Diffusion of particles has wide repercussions ranging from particle-based soft matter systems to solid state systems with particular electronic properties. Recently, in the field of magnetism, diffusion of magnetic skyrmions, topologically stabilized quasi-particles, has been demonstrated. Here we show that by applying a magnetic in-plane field and therefore breaking the symmetry of the system, the skyrmion diffusion becomes anisotropic with faster diffusion parallel to the field axis and slower diffusion perpendicular to it. We furthermore show that the absolute value of the applied field controls the absolute values of the diffusion coefficients so that one can thereby uniquely tune both the orientation of the diffusion and its strength. Based on the stochastic Thiele equation, we can explain the observed anisotropic diffusion as a result of the elliptical deformation of the skyrmions by the application of the in-plane field.
Magnetic skyrmions have attracted broad attention during recent years because they are regarded as promising candidates as bits of information in novel data storage devices. A broad range of theoretical and experimental investigations have been conducted with the consideration of rotational symmetric skyrmions in isotropic environments. However, one naturally observes a huge variety of anisotropic behavior in many experimentally relevant materials. In the present work, we investigate the influence of anisotropic environments onto the formation and behavior of the non-collinear spin states of s…
Magnetic skyrmions are localized particle-like nontrivial swirls that are promising in building high-performance topological spintronic devices. The read-out functions in skyrmionic devices require the translation of magnetic skyrmions to electrical signals. Here, we report combined real-space magnetic imaging and anisotropic magnetoresistance studies on dipolar skyrmions. A single skyrmion chain and single skyrmion are observed using Lorentz transmission electron microscopy imaging. Meanwhile, the field, helicity, and skyrmion count dependence of anisotropic magnetoresistance of the Fe3Sn2 na…
Topological defects in magnetism have attracted great attention due to fundamental research interests and potential novel spintronics applications. Rich examples of topological defects can be found in nanoscale non-uniform spin textures, such as monopoles, domain walls, vortices, and skyrmions. Recently, skyrmions stabilized by the Dzyaloshinskii-Moriya interaction have been studied extensively. However, the stabilization of antiskyrmions is less straightforward. Here, using numerical simulations we demonstrate that antiskyrmions can be a stable spin configuration in the presence of anisotropi…
We study the equilibrium and dynamical properties of skyrmions in thin films of chiral magnets with oblique magnetic field. The shape of an individual skyrmion is non-circular and the skyrmion density decreases with the tilt angle from the normal of films. As a result, the interaction between two skyrmions depends on the relative angle between them in addition to their separation. The triangular lattice of skyrmions under a perpendicular magnetic field is distorted into a centered rectangular lattice for a tilted magnetic field. For a low skyrmion density, skyrmions form a chain like structure…
Paradoxical Topological Soliton Lattice in Anisotropic Frustrated Chiral Magnets
School of Physical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute（国家科学教育研究中心物理科学学院，霍米·巴巴国立学院附属机构）；Peter Grünberg Institute, Forschungszentrum Jülich（彼得·格林伯格研究所，于利希研究中心）
The consequences of nonlinear anisotropic damping, driven by the presence of Rashba spin-orbit coupling in thin ferromagnetic metals, are examined for the dynamics of topological magnetic solitons such as domain walls, vortices, and skyrmions. The damping is found to affect Bloch and Néel walls differently in the steady state regime below Walker breakdown and leads to a monotonic increase in the wall velocity above this transition for large values of the Rashba coefficient. For vortices and skyrmions, a generalization of the damping tensor within the Thiele formalism is presented. It is found …
Magnetic skyrmions are topological solitons with a nanoscale winding spin texture that hold promise for spintronics applications. Until now, skyrmions have been observed in a variety of magnets that exhibit nearly parallel alignment for the neighbouring spins, but theoretically, skyrmions with anti-parallel neighbouring spins are also possible. The latter, antiferromagnetic skyrmions, may allow more flexible control compared to the conventional ferromagnetic skyrmions. Here, by combining neutron scattering and Monte Carlo simulations, we show that a fractional antiferromagnetic skyrmion lattic…
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, NiI$_2$. Our fi…
The length scale of the magnetization gradients in chiral magnets is determined by the relativistic Dzyaloshinskii-Moriya interaction. Thus, even conventional spin-transfer torques are controlled by the relativistic spin-orbit coupling in these systems, and additional relativistic corrections to the current-induced torques and magnetization damping become important for a complete understanding of the current-driven magnetization dynamics. We theoretically study the effects of reactive and dissipative homogeneous spin-orbit torques and anisotropic damping on the current-driven skyrmion dynamics…
An external off-resonant pumping is proposed as a tool to control the Dzyaloshinskii-Moriya interaction (DMI) in ferromagnetic layers with strong spin-orbit coupling. Combining theoretical analysis with numerical simulations for an $s$-$d$-like model we demonstrate that linearly polarized off-resonant light may help stabilizing novel noncollinear magnetic phases by inducing a strong anisotropy of the DMI. We also investigate how with the application of electromagnetic pumping one can control the stability, shape and size of individual skyrmions to make them suitable for potential applications.
The 212 species of structural phase transitions which break macroscopic symmetry are analyzed with respect to the occurrence of time-reversal invariant vector and bidirector order parameters. The possibility of discerning the orientational domain states of the low-symmetry phase by these `vectorlike' physical properties has been derived using a computer algorithm exploiting the concept of polar, axial, chiral and neutral dipoles. It is argued that for species 32 > 3, 422 > 4 and 622 > 6, Bogdanov-Yablonskii phenomenological theory for a ferromagnetic Bloch Skyrmions applies also to the ferroel…
We studied the symmetry of magnetic properties and the resulting magnetic textures in ultra-thin epitaxial Au$_{0.67}$Pt$_{0.33}$/Co/W, a model system exhibiting perpendicular magnetic anisotropy and interface Dzyaloshinskii-Moriya interaction (DMI). As a peculiar feature, the C$_\mathrm{2v}$ crystal symmetry induced by the Co/W interface results in an additional uniaxial in-plane magnetic anisotropy in the cobalt layer. Photoemission electron microscopy with magnetic sensitivity reveals the formation of self-organized magnetic stripe domains oriented parallel to the hard in-plane magnetizatio…
We investigate the anisotropic nature of magnetocrystalline coupling between the crystallographic and skyrmion crystal (SKX) lattices in the chiral magnet MnSi by magnetic field-angle resolved resonant ultrasound spectroscopy. Abrupt changes are observed in the elastic moduli and attenuation when the magnetic field is parallel to the [011] crystallographic direction. These observations are interpreted in a phenomenological Ginzburg-Landau theory that identifies switching of the SKX orientation to be the result of an anisotropic magnetocrystalline coupling potential. Our paper sheds new light o…
Integrating topologically stabilized magnetic textures such as skyrmions as nanoscale information carriers into future technologies requires the reliable control by electric currents. Here, we uncover that the relevant skyrmion Hall effect, which describes the deflection of moving skyrmions from the current flow direction, acquires important corrections owing to anisotropic spin-orbit torques that alter the dynamics of topological spin structures. Thereby, we propose a viable means for manipulating the current-induced motion of skyrmions and antiskyrmions. Based on these insights, we demonstra…
Emergent Skyrmion Hall Effect in $d$-wave Altermagnets at Finite Temperature
School of Physics Science and Information Technology, Liaocheng University（聊城大学物理科学与信息工程学院）；School of Physics and State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China（电子科技大学物理学院电子薄膜与集成器件国家重点实验室）；Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials and Institute for Advanced Materials, South China Academy of Advanced Optoelectronics, South China Normal University（华南师范大学广东省量子工程与量子材料重点实验室先进材料研究院南方先进光电子研究院）
Hybrid micromagnetic and atomistic modeling of magnetization dynamics induced by engineered defects
Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文系）；WISE - Wallenberg Initiative Materials Science for Sustainability, Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文系瓦伦堡可持续性材料科学倡议）；PDC Center for High Performance Computing, KTH Royal Institute of Technology（瑞典皇家理工学院PDC高性能计算中心）
Topological magnetic textures, characterized by integer topological charge $S$, are potential candidates in future magnetic logic and memory devices, due to their smaller size and expected low threshold current density for their motion. An essential requirement to stabilize them is the Dzyaloshinskii-Moriya interaction (DMI) which promotes a particular chirality, leading to a unique value of $S$ in a given material. However, recently coexistence of skyrmions and antiskyrmions, with opposite topological charge, in frustrated ferromagnets has been predicted using $J_1$--$J_2$--$J_3$ classical He…
Magnetic skyrmions are mesmerizing spin textures with peculiar topological and dynamical properties, typically the product of competing interactions in ferromagnets, and with great technological potential [1-5]. Researchers have long wondered whether analogous electric skyrmions might exist in ferroelectrics, maybe featuring novel behaviors and possibilities for electric and mechanical control. The results thus far are modest, though: an electric equivalent of the most typical magnetic skyrmion (which would rely on a counterpart of the Dzyaloshinskii-Moriya interaction) seems all but impossibl…
The topologically non-trivial nano-whirls, called magnetic skyrmions, are often considered attractive for spintronic applications like the racetrack data storage device. However, skyrmions do not move parallel to applied currents and typically do not coexist with other nano-objects, making the realization of such storage concepts difficult. Herein we consider materials with an anisotropic DMI, like tetragonal Heusler materials, and show that four distinct types of topologically trivial bubbles can coexist. We show that each of them can be written by spin torques and that they can be distinguis…
We have used Brillouin Light Scattering spectroscopy to independently determine the in-plane Magneto-Crystalline Anisotropy and the Dzyaloshinskii-Moriya Interaction (DMI) in out-of-plane magnetized Au/Co/W(110). We found that the DMI strength is 2-3 times larger along the bcc$[\bar{1}10]$ than along the bcc$[001]$ direction. We use analytical considerations to illustrate the relationship between the crystal symmetry of the stack and the anisotropy of microscopic DMI. Such an anisotropic DMI is the first step to realize isolated elliptical skyrmions or anti-skyrmions in thin film systems with …
Skyrmions are topologically protected non-collinear magnetic structures. Their stability and dynamics, arising from their topological character, have made them ideal information carriers e.g. in racetrack memories. The success of such a memory critically depends on the ability to stabilize and manipulate skyrmions at low magnetic fields. The driving force for skyrmion formation is the non-collinear Dzyaloshinskii-Moriya exchange interaction (DMI) originating from spin-orbit coupling (SOC). It competes with both the nearest neighbour Heisenberg exchange interaction and the magnetic anisotropy, …
We show theoretically by numerically solving the Landau-Lifshitz-Gilbert equation with a classical spin model on a two-dimensional system that both magnetic skyrmions and skyrmion lattices can be moved with microwave magnetic fields. The mechanism is enabled by breaking the axial symmetry of the skyrmion, for example through application of a static in-plane external field. The net velocity of the skyrmion depends on the frequency and amplitude of the microwave fields as well as the strength of the in-plane field. The maximum velocity is found where the frequency of the microwave coincides with…
We find closed-form solution of the Euler equation for a chiral magnet in terms of a skyrmion or a meron depending on the relative strengths of magnetic anisotropy and magnetic field. We show that the relevant length scales for these solutions primarily depend on the strengths of Dzyaloshinskii-Moriya interaction through its ratios, respectively, with magnetic field and magnetic anisotropy. We thus unambiguously determine the parameter dependencies on the radius of the topological structures particularly of the skyrmions, showing an excellent agreement with experiments and first-principle stud…
GaV$_4$S$_8$ is a multiferroic semiconductor hosting magnetic cycloid (Cyc) and Néel-type skyrmion lattice (SkL) phases with a broad region of thermal and magnetic stability. Here, we use time-resolved magneto-optical Kerr spectroscopy and micro-magnetic simulations to demonstrate the coherent generation of collective spin excitations in the Cyc and SkL phases driven by an optically-induced modulation of uniaxial anisotropy. Our results shed light on spin-dynamics in anisotropic materials hosting skyrmions and pave a new pathway for the optical control of their magnetic order.
Department of Physics, School of Science, Westlake University（西湖大学理学院物理系）；Institute of Natural Sciences, Westlake Institute for Advanced Study（西湖高等研究院自然科学研究院）
Self-organisation into spatially modulated structures has different nature from phase transition into uniform states. Skyrmions and half-skyrmions (merons) are representatives of such structures and are utilised in designing magnetoelectric, optical, and mechanoresponsive materials by controlling topological phases. However, skyrmions and half-skyrmions in molecular solids are rarely studied, though there is a universality in theoretical descriptions between magnetic and molecular systems with chiral interactions. Here we develop a simple physical system for controlling topological phases in a…
Topologically non trivial 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 Co$_{8}$Zn$_{8}$Mn$_{4}$ forms an above room temperature triangular skyrmion lattice. Here we report the synthesis procedure and characterization of a polycrystalline Co$_{8}$Zn$_{8}$Mn$_{4}$ bulk sample. We employ powder x-ray diffraction…
We present a combined analytical and numerical micromagnetic study of the equilibrium energy, size and shape of anti-skyrmionic magnetic configurations. Anti-skyrmions can be stabilized when the Dzyaloshinskii-Moriya interaction has opposite signs along two orthogonal in-plane directions, breaking the magnetic circular symmetry. We compare the equilibrium energy, size and shape of anti-skyrmions and skyrmions that are stabilized respectively in environments with anisotropic and isotropic Dzyaloshinskii-Moriya interaction, but with the same strength of the magnetic interactions.When the dipolar…
Writing and erasing skyrmions by single ultrafast laser pulses in monolayer Janus 2D magnets
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Humboldt-Universität zu Berlin（柏林洪堡大学）；Center for Quantum Matter, School of Physics, Zhejiang University（浙江大学物理学院量子物质中心）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料能源研究中心）；University of Chinese Academy of Sciences（中国科学院大学）
Room-temperature sub-100 nm Néel-type skyrmions in non-stoichiometric van der Waals ferromagnet $\rm Fe_{3-x}GaTe_{2}$ with ultrafast laser writability
Magnetic skyrmions are topological spin textures promising for future high-density and nonvolatile memory. It is crucial to understand the current-driven skyrmion dynamics in the presence of deformation, of which an analytical model, however, remains elusive. Here we extend Thiele's model by considering both the radial and tangential forces. Our model attributes the skyrmion deformation to the current-induced rotational symmetry breaking, which includes magnetization canting and domain wall width variation. Our predictions of skyrmion radius and nonlinear dynamics are consistent with micromagn…
Magnetic skyrmions are chiral nanoscale spin textures which are usually induced by Dzyaloshinskii-Moriya interaction (DMI). Recently, magnetic skyrmions have been observed in two-dimensional (2D) van der Waals (vdW) ferromagnetic materials, such as Fe$_{3}$GeTe$_{2}$. The electric control of skyrmions is important for their potential application in low-power memory technologies. Here, we predict that DMI and magnetic skyrmions in a Fe$_{3}$GeTe$_{2}$ monolayer can be controlled by ferroelectric polarization of an adjacent 2D vdW ferroelectric In$_{2}$Se$_{3}$. Based on density functional theor…
Magnetic skyrmions were thought to be stabilised only in inversion-symmetry breaking structures, but skyrmion lattices were recently discovered in inversion symmetric Gd-based compounds, spurring questions of the stabilisationmechanism. A natural consequence of a recent theoretical proposal, a coupling between itinerant electrons and localised magnetic moments, is that the skyrmions are amenable to detection using even non-magnetic probes such as spectroscopic-imaging scanning tunnellingmicroscopy (SI-STM). Here SI-STM observations of GdRu$_2$Si$_2$ reveal patterns in the local density of stat…
We present a comprehensive theory of the magnetic phases in monolayer nickel-based Janus dihalides (NiIBr, NiICl, NiBrCl) through a combination of first-principles calculations and atomistic simulations. Phonon band structure calculations and finite temperature molecular dynamics simulations show that Ni-dihalide Janus monolayers are stable. The parameters of the interacting spin Hamiltonian extracted from ab initio calculations show that nickel-dihalide Janus monolayers exhibit varying degrees of magnetic frustration together with a large Dzyaloshinskii-Moriya interaction due to their inheren…
Using Monte Carlo (MC) simulations, we study the skyrmion stability/instability as a response to uniaxial mechanical stresses. Skyrmions emerge in chiral magnetic materials as a stable spin configuration under external magnetic field $\vec{B}$ with the competition of ferromagnetic interaction and Dzyaloshinskii-Moriya interaction (DMI) at low temperature $T$. Skyrmion configurations are also known to be stable (unstable) under a compressive stress applied parallel (perpendicular) to $\vec{B}$. To understand the origin of such experimentally confirmed stability/instability, we use the Finsler g…
Anisotropic mesoscale magnetic scattering across the spin-reorientation transition in TbMn6Sn6
Spallation Neutron Source Science Center（散裂中子源科学中心）；Institute of High Energy Physics, Chinese Academy of Sciences (CAS)（中国科学院高能物理研究所）；Guangdong Provincial Key Laboratory of Extreme Conditions（广东省极端条件重点实验室）
We study realizations of spirals and skyrmions in two-dimensional antiferromagnets with a triangular lattice on an inversion-symmetry-breaking substrate. As a possible material realization, we investigate the adsorption of transition-metal atoms (Cr, Mn, Fe, or Co) on a monolayer of MoS$_2$, WS$_2$, or WSe$_2$ and obtain the exchange, anisotropy, and Dzyaloshinskii-Moriya interaction parameters using first-principles calculations. Using energy minimization and parallel-tempering Monte-Carlo simulations, we determine the magnetic phase diagrams for a wide range of interaction parameters. We fin…
We report the feasibility of using magnetoentropic mapping for the rapid identification of magnetic cycloid and skyrmion phases in uniaxial systems, based on the GaV4S8 and GaV4Se8 model skyrmion hosts with easy-axis and easy-plane anisotropies respectively. We show that these measurements can be interpreted with the help of a simple numerical model for the spin Hamiltonian to yield unambiguous assignments for both single phase regions and phase boundaries. In the two lacunar spinel chemistries, we obtain excellent agreement between the measured magnetoentropic features and a minimal spin Hami…
The centrosymmetric tetragonal itinerant magnet EuAl$_{4}$ exhibits an intricate magnetic phase diagram including rhombic and square skyrmion-lattice (SkL) phases in the external magnetic field. Here, we report a multi-axis dilatometric investigation of EuAl$_{4}$ by means of a newly designed fiber-Bragg-grating technique complemented by a resonant x-ray scattering experiment, revealing anisotropic magnetostriction and magnetovolume effect associated with successive phase transitions. The rhombic and square SkL phases are found to possess $\sim$0.10% and $\sim$0.03% orthorhombic structural dis…
It is shown here that a Kagomé magnet, with Heisenberg and Dzyaloshinskii-Moriya interactions causes non trivial topological and chiral magnetic properties. Chirality---that is, left or right handedness---is a very important concept in a broad range of scientific areas, and particularly, in condensed matter physics. Inversion symmetry breaking relates chirality with skyrmions, that are protected field configurations with particle-like and topological properties. Here, the reported numerical simulations and theoretical considerations reveal that the magnetic excitations of the Kagomé magnet can…
Skyrmion stabilization in novel magnetic systems with the B20 crystal structure is reported here, primarily based on theoretical results. The focus is on the effect of alloying on the 3d sublattice of the B20 structure by substitution of heavier 4d and 5d elements, with the ambition to tune the spin-orbit coupling and its influence on magnetic interactions. State-of-the-art methods based on density functional theory are used to calculate both isotropic and anisotropic exchange interactions. Significant enhancement of the Dzyaloshinskii-Moriya interaction is reported for 5d-doped FeSi and CoSi,…
Skyrmions can be stabilized in magnetic systems with broken inversion symmetry and chiral interactions, such as Dzyaloshinskii-Moriya interactions (DMI). Further, compensation of magnetic moments in ferrimagnetic materials can significantly reduce magnetic dipolar interactions, which tend to favor large skyrmions. Tuning DMI is essential to control skyrmion properties, with symmetry breaking at interfaces offering the greatest flexibility. However, in contrast to the ferromagnet case, few studies have investigated interfacial DMI in ferrimagnets. Here we present a systematic study of DMI in fe…
Understanding the dynamics of the magnetic skyrmion, a particle-like topologically stable spin texture, and its response dynamics to external fields are indis-pensable for the applications in spintronic devices. In this letter, the Lorentz transmis-sion electron microscopy (LTEM) was used to investigate the spin chirality of the mag-netic skyrmion bubbles (SKBs) in the centrosymmetric magnet MnNiGa at room tem-perature. The reversal of SKBs excited by the in-plane magnetic field has been revealed. Moreover, the collective behavior of interacting spin chirality can be manipulated by reversing t…
