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 that the non-zero components of the magnetoelectric multipole and magnetoelectric response tensors are uniquely determined by the topology, helicity and geometry of the spin texture. Therefore, we propose straightforward linear magnetoelectric response measurements as an alternative to Lorentz microscopy for characterizing insulating skyrmionic textures.
We present a theory of magnetoelectric magnon-photon coupling in cavities hosting noncentrosymmetric magnets. Analogously to nonreciprocal phenomena in multiferroics, the magnetoelectric coupling is time-reversal and inversion asymmetric. This asymmetry establishes a means for exceptional tunability of magnon-photon coupling, which can be switched on and off by reversing the magnetization direction. Taking the multiferroic skyrmion-host Cu$_2$OSeO$_3$ with ultralow magnetic damping as an example, we reveal the electrical activity of skyrmion eigenmodes and propose it for magnon-photon splittin…
Magnetic skyrmions are topologically protected spin-whirl quasiparticles currently considered as promising components for ultra-dense memory devices. In the bulk they form lattices that are stable over just a few Kelvin below the ordering temperature. This narrow stability range presents a key challenge for applications, and finding ways to tune the SkL stability over a wider phase space is a pressing issue. Here we show experimentally that the skyrmion phase in the magnetoelectric insulator ${\text{Cu}_2 \text{O} \text{Se} \text{O}_3}$ can either expand or shrink substantially depending on th…
We study the magnetic dynamics of magnetoelectric antiferromagnetic thin films, where an unconventional boundary ferromagnetism coexists with the bulk Néel phase below the Néel temperature. The spin exchange between the two order parameters yields an effective low-energy theory that is formally equivalent to that of a ferrimagnet. Dynamics of domain walls and skyrmions are analyzed within the collective variable approach, from which we conclude that they behave as massive particles moving in a viscous medium subjected to a gyrotropic force. We find that the film thickness can be used as a cont…
Theoretical investigation demonstrates that the composite bilayer (i.e., chiral-magnetic/ferroelectric bilayer) offers the possibility of electric-induced magnetic Skyrmions [Phys. Rev. B \textbf{94}, 014311 (2016)]. In this Article, we propose a micromagnetic model to physically manipulate magnetic Bloch Skyrmions propagating in a chiral-magnetic thin film with a polarized ferroelectric essential to drive the system through the converse magnetoelectric effect. Effects caused by different velocities of the propagation, sizes of the thin film, and strength of the magnetoelectric couplings stron…
Magnetic skyrmions and multiferroics are the most interesting objects in nanostructure science that have great potential in future spin-electronic technology. The study of the multiferroic skyrmions has attracted much interest in recent years. This paper reports on the magnetic skyrmions induced by an electric driving field on a composite multiferroic lattice. By using the spin dynamics method, we use a classical magnetic spin model and an electric pseudospin model, which are coupled by a strong magnetoelectric coupling in the dynamical simulations. Interestingly, we observe some skyrmion-like…
In multiferroic materials, the microscopic magnetic and electric textures are strongly correlated with each other by magnetoelectric (ME) coupling. Therefore, topological electric dipole textures, such as ferroelectric (FE) dipole skyrmions and periodic FE dipole crystals, are expected to be induced if ferromagnetic (FM) skyrmions and FM skyrmionic crystals (or lattices so as to be abbreviated as SLs for convenience) can be stabilized. In the present work, a quantum computational approach is utilized to simulate the topological textures of FE SLs in a two-dimensional (2D) multiferroic system. …
We investigate a mechanical method to manipulate magnetic Bloch Skyrmions by applying an electric field in a composite chiral-magnetic (CM)/ferroelectric (FE) bilayer. The magnetoelectric coupling at the interface allows the electric field to stimulate magnetic ordering. Therefore it offers the possibility to generate Skyrmions [Phys. Rev. B 94, 014311 (2016)]. Here, we design a movable and localized electric field source to drive skyrmion transport along the bilayer. A traveling velocity of the electric field source must be carefully chosen to show the stability and effciency of this process.…
We investigate the formation of a new type of composite topological excitation -- the skyrmion-vortex pair (SVP) -- in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the superconductor mediates a magnetoelectric coupling between the vortex and the skyrmion, with a sign (attractive or repulsive) that depends on the topological indices of the constituents. We determine the conditions under which a bound SVP is formed, and characterize the range and depth of the effective binding potential through analytical estimates and numerical simulat…
We study in this paper effects of Dzyaloshinskii-Moriya (DM) magnetoelectric coupling between ferroelectric and magnetic layers in a superlattice formed by alternate magnetic and ferroelectric films.Magnetic films are films of simple cubic lattice with Heisenberg spins interacting with each other via an exchange $J$ and a DM interaction with the ferroelectric interface. Electrical polarizations of $\pm{1}$ are assigned at simple cubic lattice sites in the ferroelectric films.We determine the ground-state (GS) spin configuration in the magnetic film. In zero field, the GS is periodically non co…
Magnetic Skyrmions and multiferroics are the most interesting objects in nanostructure science that have great potential in future spin-electronic technology. The study of multiferroic Skyrmions has attracted much interest in recent years. This article reports magnetic Bloch Skyrmions induced by an electric driving field in a composite bilayer (chiral-magnetic/ferroelectric bilayer) lattice. By using the spin dynamics method, we use a classical magnetic spin model and an electric pseudospin model, which are coupled by a strong magnetoelectric coupling in the dynamical simulations. Interestingl…
The intrinsic magnetism observed in two-dimensional (2D) van der Waals (vdW) materials provides a unique opportunity for exploring the 2D topological magnetic textures, in particular skyrmionic magnetic textures (SMTs) including skyrmion and its topological equivalents. Since the experimental discovery of skyrmions in the 2D vdW materials and their heterostructures, a critical challenge lies in the control of these SMTs to translate their intriguing features into spintronic applications. Here, we review the recent experimental and theoretical progresses on the modulations of SMTs in 2D vdW mon…
Several challenges in designing an operational Skyrmion racetrack memory are well-known. Among those challenges, a few contradictions can be identified if researchers were to rely only on metallic materials. Hence, expanding the exploration on Skyrmion Physics into oxide materials is essential to bridge the contradicting gap. In this topical review, we first briefly revise the theories and criteria involved in stabilizing and manipulating Skymions, followed by studying the behaviors of dipolar-stabilized magnetic bubbles. Next, we explore the properties of multiferroic Skyrmions with magnetoel…
We provide a derivation of a spin Skyrmion number classification for two-dimensional topological superconductors constructed from ferromagnetic and Rashba spin-orbit coupled semiconductor-superconductor heterostructures. We show that in the non-trivial topological phase, characterized by a non-zero Chern number, there is always a topological spin texture in the occupied bands represented by a Skyrmion number. The Skyrmion number has the advantage of being both physically intuitive and directly measurable using spin-sensitive band structure imaging techniques. In addition, we show that the Skyr…
Spin-Hall-Like Magnon Transport in a Synthetic Antiferromagnetic Skyrmion Lattice
Dongguan Institute of Materials Science and Technology, Chinese Academy of Sciences（中国科学院东莞材料基因高等理工研究院）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Shenzhen Technology University（深圳技术大学）；Hunan University（湖南大学）；Central South University（中南大学）
Symmetry classification of the magnetic vortices and skyrmions has been suggested. Relation between symmetry based predictions and direct calculation has been shown. It was shown, that electric dipole moment of the vortex is located inside the small vortex core. The antivortices and antiskyrmions do not carry the total core electric dipole induced by the flexomagnetoelectric interaction in the hexoctahedral cubic crystal. The volumetric bound electric charge is distributed around the core. Switching of the core electric dipole direction produces the switching of the core magnetization or vorte…
We present a novel approach to understanding the extraordinary diversity of magnetic skyrmion solutions. Our approach combines a new classification scheme with efficient analytical and numerical methods. We introduce the concept of chiral kinks to account for regions of disfavoured chirality in spin textures, and classify two-dimensional magnetic skyrmions in terms of closed domain walls carrying such chiral kinks. In particular, we show that the topological charge of magnetic skyrmions can be expressed in terms of the constituent closed domain walls and chiral kinks. Guided by our classificat…
Magnetic skyrmions have attracted considerable interest, especially after their recent experimental demonstration at room temperature in multilayers. The robustness, nanoscale size and non-volatility of skyrmions have triggered a substantial amount of research on skyrmion-based low-power, ultra-dense nanocomputing and neuromorphic systems such as artificial synapses. Room-temperature operation is required to integrate skyrmionic synapses in practical future devices. Here, we numerically propose a nanoscale skyrmionic synapse composed of magnetic multilayers that enables room-temperature device…
