We consider a twisted magnetic bilayer subject to the perpendicular electric field. The interplay of induced Dzyaloshinskii - Moriya interaction and spatially varying moiré exchange potential results in complex non-collinear magnetic phases in these structures. We numerically demonstrate the coexistence of intralayer skyrmions and bound interlayer skyrmion pairs and show that they are characterized by distinct dynamics under the action of external in-plane electric field. Specifically we demonstrate the railing behaviour of skyrmions along the domain walls which could find applications in spintronic devices based on van der Waals magnets.
We explore the skyrmion formation and control possibilities in 2D magnets from the ubiquitous moiré pattern in vdW heterostructures. Using the example of a ferromagnetic monolayer on an antiferromagnetic substrate, we demonstrate a new origin of skyrmions in the 2D magnets, from the lateral modulation of interlayer magnetic coupling by the locally different atomic registries in moiré. The moiré skyrmions are doubly degenerate with opposite topological charge, and trapped at an ordered array of sites with the moiré periodicity that can be dramatically tuned by strain and interlayer translation.…
We study untwisted heterobilayers of ferromagnetic and antiferromagnetic van der Waals materials, with in particular a Dzyaloshinskii-Moriya interaction in the ferromagnetic layer. A continuum low energy field theory is utilized to study such systems. We develop a phase diagram as a function of the strength of inter-layer exchange and Dzyaloshinskii-Moriya interactions, combining perturbative and strong coupling analyses with numerical simulations using Landau-Lifshitz-Gilbert equations. Various moiré-periodic commensurate phases are found, and the commensurate-incommensurate transition is dis…
Magnetic skyrmions in 2D chiral magnets are in general stabilized by a combination of Dzyaloshinskii-Moriya interaction and external magnetic field. Here, we show that skyrmions can also be stabilized in twisted moiré superlattices in the absence of an external magnetic field. Our setup consists of a 2D ferromagnetic layer twisted on top of an antiferromagnetic substrate. The coupling between the ferromagnetic layer and the substrate generates an effective alternating exchange field. We find a large region of skyrmion crystal phase when the length scales of the moiré periodicity and skyrmions …
The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating $|C|=2$ dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity are matched. Following the Wilczek argument, the statistics of the charge-carrying excitations…
Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers
University of Texas at Austin（德克萨斯大学奥斯汀分校）；The University of Hong Kong（香港大学）；National Yang Ming Chiao Tung University（阳明交通大学）；Pennsylvania State University（宾夕法尼亚州立大学）；National Institute for Materials Science（日本物质材料研究机构）
The moiré engineering of two-dimensional magnets opens unprecedented opportunities to design novel magnetic states with promises for spintronic device applications. The possibility of stabilizing skyrmions in these materials without chiral spin-orbit couplings or dipolar interactions is yet to be explored. Here, we investigate the formation and control of ground state topological spin textures (TSTs) in moiré CrI3 using stochastic Landau-Lifshitz-Gilbert simulations. We unveil the emergence of interlayer vortex and antivortex Heisenberg exchange fields, stabilizing spontaneous and field-assist…
We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS$_2$, spin-orbit coupling in the conduction band states from $\pm K$ valleys can give rise to moiré flat bands with nonzero Chern numbers in each valley. The nontrivial band topology originates from a unique combination of angular twist and local mirror symmetry breaking in each individual layer, which results in unusual skyrmionic spin textures in momentum space with skyrmion number $\mathcal{S} = \pm 2$. Our Hartree-Fock analysis further suggests that density-density interactions generically drive the system at $1…
The profile and energy of chiral skyrmions, found in magnetic materials with the Dzyaloshinskii-Moriya interaction, can be approximated by formulae obtained through asymptotic analysis in the limits of small and large skyrmion radius. Using fitting techniques, we modify these formulae so that their validity extends to almost the entire range of skyrmion radii. Such formulae are obtained for skyrmions that are stabilised in the presence of an external field or easy-axis anisotropy or a combination of these. We further study the effect of the magnetostatic field on the skyrmion profile. We compa…
We study the stability and energetics associated to skyrmions appear- ing as excitations on curved surfaces. Using a continuum model we show that the presence of cylindrically radial and azimuthal fields destabilizes the skyrmions that appear in the absence of an external field. Weak fields generate fractional skyrmions while strong magnetic fields yield stable 2{$π$}- skyrmions, which have their widths diminished by the magnetic field strength. Under azimuthal fields vortex appear as stable states on the curved surface.
Moiré spintronics: Emergent phenomena, material realization and machine learning accelerating discovery
Center for Quantum Matter, School of Physics, Zhejiang University（浙江大学物理学院量子物质中心）；Department of Physics, University of Houston（休斯顿大学物理系）；Institute for Superconducting and Electronic Materials (ISEM), University of Wollongong（伍伦贡大学超导与电子材料研究所）
Axisymmetric magnetic lines of nanometer sizes (chiral vortices or skyrmions) have been predicted to exist in a large group of noncentrosymmetric crystals more than two decades ago. Recently these magnetic textures have been directly observed in nanolayers of cubic helimagnets and monolayers of magnetic metals. We develop a micromagnetic theory of chiral skyrmions in thin magnetic layers for magnetic materials with intrinsic and induced chirality. Such particle-like and stable micromagnetic objects can exist in broad ranges of applied magnetic fields including zero field. Chiral skyrmions can …
We present a theory of electron scattring on a magnetic skyrmion for the case when exchange interaction is moderate so that adiabatic approximation and Berry phase approach is not applicable. The theory explains the appearance of a topological Hall current in the systems with magnetic skyrmions, of a special importance its applicability to dilute magnetic semiconductors with a weak exchange interaction.
Magnetic skyrmions are localised non-collinear spin textures with high potential for future spintronic applications. Skyrmion phases have been discovered in a number of materials and a focus of current research is the preparation, detection, and manipulation of individual skyrmions for an implementation in devices. Local experimental characterization of skyrmions has been performed by, e.g., Lorentz microscopy or atomic-scale tunnel magnetoresistance measurements using spin-polarised scanning tunneling microscopy. Here, we report on a drastic change of the differential tunnel conductance for m…
The internal and lattice structures of magnetic skyrmions in B20-type FeGe are investigated using off-axis electron holography. The temperature, magnetic field and angular dependence of the magnetic moments of individual skyrmions are analyzed. Whereas the internal skyrmion shape is found to vary with magnetic field, the inter-skyrmion distance remains almost unchanged in the lattice phase. The amplitude of the local magnetic moment is found to depend on temperature, while the skyrmion shape does not. Deviations from a circular to a hexagonal skyrmion structure are observed in the lattice phas…
In bulk non-centrosymmetric magnets the chiral Dzyaloshinskii-Moriya exchange stabilizes tubular skyrmions with a reversed magnetization in their centers. While the double-twist is favorable in the center of a skyrmion, it gives rise to an excess of the energy density at the outskirt. Therefore, magnetic anisotropies are required to make skyrmions more favorable than the conical spiral state in bulk materials. Using Monte Carlo simulations, we show that in magnetic nanowires unusual skyrmions with a doubly twisted core and a number of concentric helicoidal undulations (target-skyrmions) are th…
We develop a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. We apply our formalism to skyrmions and anti-skyrmions of different helicities, as well as to magnetic bimerons, which are topologically, but not geometrically, equivalent to skyrmions. We show th…
In this work, we utilize voltage controlled magnetic anisotropy (VCMA) to manipulate magnetic skyrmions that are fixed in space. Memory devices based on this strategy can potentially be of smaller footprint and better energy efficiency than current-controlled motion-based skyrmionic devices. To demonstrate VCMA induced manipulation of skyrmions, we fabricate antiferromagnet/ferromagnet/oxide heterostructure films where skyrmions can be stabilized without any external magnetic field due to the presence of exchange bias. These isolated skyrmions were annihilated by applying a voltage pulse that …
We study inter-skyrmion interactions and stable spin configurations in a 2D chiral magnet with in-plane anisotropies of a tilted magnetic field and the magneto-crystalline anisotropy on a (011) thin film. We find that in both cases a small deformation of a skyrmion shape makes the inter-skyrmion interaction anisotropic, and that the skyrmions are weakly bounded along a certain direction due to an emergent attractive interaction. Furthermore, when the magneto-crystalline anisotropy is comparable to the Zeeman energy, skyrmions embedded in a uniform magnetization are tightly bound by creating a …
We study spin-wave excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex and skyrmion states. Gradual change in the strength of the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction leads to continuous phase transitions between different stable magnetic configurations and allows for mapping of dynamic spin modes in and between the vortex, Bloch-type skyrmion and Néel-type skyrmion states. Our study elucidates the connections between gyrotropic modes, azimuthal spin waves…
Magnetic skyrmionium is a novel magnetization configuration with zero skyrmion number, which is composed by two skyrmions with opposite skyrmion number. Here, we study the dynamics of skyrmionium under an anisotropy gradient. We find that the skyrmionium can be efficiently driven by an anisotropy gradient with moving straightly along the direction of gradient. The skyrmion Hall angle for skyrmionium is close to zero which is much smaller than that of skyrmion. while the speed is much larger. We also demonstrate that the skyrmionium motion depends on the damping cofficient, and the skyrmionium …
A magnetic skyrmion isusually refers to a twisted spin texture surrounded by uniformly aligned out-of-plane spinsin the background of a uniformly magnetized state. The invariance of the magnetic skyrmion conserves its topological charge under any continuous transformations of the spin textures, leads to which represents the robustness of a magnetic skyrmion their texture against external perturbations, making it ideal to use skyrmions as . Such a behaviour is required for an ideal information carriers. To date, most magnetic skyrmion studies have been performedfocused on in perpendicularly mag…
Magnetic skyrmion crystals are topological magnetic textures arising in the chiral ferromagnetic materials with Dzyaloshinskii-Moriya interaction. The magnetostatic fields generated by magnetic skyrmion crystals are first studied by micromagnetic simulations. For Néel-type skyrmion crystals, the fields will vanish on one side of the crystal plane, which depend on the helicity; while for Bloch-type skyrmion crystals, the fields will distribute over both sides, and are identical for the two helicities. These features and the symmetry relations of the magetostatic fields are understood from the m…
The Hofstadter butterfly spectral patterns of lattice electrons in an external magnetic field yield some of the most beguiling images in physics. Here we explore the magneto-electronic spectra of systems with moire spatial patterns, concentrating on the case of twisted bilayer graphene. Because long-period spatial patterns are accurately formed at small twist angles, fractal butterfly spectra and associated magneto-transport and magneto-mechanical anomalies emerge at accessible magnetic field strengths.
Skyrmions dynamics in the approximation of point-particle skyrmions is considered in the multiferroic insulators, where the spiral magnetic structure is accompanied by finite electric dipole moment. The skyrmion motion is studied in the gradients of perpendicular magnetic and electric fields. The nonuniform magnetic field with a fixed gradient magnitude leads to the spiral motion, where skyrmion circulates in the plane perpendicular to the direction of magnetic field. The frequency of circulation is fixed by the derivative of the external magnetic field and the magnitude of the dipole moment. …
Using micromagnetic simulations we demonstrate core reversal of a fixed magnetic skyrmion by modulating the perpendicular magnetic anisotropy of a nanomagnet with an electric field. We can switch reversibly between two skyrmion states and two ferromagnetic states, i.e. skyrmion states with the magnetization of the core pointing down/up and periphery pointing up/down, and ferromagnetic states with magnetization pointing up/down, by sequential increase and decrease of the perpendicular magnetic anisotropy. The switching between these states is explained by the fact that the spin texture correspo…
Magnetic skyrmions are particle-like topological excitations recently discovered in chiral magnets. Their small size, topological protection and the ease with which they can be manipulated by electric currents generated much interest in using skyrmions for information storage and processing. Recently, it was suggested that skyrmions with additional degrees of freedom can exist in magnetically frustrated materials. Here, we show that dynamics of skyrmions and antiskyrmions in nanostripes of frustrated magnets is strongly affected by complex spin states formed at the stripe edges. These states c…
Magnetic skyrmions formed at temperatures around room temperature in square-based parallelepiped magnetic FePt nanoparticles with perpendicular magnetocrystalline anisotropy (MCA) were studied during the magnetization reversal using micromagnetic simulations. Finite Differences (FD) method were used for the solution of the Landau-Lifshitz-Gilbert equation. Magnetic configurations exhibiting Néel skyrmionic formations were detected. The magnetic skyrmions can be created in different systems generated by the variation of external field, side length and width of the squared-based parallelepiped m…
We introduce a new class of isolated magnetic skyrmions emerging within tilted ferromagnetic phases of polar magnets with easy-plane anisotropy. The asymmetric magnetic structure of these skyrmions is associated with an intricate pattern of the energy density, which exhibits positive and negative asymptotics with respect to the surrounding state with a ferromagnetic moment tilted away from the polar axis. Correspondingly, the skyrmion-skyrmion interaction has an anisotropic character and can be either attractive or repulsive depending on the relative orientation of the skyrmion pair. We invest…
A magnetic skyrmion is a topological magnetization structure with a nanometric size and a well-defined swirling spin distribution, which is anticipated to be an essential building block for novel skyrmion-based device applications. We study the motion of magnetic skyrmions in multilayer synthetic antiferromagnetic (SAF) racetracks as well as in conventional monolayer ferromagnetic (FM) racetracks at finite temperature. There is an odd-even effect of the constituent FM layer number on the skyrmion Hall effect (SkHE). Namely, due to the suppression of the SkHE, the magnetic skyrmion has no trans…
Skyrmions were originally introduced in Particle Physics as a possible mechanism to explain the stability of particles. Lately the concept has been applied in Condensed Matter Physics to describe the newly discovered topologically protected magnetic configurations called the magnetic Skyrmions. This elementary review introduces the concept at a level suitable for beginning students of Physics.
Magnetic skyrmions are topologically protected nanoscale objects, which are promising building blocks for novel magnetic and spintronic devices. Here, we investigate the dynamics of a skyrmion driven by a spin wave in a magnetic nanowire. It is found that (i) the skyrmion is first accelerated and then decelerated exponentially; (ii) it can turn L-corners with both right and left turns; and (iii) it always turns left (right) when the skyrmion number is positive (negative) in the T- and Y-junctions. Our results will be the basis of skyrmionic devices driven by a spin wave.
RKKY-like interactions between two magnetic skyrmions
School of Science and Engineering, Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳）理工学院）；Institute for Advanced Study in Physics, Zhejiang University（浙江大学物理高等研究院）
Magnetic skyrmions are topologically-protected spin textures existing in helimagentic materials, which can be utilized as information carriers for non-volatile memories and logic circuits in spintronics. Searching simple and controllable way to create isolated magnetic skyrmions is desirable for further technology developments and industrial designs. Based on micromagnetic simulations, we show that the temporal dissipative structure can be developed in the T-shaped helimagnetic nanojunction when it is driven to the far-from-equilibrium regime by a constant spin-polarized current. Then the magn…
We report the results of simulations of magnetic skyrmion stability in ultrathin magnetic multilayer nanodots with interfacial Dzyaloshinskii-Moriya exchange interaction (DMI). We found that in presence of the lateral confinement the magnetostatic energy significantly influences the skyrmion stability and leads to stabilization of large radius skyrmion even at low values of the DMI strength, in addition to small radius skyrmion stabilized by DMI. In particular, stabilization of the skyrmion state with two different radii (bi-stability) is found in dipolarly-coupled (Pt/Co/Ir)$_{n}$ circular na…
We theoretically study the effect of magnetic moiré superlattice on the topological surface states by introducing a continuum model of Dirac electrons with a single Dirac cone moving in the time-reversal symmetry breaking periodic pontential. The Zeeman-type moiré potentials generically gap out the moiré surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $\pm1$. This result provides a promising platform for realizing the time-reversal breaking correlated topological phases. In a $C_6$ periodic potential, when the scalar $U_0$ and Zeeman $Δ_1$ moiré potential s…
We study skyrmions in magnetic thin films with structural inversion asymmetry perpendicular to the film plane. We determine the magnetization texture of a single skyrmion and its dependence on the strength of the Dzyaloshinskii-Moriya interaction relative to the magnetostatic energy. Furthermore, we construct a phenomenological model that describes the interaction between the motion of skyrmions and electric currents to lowest order in spin-orbit coupling. We estimate the experimental verifiable velocities for current-driven motion of skyrmion textures based on available results obtained from …
Skyrmions are localized solitonic spin textures with protected topology, which are promising as information carriers in ultra-dense and energy-efficient logic and memory devices. Recently, magnetic skyrmions have been observed in magnetic thin films, and are stabilized by the extrinsic interfacial Dzyaloshinskii-Moriya interaction (DMI) and/or external magnetic fields. The specific effects in magnetic monolayer materials have not been thoroughly studied. Here, we investigate the intrinsic magnetic skyrmions in a family of monolayer Janus van der Waals magnets, MnSTe, MnSeTe, VSeTe, and MnSSe, …
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…
Quantum collapse of a small skyrmion in a thin magnetic film with Dzyalishinskii-Moriya (DMI) interaction has been studied. The energy of the skyrmion and the stability threshold determined by the DMI, the external magnetic field, and the underlying atomic lattice are investigated analytically and numerically. The Lagrangian describing the coupled dynamics of the skyrmion size and the chirality angle is derived. Equations of motion possess an instanton solution that corresponds to the skyrmion underbarrier contraction via quantum tunneling with subsequent collapse and decay of the topological …
The analytical model is developed for description of skyrmions and skyrmion-like magnetic structures in a two-sublattice antiferromagnet with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Relativistic contraction of skyrmion size in the direction of motion is demonstrated for subcritical case when the skyrmion velocity is less than spin wave velocity in antiferromagnet. Lorentz-like supercritical transformation are found for skyrmion-like magnetic structures moving with velocity greater than spin wave velocity in antiferromagnet.
Magnetic skyrmion, a swirling spin texture, in chiral magnets is characterized by (i) nano-scale size ($\sim$1nm -- 100nm), (ii) topological stability, and (iii) gyro-dynamics. These features are shown to be advantageous for (a) high-density data-storage, (b) nonvolatile memory, and (c) ultra-low current and energy cost manipulation, respectively. By the numerical simulations of Landau-Lifshitz-Gilbert equation, the elementary functions of skyrmions are demonstrated aiming at the design principles of skyrmionic memory devices.
Magnetic skyrmions are particle-like chiral spin textures found in a magnetic film with out-of-planeanisotropy and are considered to be potential candidates as information carriers in next generationdata storage devices. Despite intense research into the nature of skyrmions and their dynamic prop-erties, there are several key challenges that still need to be addressed. In particular, the outstandingissues are the reproducible generation, stabilization and confinement of skyrmions at room tempera-ture. Here, we present a method for the capture of nanometer sized magnetic skyrmions in an arrayof…
The theoretical study considers chiral spin texture induced in a 2D electron gas (2DEG) by magnetic skyrmions. We calculate the electron gas spin density as a linear response to the exchange interaction between the 2DEG and the magnetization field of a magnetic skyrmion. Two physically distinct regimes occur. When the size of the skyrmion is larger than the inverse Fermi wavevector $k_F^{-1}$, the spin density response follows the magnetization profile of the skyrmion. In the opposite case of a small skyrmion the emerging spin structure of 2DEG has a characteristic size of $k_F^{-1}$ and the r…
Magnetic skyrmions are promising candidates for the next generation of spintronic devices due to their small size and topologically protected structure. One challenge for using these magnetic states in applications lies on controlling the nucleation process and stabilization that usually requires an external force. Here, we report on the evidence of skyrmions in unpatterned symmetric Pd/Co/Pd multilayers at room temperature without prior application of neither electric current nor magnetic field. By decreasing the ferromagnetic interlayer thickness, the tuning of the physical properties across…
Reliable transport of magnetic skyrmions is required for any future skyrmion-based information processing devices. Here we present a micromagnetic study of the in-plane current-driven motion of a skyrmion in a ferromagnetic nanotrack with spatially sinusoidally varying Gilbert damping and/or non-adiabatic spin-transfer torque coefficients. It is found that the skyrmion moves in a sinusoidal pattern as a result of the spatially varying Gilbert damping and/or non-adiabatic spin-transfer torque in the nanotrack, which could prevent the destruction of the skyrmion caused by the skyrmion Hall effec…
Magnetic skyrmions are believed to be the promising candidate of information carriers in spintronics. However, the skyrmion Hall effect due to the nontrivial topology of skyrmions can induce a skyrmion accumulation or even annihilation at the edge of the devices, which hinders the real-world applications of skyrmions. In this work, we theoretically investigate the current-driven skyrmion motion on magnetic nanotubes which can be regarded as "edgeless" in the tangential direction. By performing micromagnetic simulations, we find that the skyrmion motion exhibits a helical trajectory on the nano…
The magnetic skyrmion structure can be formed in the chiral magnets (CMs) with strong Dzyaloshinskii-Moriya interactions. In this work, we propose a way of artificially tailoring the topological details of the skyrmion such as its radial and whirling symmetric patterns by external magnetic fields besieging the CM slab. As long as the boundary magnetic fields are strong enough to fix the boundary ferromagnetism, the attained skyrmion profile is stable over time. The dynamics of spins is considered by numerically solving the non-equilibrium Landau-Lifshitz-Gilbert equation.
