The chiral spin textures of a two-dimensional (2D) triangular system, where both antiferromagnetic (AF) Heisenberg exchange and chiral Dzyaloshinsky-Moriya interactions co-exist, are investigated numerically with an optimized quantum Monte Carlo method based on mean-field theory. We find that: helical, skyrmionic and vortical AF crystals can be formed when an external magnetic field is applied perpendicular to the 2D monolayer; the sizes of these skyrmions and vortices change abruptly at several critical points of the external magnetic field; each of these AF crystals can be decomposed into three periodical ferromagnetic (FM) sublattices. The quantum ingredient implemented into the theoeretical framework helps to track the existence of AF skyrmion lattices down to low temperatures.
Magnetic skyrmions are nano-scale spin structures that are promising for ultra-dense memory and logic devices. Recent progresses in two-dimensional magnets encourage the idea to realize skyrmionic states in freestanding monolayers. However, monolayers such as CrI3 lack Dzyaloshinskii-Moriya interactions (DMI) and thus do not naturally exhibit skyrmions but rather a ferromagnetic state. Here we propose the fabrication of Cr(I,X)3 Janus monolayers, in which the Cr atoms are covalently bonded to the underlying I ions and top-layer Br or Cl atoms. By performing first-principles calculations and Mo…
Antiferromagnetic skyrmion crystal (AF-SkX), a regular array of antiferromagnetic skyrmions, is a fundamental phenomenon in the field of condensed-matter physics. So far, only very few proposals have been made to realize the AF-SkX, and most based on three-dimensional (3D) materials. Herein, using first-principles calculations and Monte-Carlo simulations, we report the identification of AF-SkX in two-dimensional lattice of Janus monolayer CrSi2N2As2. Arising from the broken inversion symmetry and strong spin-orbit coupling, large Dzyaloshinskii-Moriya interaction is obtained in Janus monolayer…
We investigate the magnetic phase diagram of 1T-vanadium dichalcogenide monolayers in Janus configuration (VSeTe, VSSe, and VSTe) from first principles. The magnetic exchange, magnetocrystalline anisotropy and Dzyaloshinskii-Moriya interaction (DMI) are computed using density functional theory calculations, while the temperature- and field-dependent magnetic phase diagram is simulated using large-scale atomistic spin modeling in the presence of thermal fluctuations. The boundaries between magnetic ordered phases and paramagnetic phases are determined by cross-analyzing the average topological …
In this letter, we report the visualization of topologically protected spin textures, in the form of magnetic skyrmions, in recently discovered monoatomic-thin two-dimensional CrI$_3$. By combining density functional theory and atomistic spin dynamic simulation, we demonstrate that an application of out-of-plane electric field to CrI$_3$ lattice favors the formation of sub-10 nm skyrmions at 0 K temperature. The spin texture arises due to a strong correlation between magneto-crystalline anisotropy, Dzyaloshinskii-Moriya interaction and the vertical electric field, whose shape and size could be…
We report the current-driven dynamics of frustrated skyrmions in an antiferromagnetically exchange coupled bilayer system, where the bilayer skyrmion consists of two monolayer skyrmions with opposite skyrmion numbers $Q$. We show that the in-plane current-driven bilayer skyrmion moves in a straight path, while the out-of-plane current-driven bilayer skyrmion moves in a circular path. It is found that the in-plane current-driven mobility of a bilayer skyrmion is much better than the monolayer one at a large ratio of $β/α$, where $α$ and $β$ denote the damping parameter and non-adiabatic spin tr…
Recently, great effort has been devoted to the search for two-dimensional (2D) ferromagnetic materials with inherent strong Dzyaloshinskii--Moriya interaction (DMI). Here, through a first-principles approach, we systematically investigate the effect of biaxial strain on the DMI, the Heisenberg exchange interaction, and the magnetic anisotropy energy (MAE) of Janus Cr$_{2}$X$_{3}$Y$_{3}$ (X, Y = Cl, Br, I, X $\neq$ Y) monolayers. Both DMI and MAE can be significantly enhanced by tensile strain, while a reversal of the chirality of DMI in Cr$_{2}$Cl$_{3}$Br$_{3}$ and a switch of MAE from off-pla…
Chiral spin textures are fundamentally interesting, with promise for device applications. Stabilizing chirality is conventionally achieved by introducing Dzyaloshinskii-Moriya interaction (DMI) in asymmetric multilayers where the thickness of each layer is at least a few monolayers. Here we report an ultrasensitive chirality switching in (Ni/Co)n multilayer induced by capping with only 0.22 monolayer of Pd. Using spin-polarized low-energy electron microscopy, we monitor the gradual evolution of domain walls from left-handed to right-handed Neel walls and quantify the DMI induced by the Pd capp…
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…
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…
Ordering of the frustrated classical Heisenberg model on the triangular-lattice with an incommensurate spiral spin structure is studied under magnetic fields by means of a mean-field analysis and a Monte Carlo simulation. Several types of multiple-q states including the "skyrmion-lattice" state is observed in addition to the standard single-q state. In contrast to the Dzyaloshinskii-Moriya interaction driven system, the present model allows both skyrmions and anti-skyrmions, together with a new thermodynamic phase where skyrmion and anti-skyrmion lattices form a domain state.
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）
Chromium iodide monolayers, which have different magnetic properties in comparison to the bulk chromium iodide, have been shown to form skyrmionic states in applied electromagnetic fields or in Janus-layer devices. In this work, we demonstrate that spin-canted solutions can be induced into monolayer chromium iodide by select substitution of iodide atoms with isovalent impurities. Several concentrations and spatial configurations of halide substitutional defects are selected to probe the coupling between the local defect-induced geometric distortions and orientation of chromium magnetic moments…
Magnetic skyrmions are topological magnetic structures, which exhibit quasi-particle properties and can show enhanced stability against perturbation from thermal noise. Recently, thermal Brownian diffusion of these quasi-particles has been found in continuous films and applications in unconventional computing have received significant attention, which however require structured elements. Thus, as the next necessary step, we here study skyrmion diffusion in confined geometries and find it to be qualitatively different: The diffusion is governed by the interplay between the total number of skyrm…
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 CrISe monolayer as a room temperature ferromagnetic semiconductor with the Curie temperature ($T_C$), magnetic anisotropy energy (MAE) and band gap being 322 K, 113 $μ$eV and 0.67 eV, respectively. The $T_C$ and MAE can be further enhanced up to 385 K and 313 $μ$eV by tensile strain. More interestingly, the magnetic easy axis can be switched between off-plane and in-plane by compressive strain. Particularly, due to the broken inversion symmetry and strong spin-orbit coupling of Se atoms, a large Dzyaloshinskii-Moriya interaction (DMI) of 2.40 meV is obtained. More importantly, by mic…
Skyrmions are disk-like objects that typically form triangular crystals in two dimensional systems. This situation is analogous to the so-called "pancake vortices" of quasi-two dimensional superconductors. The way in which skyrmion disks or pancake skyrmions pile up in layered centro-symmetric materials is dictated by the inter-layer exchange. Unbiased Monte Carlo simulations and simple stabilization arguments reveal face centered cubic and hexagonal close packed skyrmion crystals for different choices of the inter-layer exchange, in addition to the conventional triangular crystal of skyrmion …
We study in this article a triangular lattice with Heisenberg spins interacting with each other via an antiferromagnetic exchange interaction $J$ and a Dzyaloshinskii-Moriya (DM) interaction $D$, between nearest-neighbors (NN). We consider two cases: the first case in which the DM vector $\mathbf D$ is perpendicular to the lattice plane and the second case where it lies in the plane. A magnetic field $H$ is applied perpendicular to the spin plane in both cases. The ground state (GS) of this system is calculated by minimizing the energy using the very fast steepest-descent method in the two cas…
The Dzyaloshinskii-Moriya interaction (DMI), which only exists in noncentrosymmetric systems, is responsible for the formation of exotic chiral magnetic states. The absence of DMI in most two-dimensional (2D) magnetic materials is due to their intrinsic inversion symmetry. Here, using first-principles calculations, we demonstrate that significant DMI can be obtained in a series of Janus monolayers of manganese dichalcogenides MnXY in which the difference between X and Y on the opposites sides of Mn breaks the inversion symmetry. In particular, the DMI amplitudes of MnSeTe and MnSTe are compara…
Novel 2D material CrI3 reveals unique combination of 2D ferromagnetism and robust excitonic response. We demonstrate that the possibility of the formation of magnetic topological defects, such as Neel skyrmions, together with large excitonic Zeeman splitting, leads to giant scattering asymmetry, which is the necessary prerequisite for the excitonic anomalous Hall effect. In addition, the diamagnetic effect breaks the inversion symmetry, and in certain cases can result in exciton localization on the skyrmion. This enables the formation of magnetoexcitonic quantum dots with tunable parameters.
Magnetic skyrmions are magnetic quasi-particles with enhanced stability and different manipulation mechanisms using external fields and currents making them promising candidates for future applications for instance in neuromorphic computing. Recently, several measurements and simulations have shown that thermally activated skyrmions in confined geometries, as they are necessary for device applications, arrange themselves predominantly based on commensurability effects. In this simulational study, based on the Thiele model, we investigate the enhanced dynamics and degenerate non-equilibrium ste…
Magnetic skyrmions are topologically stable spin swirls with particle-like character and potentially suitable for the design of high-density information bits. While most known skyrmion systems arise in noncentrosymmetric systems with Dzyaloshinskii-Moriya interaction, also centrosymmetric magnets with a triangular lattice can give rise to skyrmion formation, with geometrically-frustrated lattice being considered essential in this case. Until today, it remains an open question if skyrmions can also exist in the absence of both geometrically-frustrated lattice and inversion symmetry breaking. He…
We report on a general principle using the interlayer exchange coupling to extend the regime of chiral magnetic films in which stable or metastable magnetic skyrmions can appear at zero magnetic field. We verify this concept on the basis of a first-principles model for a Mn monolayer on W(001) substrate, a prototype chiral magnet for which the atomic-scale magnetic texture is determined by the frustration of exchange interactions, impossible to unwind by laboratory magnetic fields. By means of \textit{ab initio} calculations for the Mn/W$_m$/Co$_n$/Pt/W(001) multilayer system we show that for …
A key element to tailor the properties of magnetic multilayers is the coupling between the individual magnetic layers. In case of skyrmion hosting multilayers, coupling of skyrmions across the magnetic layers is highly desirable. Here the magnetic interlayer coupling was studied in epitaxial all-oxide heterostructures of ferromagnetic perovskite SrRuO$_3$ layers separated by spacers of the strong spin-orbit coupling oxide SrIrO$_3$. This combination of oxide layers is being discussed as a potential candidate system to host Néel skyrmions. First order reversal curve (FORC) measurements were per…
A sizable transverse thermoelectric coefficient N , large to the extent that it potentially serves applications, is predicted to arise, by means of first-principles calculations, in a Skyrmion crystal assumed on EuO monolayer where carrier electrons are introduced upon a quantum anomalous Hall insulating phase of Chern number C = 2. This encourages future experiments to pursue such an effect.
Using symmetry analysis and density functional theory calculations, we uncover the nature of Dzyaloshinskii-Moriya interaction in Fe$_3$GeTe$_2$ monolayer. We show that while such an interaction might result in small distortion of the magnetic texture on the short range, on the longrange Dzyaloshinskii-Moriya interaction favors in-plane Néel spin-spirals along equivalent directions of the crystal structure. Whereas our results show that the observed Néel skyrmions cannot be explained by the Dzyaloshinskii-Moriya interaction at the monolayer level, they suggest that canted magnetic texture shal…
Xenes, graphene-like two-dimensional (2D) monoelemental crystals with a honeycomb symmetry, have been the focus of numerous experimental and theoretical studies. In comparison, single-element 2D materials with a triangular lattice symmetry have not received due attention. Here, taking Pb as an example, we investigate the triangular-lattice monolayer made of group-IV atoms employing first-principles density functional theory calculations. The flat Pb monolayer supports a mirror-symmetry-protected spinless nodal line in the absence spin-orbit coupling (SOC). The introduction of an out-of-plane b…
The study of skyrmion/antiskyrmion motion in magnetic materials is very important in particular for the spintronics applications. In this work, we study the dynamics of isolated skyrmions and antiskyrmions in frustrated magnets driven by magnetic field gradient, using the Landau-Lifshitz-Gilbert simulations on the frustrated classical Heisenberg model on the triangular lattice. A Hall-like motion induced by the gradient is revealed in bulk system, similar to that in the well-studied chiral magnets. More interestingly, our work suggests that the lateral confinement in nano-stripes of the frustr…
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…
The current driven motion of skyrmions in MnSi and FeGe thinned single crystals could be initiated at current densities of the order of $10^6$ A/m, five orders of magnitude smaller than for magnetic domain walls. The technologically crucial step of replicating these results in thin films has not been successful to date, but the reasons are not clear. Elucidating them requires analyzing system characteristics at scales of few nm where the key Dzyaloshinskii Moriya (DM) interactions vary, and doing so in near application conditions, i.e. oxidation protected systems at room temperature. In this w…
Long lifetimes of nanoscale skyrmions in lithium-decorated van der Waals ferromagnet Fe$_3$GeTe$_2$
Institute of Theoretical Physics and Astrophysics, University of Kiel（基尔大学理论物理与天体物理研究所）；CEMES, Université de Toulouse, CNRS（图卢兹大学CNRS CEMES）；Kiel Nano, Surface, and Interface Science (KiNSIS), University of Kiel（基尔大学基尔纳米、表面与界面科学(KiNSIS)）
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, …
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…
The microscopic process of oxidative etching of two-dimensional molybdenum disulfide (2D MoS2) at an atomic scale is investigated using a correlative TEM-etching study. MoS2 flakes on graphene TEM grids are precisely tracked and characterized by TEM before and after the oxidative etching. This allows us to determine the structural change with an atomic resolution on the edges of the domains, of well-oriented triangular pits and along the grain boundaries. We observe that the etching mostly starts from the open edges, grain boundaries and pre-existing atomic defects. A zigzag Mo edge is assigne…
We study the triangular $t$-$J$ model with multiple spin exchange interactions using exact diagonalization of small clusters, as a model of monolayer liquid $^3$He. A phase where the energy spectrum suggest the behaviors of spin-charge separation is realized in the doped-Mott region due to the competition between ferromagnetic two-spin and antiferromagnetic four-spin exchange interactions. This behavior gives an interpretation of the double peaked heat capacity recently observed in monolayer liquid $^3$He adsorbed on a graphite.
The experimental realization of magnetic skyrmions in centrosymmetric materials has been driven by theoretical understanding of how a delicate balance of anisotropy and frustration can stabilize topological spin structures in applied magnetic fields. Recently, the centrosymmetric material Gd$_{2}$PdSi$_{3}$ was shown to host a field-induced skyrmion phase, but the skyrmion stabilization mechanism remains unclear. Here, we employ neutron-scattering measurements on an isotopically-enriched polycrystalline Gd$_{2}$PdSi$_{3}$ sample to quantify the interactions that drive skyrmion formation. Our a…
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…
We have carried out magnetization, heat capacity, electrical and magnetoresistance measurements (2-300 K) for the polycrystalline form of intermetallic compounds, R2RhSi3 (R= Gd, Tb, and Dy), forming in a AlB2 derived hexagonal structure with a triangular R network. This work was primarily motivated by a revival of interest on Gd2PdSi3 after about two decades in the field of Toplogical Hall Effect due to magnetic skyrmions. We report here that these compounds are characterized by double antiferromagnetic transitions (T_N= 13.5 and 12 K for Gd, 13.5 and 6.5 K for Tb; 6.5 and 2.5 for Dy), but an…
We study the equilibrium phase diagram of ultrathin chiral magnets with easy-plane anisotropy $A$. The vast triangular skyrmion lattice phase that is stabilized by an external magnetic field evolves continuously as a function of increasing $A$ into a regime in which nearest-neighbor skyrmions start overlapping with each other. This overlap leads to a continuous reduction of the skyrmion number from its quantized value $Q=1$ and to the emergence of antivortices at the center of the triangles formed by nearest-neighbor skyrmions. The antivortices also carry a small "skyrmion number" $Q_A \ll 1$ …
Frustrated topological spin textures have unique properties that may enable novel spintronic applications, such as helicity-based information storage and computing. Here, we report the statics and current-induced dynamics of two-dimensional (2D) pancake skyrmions in a stack of weakly coupled frustrated magnetic monolayers, which form a three-dimensional (3D) skyrmion string. The Bloch-type skyrmion string is energetically more stable than its Néel-type counterpart. It can be driven into translational motion by the dampinglike spin-orbit torque and shows the damping-dependent skyrmion Hall effe…
