundamentals of magnetic exchange interactions, providing a powerful tool for modulating spin dynamics with atomically precise control is demonstrated.

Spin disorder control of topological spin texture

Stabilization of topological spin textures in layered magnets has the potential to drive the development of advanced low-dimensional spintronics devices. However, achieving reliable and flexible manipulation of the topological spin textures beyond skyrmion in a two-dimensional magnet system remains challenging. Here, we demonstrate the introduction of magnetic iron atoms between the van der Waals gap of a layered magnet, Fe3GaTe2, to modify local anisotropic magnetic interactions. Consequently, we present direct observations of the order-disorder skyrmion lattices transition. In addition, non-trivial topological solitons, such as skyrmioniums and skyrmion bags, are realized at room temperature. Our work highlights the influence of random spin control of non-trivial topological spin textures.

Bloch Point Quadrupole Constituting Hybrid Topological Strings Revealed with Electron Holographic Vector Field Tomography

Topological magnetic (anti)skyrmions are robust string-like objects heralded as potential components in next-generation topological spintronics devices due to their low-energy manipulability via stimuli such as magnetic fields, heat, and electric/thermal current. While these 2D topological objects are widely studied, intrinsically 3D electron-spin real-space topology remains less explored despite its prevalence in bulky magnets. 2D-imaging studies reveal peculiar vortex-like contrast in the core regions of spin textures present in antiskyrmion-hosting thin plate magnets with S4 crystal symmetry, suggesting a more complex 3D real-space structure than the 2D model suggests. Here, holographic vector field electron tomography captures the 3D structure of antiskyrmions in a single-crystal, precision-doped (Fe0.63Ni0.3Pd0.07)3P (FNPP) lamellae at room temperature and zero field. These measurements reveal hybrid string-like solitons composed of skyrmions with topological number W = -1 on the lamellae's surfaces and an antiskyrmion (W = + 1) connecting them. High-resolution images uncover a Bloch point quadrupole (four magnetic (anti)monopoles that are undetectable in 2D imaging) which enables the observed lengthwise topological transitions. Numerical calculations corroborate the stability of hybrid strings over their conventional (anti)skyrmion counterparts. Hybrid strings result in topological tuning, a tunable topological Hall effect, and the suppression of skyrmion Hall motion, disrupting existing paradigms within spintronics.

Thickness-Tunable Zoology of Magnetic Spin Textures Observed in Fe5GeTe2

The family of two-dimensional (2D) van der Waals (vdW) materials provides a playground for tuning structural and magnetic interactions to create a wide variety of spin textures. Of particular interest is the ferromagnetic compound Fe5GeTe2 that we show displays a range of complex spin textures as well as complex crystal structures. Here, using a high-brailliance laboratory X-ray source, we show that the majority (1 × 1) Fe5GeTe2 (FGT5) phase exhibits a structure that was previously considered as being centrosymmetric but rather lacks inversion symmetry. In addition, FGT5 exhibits a minority phase that exhibits a long-range ordered (√3 × √3)-R30° superstructure. This superstructure is highly interesting in that it is innately 2D without any lattice periodicity perpendicular to the vdW layers, and furthermore, the superstructure is a result of ordered Te vacancies in one of the topmost layers of the FGT5 sheets rather than being a result of vertical Fe ordering as earlier suggested. We show, from direct real-space magnetic imaging, evidence for three distinct magnetic ground states in lamellae of FGT5 that are stabilized with increasing lamella thickness, namely, a multidomain state, a stripe phase, and an unusual fractal state. In the stripe phase we also observe unconventional type-I and type-II bubbles where the spin texture in the central region of the bubbles is nonuniform, unlike conventional bubbles. In addition, we find a bobber or a cocoon-like spin texture in thick (∼170 μm) FGT5 that emerges from the fractal state in the presence of a magnetic field. Among all the 2D vdW magnets we have thus demonstrated that FGT5 hosts perhaps the richest variety of magnetic phases that, thereby, make it a highly interesting platform for the subtle tuning of magnetic interactions.

Transition between distinct hybrid skyrmion textures through their hexagonal-to-square crystal transformation in a polar magnet

Magnetic skyrmions, topological vortex-like spin textures, garner significant interest due to their unique properties and potential applications in nanotechnology. While they typically form a hexagonal crystal with distinct internal magnetisation textures known as Bloch- or Néel-type, recent theories suggest the possibility for direct transitions between skyrmion crystals of different lattice structures and internal textures. To date however, experimental evidence for these potentially useful phenomena have remained scarce. Here, we discover the polar tetragonal magnet EuNiGe3 to host two hybrid skyrmion phases, each with distinct internal textures characterised by anisotropic combinations of Bloch- and Néel-type windings. Variation of the magnetic field drives a direct transition between the two phases, with the modification of the hybrid texture concomitant with a hexagonal-to-square skyrmion crystal transformation. We explain these observations with a theory that includes the key ingredients of momentum-resolved Ruderman-Kittel-Kasuya-Yosida and Dzyaloshinskii-Moriya interactions that compete at the observed low symmetry magnetic skyrmion crystal wavevectors. Our findings underscore the potential of polar magnets with rich interaction schemes as promising for discovering new topological magnetic phases.

Heat current-driven topological spin texture transformations and helical q-vector switching

The use of magnetic states in memory devices has a history dating back decades, and the experimental discovery of magnetic skyrmions and subsequent demonstrations of their control via magnetic fields, heat, and electric/thermal currents have ushered in a new era for spintronics research and development. Recent studies have experimentally discovered the antiskyrmion, the skyrmion's antiparticle, and while several host materials have been identified, control via thermal current remains elusive. In this work, we use thermal current to drive the transformation between skyrmions, antiskyrmions and non-topological bubbles, as well as the switching of helical states in the antiskyrmion-hosting ferromagnet (Fe0.63Ni0.3Pd0.07)3P at room temperature. We discover that a temperature gradient [Formula: see text] drives a transformation from antiskyrmions to non-topological bubbles to skyrmions while under a magnetic field and observe the opposite, unidirectional transformation from skyrmions to antiskyrmions at zero-field, suggesting that the antiskyrmion, more so than the skyrmion, is robustly metastable at zero field.

A method for estimating magnetic field of TEM objective lens

We propose a method for calibration of magnetic field in the objective lens of transmission electron microscope. The calibration process is based on classical Fresnel imaging of Permalloy disks and measuring the displacement of the magnetic vortex core when the sample is tilted at various excitations of the objective lens. We adopted the Carl Zeiss LIBRA 200 MC transmission electron microscope for Lorentz electron microscopy using this method. The objective lens magnetic field evaluation is tested on the Co/Pt multilayered films with known magnetic properties.

Bloch-type magnetic skyrmions in two-dimensional lattices

Magnetic skyrmions in two-dimensional lattices are a prominent topic of condensed matter physics and materials science. Current research efforts in this field are exclusively constrained to Néel-type and antiskyrmions, while Bloch-type magnetic skyrmions are rarely explored. Here, we report the discovery of Bloch-type magnetic skyrmions in a two-dimensional lattice of MnInP2Te6, using first-principles calculations and Monte-Carlo simulations. Arising from the joint effect of broken inversion symmetry and strong spin-orbit coupling, monolayer MnInP2Te6 presents large Dzyaloshinskii-Moriya interaction. This, along with ferromagnetic exchange interaction and out-of-plane magnetic anisotropy, gives rise to skyrmion physics in monolayer MnInP2Te6, in the absence of a magnetic field. Remarkably, different from all previous works on two-dimensional lattices, the resultant magnetic skyrmions feature Bloch-type magnetism, which is protected by D3 symmetry. Furthermore, Bloch-type magnetic bimerons are also identified in monolayer MnTlP2Te6. The phase diagrams of these Bloch-type topological magnetisms under a magnetic field, temperature and strain are mapped out. Our results greatly enrich the research on magnetic skyrmions in two-dimensional lattices.

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.

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.

Skyrmions Under Control-FIB Irradiation as a Versatile Tool for Skyrmion Circuits

Magnetic data storage and processing offer certain advances over conventional technologies, amongst which nonvolatility and low power operation are the most outstanding ones. Skyrmions are a promising candidate as a magnetic data carrier. However, the sputtering of skyrmion films and the control of the skyrmion nucleation, motion, and annihilation remains challenging. This work demonstrates that using optimized focused ion beam irradiation and annealing protocols enables the skyrmion phase in W/CoFeB/MgO thin films to be accessed easily. By analyzing ion-beam-engineered skyrmion hosting wires, excited by sub-100 ns current pulses, possibilities to control skyrmion nucleation, guide their motion, and control their annihilation unfold. Overall, the key elements needed to develop extensive skyrmion networks are presented.

Real-Space Observations of Three-Dimensional Antiskyrmions and Skyrmion Strings

Nanometric topological spin textures, such as skyrmions (Sks) and antiskyrmions (antiSks), have attracted much attention recently. However, most studies have focused on two-dimensional spin textures in films with inherent or synthetic antisymmetric spin-exchange interaction, termed Dzyaloshinskii-Moriya interaction, although three-dimensional (3D) topological spin textures, such as antiSks composed of alternating Bloch- and Néel-type spin spirals, chiral bobbers carrying emergent magnetic monopoles, and deformed Sk strings, are ubiquitous. To elucidate these textures, we have developed a 3D nanometric magnetic imaging technique, tomographic Lorentz transmission electron microscopy (TEM). The approach enables the visualization of the 3D shape of magnetic objects and their 3D vector field mapping. Here we report 3D vector field maps of deformed Sk-strings and antiSk using the technique. This research approach will lead to discoveries and understanding of fertile 3D magnetic structures in a broad class of magnets, providing insight into 3D topological magnetism.

Synthesis of stable γ-phase MnS1-xSex nanoflakes with inversion symmetry breaking

Inversion symmetry breaking plays a critical role in the formation of magnetic skyrmions. Therefore, for the application of skyrmion-based devices, it is important to develop novel engineering techniques and explore new non-centrosymmetric lattices. In this paper, we report the rational synthesis of stable γ-phase MnS_1-xSe_x (0 ≤ x ≤ 0.45) nanoflakes with an asymmetric distribution of the elemental content, which persists on inversion symmetry breaking. The temperature dependence of resonant second-harmonic generation characterization reveals that a non-centrosymmetric crystal structure exists in our as-grown γ-phase MnS_1-xSe_x with spatial-inversion symmetry breaking. By tuning the parameters of nucleation temperature and growth time, we produced a detailed growth phase diagram, revealing a controllable as-grown structure evolution from γ-phase wurtzite-type to α-phase rock-salt type structure of MnS_1-xSe_x nanoflakes. Our work provides a new playground to explore novel materials that have broken inversion symmetry.

Simulating anti-skyrmions on a lattice

Magnetic skyrmions are meta-stable spin structures that naturally emerge in magnetic materials. While a vast amount of effort has gone into the study of their properties, their counterpart of opposite topological charge, the anti-skyrmion, has not received as much attention. We aim to close this gap by deploying Monte Carlo simulations of spin-lattice systems in order to investigate which interactions support anti-skyrmions, as well as skyrmions of Bloch and Néel type. We find that the combination of ferromagnetic exchange and Dzyaloshinskii–Moriya (DM) interactions is able to stabilize each of the three types, depending on the specific structure of the DM interactions. Considering a three-dimensional spin lattice model, we provide a finite-temperature phase diagram featuring a stable anti-skyrmion lattice phase for a large range of temperatures. In addition, we also shed light on the creation and annihilation processes of these anti-skyrmion tubes and study the effects of the DM interaction strength on their typical size.

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.

Magnetic Skyrmions with Unconventional Helicity Polarization in a Van Der Waals Ferromagnet

Skyrmion helicity, which defines the spin swirling direction, is a fundamental parameter that may be utilized to encode data bits in future memory devices. Generally, in centrosymmetric ferromagnets, dipole skyrmions with helicity of -π/2 and π/2 are degenerate in energy, leading to equal populations of both helicities. On the other hand, in chiral materials where the Dzyaloshinskii-Moriya interaction (DMI) prevails and the dipolar interaction is negligible, only a preferred helicity is selected by the type of DMI. However, whether there is a rigid boundary between these two regimes remains an open question. Herein, the observation of dipole skyrmions with unconventional helicity polarization in a van der Waals ferromagnet, Fe_{5- δ} GeTe₂ , is reported. Combining magnetometry, Lorentz transmission electron microscopy, electrical transport measurements, and micromagnetic simulations, the short-range superstructures in Fe_{5- δ} GeTe₂ resulting in a localized DMI contribution, which breaks the degeneracy of the opposite helicities and leads to the helicity polarization, is demonstrated. Therefore, the helicity feature in Fe_{5- δ} GeTe₂ is controlled by both the dipolar interaction and DMI that the former leads to Bloch-type skyrmions with helicity of ±π/2 whereas the latter breaks the helicity degeneracy. This work provides new insights into the skyrmion topology in van der Waals materials.

Formation and Control of Zero-Field Antiskyrmions in Confining Geometries

Magnetic skyrmions and antiskyrmions have attracted much interest owing to their topological features and spintronic functionalities. In contrast to skyrmions, the generation of antiskyrmions relies on tunning both the magnitude and direction of the external magnetic field. Here, it is reported that antiskyrmions can be efficiently created via quenching and robustly persist at zero field in the Fe_1.9 Ni_0.9 Pd_0.2 P magnet with the S₄ -symmetry. It is demonstrated that well-ordered antiskyrmions form in a square lattice in a confining micrometer-scale square geometry, while the antiskyrmion lattice distorts in triangular, circular, or rotated-square geometry; the distortion depends on the relative configuration between sample edges and the two q-vectors arising from the anisotropic Dzyaloshinskii-Moriya interaction, in good agreement with micromagnetic simulations. It is also characterized transformations from antiskyrmions to skyrmions and nontopological bubbles at different directions and values of external field. These results demonstrate a roadmap for generating and controlling antiskyrmions in a confining geometry.

Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers

We investigate an instability toward a square-lattice formation of magnetic skyrmions in centrosymmetric layered systems. By focusing on a bilayer square-lattice structure with the inversion center at the interlayer bond instead of the atomic site, we numerically examine the stability of the square skyrmion crystal (SkX) based on an effective spin model with the momentum-resolved interaction in the ground state through the simulated annealing. As a result, we find that a layer-dependent staggered Dzyaloshinskii-Moriya (DM) interaction built in the lattice structure becomes the origin of the square SkX in an external magnetic field irrespective of the sign of the interlayer exchange interaction. The obtained square SkX is constituted of the SkXs with different helicities in each layer due to the staggered DM interaction. Furthermore, we show that the interplay between the staggered DM interaction and the interlayer exchange interaction gives rise to a double-Qstate with a uniform component of the scalar chirality in the low-field region. The present results provide another way of stabilizing the square SkX in centrosymmetric magnets, which will be useful to explore further exotic topological spin textures.

Observation of fractional spin textures in a Heusler material

Recently a zoology of non-collinear chiral spin textures has been discovered, most of which, such as skyrmions and antiskyrmions, have integer topological charges. Here we report the experimental real-space observation of the formation and stability of fractional antiskyrmions and fractional elliptical skyrmions in a Heusler material. These fractional objects appear, over a wide range of temperature and magnetic field, at the edges of a sample, whose interior is occupied by an array of nano-objects with integer topological charges, in agreement with our simulations. We explore the evolution of these objects in the presence of magnetic fields and show their interconversion to objects with integer topological charges. This means the topological charge can be varied continuously. These fractional spin textures are not just another type of skyrmion, but are essentially a new state of matter that emerges and lives only at the boundary of a magnetic system. The coexistence of both integer and fractionally charged spin textures in the same material makes the Heusler family of compounds unique for the manipulation of the real-space topology of spin textures and thus an exciting platform for spintronic and magnonic applications.

Skyrmions and anti-skyrmions are magnetic textures that have garnered much interest due to their stability. Here, Jena et al demonstrate the existence of fractional spin textures at the edges of Heusler alloy sample, which can have continuous variable topological charges.

Anisotropic Dzyaloshinskii-Moriya Interaction and Topological Magnetism in Two-Dimensional Magnets Protected by P4̅m2 Crystal Symmetry

As a fundamental magnetic parameter, Dzyaloshinskii-Moriya interaction (DMI), has gained a great deal of attention in the last two decades due to its critical role in formation of magnetic skyrmions. Recent discoveries of two-dimensional (2D) van der Waals (vdW) magnets has also gained a great deal of attention due to appealing physical properties, such as gate tunability, flexibility, and miniaturization. Intensive studies have shown that isotropic DMI stabilizes ferromagnetic (FM) topological spin textures in 2D magnets or their corresponding heterostructures. However, the investigation of anisotropic DMI and antiferromagnetic (AFM) topological spin configurations remains elusive. Here, we propose and demonstrate a family of 2D magnets with P4m2 symmetry-protected anisotropic DMI. More interestingly, various topological spin configurations, including FM/AFM antiskyrmion and AFM vortex-antivortex pair, emerge in this family. These results give a general method to design anisotropic DMI and pave the way toward topological magnetism in 2D materials using crystal symmetry.

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.

Study of Integer Spin S = 1 in the Polar Magnet β-Ni(IO3)2

Polar magnetic materials exhibiting appreciable asymmetric exchange interactions can potentially host new topological states of matter such as vortex-like spin textures; however, realizations have been mostly limited to half-integer spins due to rare numbers of integer spin systems with broken spatial inversion lattice symmetries. Here, we studied the structure and magnetic properties of the S = 1 integer spin polar magnet β-Ni(IO₃)₂ (Ni²⁺, d⁸, ³F). We synthesized single crystals and bulk polycrystalline samples of β-Ni(IO₃)₂ by combining low-temperature chemistry techniques and thermal analysis and characterized its crystal structure and physical properties. Single crystal X-ray and powder X-ray diffraction measurements demonstrated that β-Ni(IO₃)₂ crystallizes in the noncentrosymmetric polar monoclinic structure with space group P2₁. The combination of the macroscopic electric polarization driven by the coalignment of the (IO₃)⁻ trigonal pyramids along the b axis and the S = 1 state of the Ni²⁺ cation was chosen to investigate integer spin and lattice dynamics in magnetism. The effective magnetic moment of Ni²⁺ was extracted from magnetization measurements to be 3.2(1) µ_B, confirming the S = 1 integer spin state of Ni²⁺ with some orbital contribution. β-Ni(IO₃)₂ undergoes a magnetic ordering at T = 3 K at a low magnetic field, μ₀H = 0.1 T; the phase transition, nevertheless, is suppressed at a higher field, μ₀H = 3 T. An anomaly resembling a phase transition is observed at T ≈ 2.7 K in the C_p/T vs. T plot, which is the approximate temperature of the magnetic phase transition of the material, indicating that the transition is magnetically driven. This work offers a useful route for exploring integer spin noncentrosymmetric materials, broadening the phase space of polar magnet candidates, which can harbor new topological spin physics.

Spin and Orbital Effects on Asymmetric Exchange Interaction in Polar Magnets: M(IO3)2 (M = Cu and Mn)

Magnetic polar materials feature an astonishing range of physical properties, such as magnetoelectric coupling, chiral spin textures, and related new spin topology physics. This is primarily attributable to their lack of space inversion symmetry in conjunction with unpaired electrons, potentially facilitating an asymmetric Dzyaloshinskii-Moriya (DM) exchange interaction supported by spin-orbital and electron-lattice coupling. However, engineering the appropriate ensemble of coupled degrees of freedom necessary for enhanced DM exchange has remained elusive for polar magnets. Here, we study how spin and orbital components influence the capability of promoting the magnetic interaction by studying two magnetic polar materials, α-Cu(IO₃)₂ (²D) and Mn(IO₃)₂ (⁶S), and connecting their electronic and magnetic properties with their structures. The chemically controlled low-temperature synthesis of these complexes resulted in pure polycrystalline samples, providing a viable pathway to prepare bulk forms of transition-metal iodates. Rietveld refinements of the powder synchrotron X-ray diffraction data reveal that these materials exhibit different crystal structures but crystallize in the same polar and chiral P2₁ space group, giving rise to an electric polarization along the b-axis direction. The presence and absence of an evident phase transition to a possible topologically distinct state observed in α-Cu(IO₃)₂ and Mn(IO₃)₂, respectively, imply the important role of spin-orbit coupling. Neutron diffraction experiments reveal helpful insights into the magnetic ground state of these materials. While the long-wavelength incommensurability of α-Cu(IO₃)₂ is in harmony with sizable asymmetric DM interaction and low dimensionality of the electronic structure, the commensurate stripe AFM ground state of Mn(IO₃)₂ is attributed to negligible DM exchange and isotropic orbital overlapping. The work demonstrates connections between combined spin and orbital effects, magnetic coupling dimensionality, and DM exchange, providing a worthwhile approach for tuning asymmetric interaction, which promotes evolution of topologically distinct spin phases.

Field-free topological behavior in the magnetic domain wall of ferrimagnetic GdFeCo

Exploring and controlling topological textures such as merons and skyrmions has attracted enormous interests from the perspective of fundamental research and spintronic applications. It has been predicted theoretically and proved experimentally that the lattice form of topological meron-skyrmion transformation can be realized with the requirement of external magnetic fields in chiral ferromagnets. However, such topological transition behavior has yet to be verified in other materials. Here, we report real-space observation of magnetic topology transformation between meron pairs and skyrmions in the localized domain wall of ferrimagnetic GdFeCo films without the need of magnetic fields. The topological transformation in the domain wall of ferrimagnet is introduced by temperature-induced spin reorientation transition (SRT) and the underlying mechanism is revealed by micromagnetic simulations. The convenient electric-controlling topology transformation and driving motion along the confined domain wall is further anticipated, which will enable advanced application in magnetic devices.

Merons and Skyrmions, two topological spin-textures, have attracted a lot of interests due to their potential use in information storage. Here, the authors demonstrate the transformation of Meron pairs into Skyrmions without an applied magnetic field within domain walls of GdFeCo films.

Stimulated Nucleation of Skyrmions in a Centrosymmetric Magnet

Understanding the dynamics of skyrmion nucleation and manipulation is important for applications in spintronic devices. In this contribution, the spin textures at magnetic domain-boundaries stimulated by application of in-plane magnetic fields in a centrosymmetric kagome ferromagnet, Fe₃Sn₂, with thickness gradient are investigated using Lorentz transmission electron microscopy. Switching of the in-plane magnetic field is shown to induce a reversible transformation from magnetic stripes to skyrmions, or vice versa, at the interface between differently oriented domains. Micromagnetic simulations combined with experiments reveal that the rotatable anisotropy and thickness dependence of the response to the external in-plane field are the critical factors for the skyrmion formation. In addition, it is shown that the helicity of skyrmions can also be controlled using this dynamic process. The results suggest that magnetic materials with rotatable anisotropy are potential skyrmionic systems and provides a different approach for nucleation and manipulation of skyrmions in spintronic 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.

Current-Controlled Topological Magnetic Transformations in a Nanostructured Kagome Magnet

Topological magnetic charge Q is a fundamental parameter that describes the magnetic domains and determines their intriguing electromagnetic properties. The ability to switch Q in a controlled way by electrical methods allows for flexible manipulation of electromagnetic behavior in future spintronic devices. Here, the room-temperature current-controlled topological magnetic transformations between Q = -1 skyrmions and Q = 0 stripes or type-II bubbles in a kagome crystal Fe₃ Sn₂ are reported. It is shown that reproducible and reversible skyrmion-bubble and skyrmion-stripe transformations can be achieved by tuning the density of nanosecond pulsed current of the order of ≈10¹⁰ A m^-2 . Further numerical simulations suggest that spin-transfer torque combined with Joule thermal heating effects determine the current-induced topological magnetic transformations.

Nanoscale Noncollinear Spin Textures in Thin Films of a D2d Heusler Compound

Magnetic nano-objects, namely antiskyrmions and Bloch skyrmions, have been found to coexist in single-crystalline lamellae formed from bulk crystals of inverse tetragonal Heusler compounds with D_2d symmetry. Here evidence is shown for magnetic nano-objects in epitaxial thin films of Mn₂ RhSn formed by magnetron sputtering. These nano-objects exhibit a wide range of sizes with stability with respect to magnetic field and temperature that is similar to single-crystalline lamellae. However, the nano-objects do not form well-defined arrays, nor is any evidence found for helical spin textures. This is speculated to likely be a consequence of the poorer homogeneity of chemical ordering in the thin films. However, evidence is found for elliptically distorted nano-objects along perpendicular crystallographic directions within the epitaxial films, which is consistent with elliptical Bloch skyrmions observed in single-crystalline lamellae. Thus, these measurements provide strong evidence for the formation of noncollinear spin textures in thin films of Mn₂ RhSn. Using these films, it is shown that individual nano-objects can be deleted using a local magnetic field from a magnetic tip and collections of nano-objects can be similarly written. These observations suggest a path toward the use of these objects in thin films with D_2d symmetry as magnetic memory elements.

Interplay between Single-Ion and Two-Ion Anisotropies in Frustrated 2D Semiconductors and Tuning of Magnetic Structures Topology

The effects of competing magnetic interactions in stabilizing different spin configurations are drawing renewed attention in order to unveil emerging topological spin textures and to highlight microscopic mechanisms leading to their stabilization. The possible key role of the two-site exchange anisotropy in selecting specific helicity and vorticity of skyrmionic lattices has only recently been proposed. In this work, we explore the phase diagram of a frustrated localized magnet characterized by a two-dimensional centrosymmetric triangular lattice, focusing on the interplay between the two-ion anisotropy and the single-ion anisotropy. The effects of an external magnetic field applied perpendicularly to the magnetic layer, are also investigated. By means of Monte Carlo simulations, we find an abundance of different spin configurations, going from trivial to high-order Q skyrmionic and meronic lattices. In closer detail, we find that a dominant role is played by the two-ion over the single-ion anisotropy in determining the planar spin texture; the strength and the sign of single ion anisotropy, together with the magnitude of the magnetic field, tune the perpendicular spin components, mostly affecting the polarity (and, in turn, the topology) of the spin texture. Our analysis confirms the crucial role of the anisotropic symmetric exchange in systems with dominant short-range interactions; at the same time, we predict a rich variety of complex magnetic textures, which may arise from a fine tuning of competing anisotropic mechanisms.

Dipolar-stabilized first and second-order antiskyrmions in ferrimagnetic multilayers

Skyrmions and antiskyrmions are topologically protected spin structures with opposite vorticities. Particularly in coexisting phases, these two types of magnetic quasi-particles may show fascinating physics and potential for spintronic devices. While skyrmions are observed in a wide range of materials, until now antiskyrmions were exclusive to materials with D2d symmetry. In this work, we show first and second-order antiskyrmions stabilized by magnetic dipole-dipole interaction in Fe/Gd-based multilayers. We modify the magnetic properties of the multilayers by Ir insertion layers. Using Lorentz transmission electron microscopy imaging, we observe coexisting antiskyrmions, Bloch skyrmions, and type-2 bubbles and determine the range of material properties and magnetic fields where the different spin objects form and dissipate. We perform micromagnetic simulations to obtain more insight into the studied system and conclude that the reduction of saturation magnetization and uniaxial magnetic anisotropy leads to the existence of this zoo of different spin objects and that they are primarily stabilized by dipolar interaction.

Elastocaloric-effect-induced adiabatic magnetization in paramagnetic salts due to the mutual interactions

The temperature change under adiabatic stress, i.e., the elastocaloric effect, is a well-understood phenomenon and of particular interest due to its potential application in alternative ways for refrigeration. Here, we demonstrate that in the regime of low-temperatures (a few mK) real paramagnets can be magnetized when compressed adiabatically without applied magnetic field. Such adiabatic magnetization is a genuine many-body problem, stemming from the inherent dipolar mutual interactions between adjacent magnetic moments. We showcase experimental setups to carry out adiabatic magnetization and thus to access such a subtle effect. Perspectives of further investigations by controlling the mutual interactions in Bose-Einstein condensates in magnetic insulators and dipolar spin-ice systems via the adiabatic increase of temperature are also presented. Yet, we discuss the connection between the elastic Grüneisen parameter and the shift on the critical temperature of second-order phase transitions under adiabatic stress, as well as its connection with the Ehrenfest relation.

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.

Room-temperature antiskyrmions and sawtooth surface textures in a non-centrosymmetric magnet with S4 symmetry

Topological spin textures have attracted much attention both for fundamental physics and spintronics applications. Among them, antiskyrmions possess a unique spin configuration with Bloch-type and Néel-type domain walls owing to anisotropic Dzyaloshinskii-Moriya interaction in the non-centrosymmetric crystal structure. However, antiskyrmions have thus far only been observed in a few Heusler compounds with D_2d symmetry. Here we report a new material, Fe_1.9Ni_0.9Pd_0.2P, in a different symmetry class (S₄), in which antiskyrmions exist over a wide temperature range that includes room temperature, and transform into skyrmions on changing magnetic field and lamella thickness. The periodicity of magnetic textures greatly depends on the crystal thickness, and domains with anisotropic sawtooth fractals were observed at the surface of thick crystals and attributed to the interplay between the dipolar interaction and the Dzyaloshinskii-Moriya interaction as governed by crystal symmetry. Our findings provide an arena in which to study antiskyrmions, and should stimulate further research on topological spin textures and their applications.

Evolution and competition between chiral spin textures in nanostripes with D 2d symmetry

Chiral spin textures are of considerable interest for applications in spintronics. It has recently been shown that magnetic materials with D _2d symmetry can sustain several distinct spin textures. Here, we show, using Lorentz transmission electron microscopy, that single and double chains of antiskyrmions can be generated at room temperature in nanostripes less than 0.5 μm in width formed from the D _2d Heusler compound Mn_1.4Pt_0.9Pd_0.1Sn. Typically, truncated helical spin textures are formed in low magnetic fields, whose edges are terminated by half antiskyrmions. These evolve into chains of antiskyrmions with increasing magnetic field. Single chains of these objects are located in the middle of the nanostripes even when the stripes are much wider than the antiskyrmions. Moreover, the chains can even include elliptical Bloch skyrmions depending on details of the applied magnetic field history. These findings make D _2d materials special and highly interesting for applications such as magnetic racetrack memory storage devices.

Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer

Topological spin structures, such as magnetic skyrmions, hold great promises for data storage applications, thanks to their inherent stability. In most cases, skyrmions are stabilized by magnetic fields in non-centrosymmetric systems displaying the chiral Dzyaloshinskii-Moriya exchange interaction, while spontaneous skyrmion lattices have been reported in centrosymmetric itinerant magnets with long-range interactions. Here, a spontaneous anti-biskyrmion lattice with unique topology and chirality is predicted in the monolayer of a semiconducting and centrosymmetric metal halide, NiI₂. Our first-principles and Monte Carlo simulations reveal that the anisotropies of the short-range symmetric exchange, when combined with magnetic frustration, can lead to an emergent chiral interaction that is responsible for the predicted topological spin structures. The proposed mechanism finds a prototypical manifestation in two-dimensional magnets, thus broadening the class of materials that can host spontaneous skyrmionic states.

Bloch Lines Constituting Antiskyrmions Captured via Differential Phase Contrast

Much scientific capital has been directed toward exotic magnetic spin textures called Bloch lines, that is, Néel-type line boundaries within domain walls, because their geometry promises high-density magnetic storage. While predicted to arise in high-anisotropy magnets, bulk soft magnets, and thin films with in-plane magnetization, Bloch lines also constitute magnetic antiskyrmions, that is, topological antiparticles of skyrmions. Most domain walls occur as Bloch-type or Néel-type, in which the magnetization rotates parallel or perpendicular to the domain wall across its profile, respectively. The Bloch lines' Néel-type rotation and their minute size make them difficult to directly measure. This work utilizes differential phase contrast (DPC) scanning transmission electron microscopy (STEM) to measure the in-plane magnetization of Bloch lines within antiskyrmions emergent in a non-centrosymmetric Heusler magnet with D_2d symmetry, Mn_1.4 Pt_0.9 Pd_0.1 Sn, in addition to Bloch-type skyrmions in an FeGe magnet with B20-type crystal structure to benchmark the DPC technique. Both in-focus measurement and identification of Bloch lines at the antiskyrmion's corners are provided.

Real-Space Observation of Topological Defects in Extended Skyrmion-Strings

Exotic topological spin textures such as emergent magnetic monopole/anti-monopoles (hedgehog/anti-hedgehog) in the metastable extended skyrmion-strings attract much attention to the fundamental physics owing to their novel electromagnetic properties. However, the direct imaging of such spin textures is lacking. Here, we report the real-space observation of emergent magnetic monopoles involved in extended skyrmion-strings by Lorentz transmission electron microscopy (TEM) in combination with micromagnetic simulations. The in-plane extended skyrmion-strings are observed directly by Lorentz TEM to accompany the topological hedgehog-like defect, where the skyrmion-string terminates or merges with another skyrmion-string, as well as the surface-related defects where skyrmion-string bends 90° and ends on the surface. We also demonstrate the transformation of a metastabilized lattice of out-of-plane short skyrmion-strings into an in-plane array of extended skyrmion-strings by tuning the magnitude of oblique fields in a room-temperature helimagnet, revealing the stability of such topological spin textures and the possibility to control them.

Electric-Field Switching of Magnetic Topological Charge in Type-I Multiferroics

Applying electric field to control magnetic properties is a very efficient way for spintronics devices. However, the control of magnetic characteristics by electric fields is not straightforward, due to the time-reversal symmetry of magnetism versus spatial inversion symmetry of electricity. Such fundamental difficulty makes it challenging to modify the topology of magnetic skyrmionic states with electric field. Here, we propose a novel mechanism that realizes the electric-field (E) switching of magnetic topological charge (Q) in a controllable and reversible fashion, through the mediation of electric polarization (P) and Dzyaloshinskii-Moriya interaction (D). Such a mechanism is coined here EPDQ. Its validity is demonstrated in a multiferroic VOI_{2} monolayer, which is predicted to host magnetic bimerons. The change in magnetic anisotropy is found to play a crucial role in realizing the EPDQ process and its microscopic origin is discussed. Our study thus provides a new approach toward the highly desired electric-field control of magnetism.

Tunable Magnetic Antiskyrmion Size and Helical Period from Nanometers to Micrometers in a D2d Heusler Compound

Skyrmions and antiskyrmions are magnetic nano-objects with distinct chiral, noncollinear spin textures that are found in various magnetic systems with crystal symmetries that give rise to specific Dzyaloshinskii-Moriya exchange vectors. These magnetic nano-objects are associated with closely related helical spin textures that can form in the same material. The skyrmion size and the period of the helix are generally considered as being determined, in large part, by the ratio of the magnitude of the Heisenberg to that of the Dzyaloshinskii-Moriya exchange interaction. In this work, it is shown by real-space magnetic imaging that the helix period λ and the size of the antiskyrmion d_aSk in the D_2d compound Mn_1.4 PtSn can be systematically tuned by more than an order of magnitude from ≈100 nm to more than 1.1 µm by varying the thickness of the lamella in which they are observed. The chiral spin texture is verified to be preserved even up to micrometer-thick layers. This extreme size tunability is shown to arise from long-range magnetodipolar interactions, which typically play a much less important role for B20 skyrmions. This tunability in size makes antiskyrmions very attractive for technological applications.