We formulate an energy-storage concept based on the free energy associated with metastable magnetic configurations. Despite the active, magnetic region of the battery being electrically insulating, it can sustain effective hydrodynamics of spin textures, whose conservation law is governed by topology. To illustrate the key physics and potential functionality, we focus here on the simplest quasi-one-dimensional case of planar winding of the magnetic order parameter. The energy is stored in the metastable winding number, which can be injected electrically by an appropriately tailored spin torque. Due to the nonvolatility and the endurance of magnetic systems, the injected energy can be stored essentially indefinitely, with charging/discharging cycles that do not degrade over time.
An experimentally feasible energy-storage concept is formulated based on vorticity (hydro)dynamics within an easy-plane insulating magnet. The free energy, associated with the magnetic winding texture, is built up in a circular easy-plane magnetic structure by injecting a vorticity flow in the radial direction. The latter is accomplished by electrically induced spin-transfer torque, which pumps energy into the magnetic system in proportion to the vortex flux. The resultant magnetic metastable state with a finite winding number can be maintained for a long time because the process of its relaxa…
A three-dimensional topological insulator manifests gapless surface modes, described by two-dimensional Dirac equation. We study magnetic textures, such as domain walls and vortices, in a ferromagnetic thin film deposited on a three-dimensional topological insulator. It is shown that these textures can be electrically charged, ascribed to the proximity effect with the Dirac surface states. We derive a general relation between the electric and the magnetic charges. As a physical consequence, we discuss domain wall motion driven by an applied electric field, which promises magnetic devices with …
The opening of a band gap due to compressive uniaxial strain renders bulk HgTe a strong three-dimensional topological insulators with protected gapless surface states at any surface. By employing a six-band k.p model, we determine the spin textures of the topological surface states of strained HgTe using their close relations with the mirror Chern numbers of the system and the orbital composition of the surface states. We show that at surfaces with C2v point group symmetry an increase in the strain magnitude triggers a topological phase transition where the winding number of the surface state …
The surfaces of intrinsic magnetic topological insulators (TIs) host magnetic moments exchange-coupled to Dirac electrons. We study the magnetic phases arising from tuning the electron density using variational and exact diagonalization approaches. In the dilute limit, we find that magnetic skrymions are formed which bind to electrons leading to a skyrmion Wigner crystal phase while at higher densities spin spirals accompanied by chiral 1d channels of electrons are formed. The binding of electrons to textures raises the possibility of manipulating textures with electrostatic gating. We determi…
The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like "spin" texture in momentum space. Here, we apply the previously formulated low-energy model for Bi$_2$Se$_3$, a parent compound for magnetic topological insulators, to a slab geometry in which an exchange field acts only within one of the surface layers. In this sample set up, the hedgehog transforms into a skyrmion texture beyond a critical exchange field. This critical field marks a transi…
Based upon first-principles methods, we investigate the magnetic anisotropy and the spin-texture of Co adatoms embedded in the topmost Se network of the topological insulator Bi$_2$Se$_3$ surface. We find the formation of energetically stable magnetic moment perpendicular to the surface plane, S$_z$. Our results for the pristine Bi$_2$Se$_3$ surface indicate the presence of helical spin-texture not only in the massless surface Dirac states, but also surface states resonant within the valence band present spin-texture. On the other hand, upon the presence of Co adatoms we find that the out-of-p…
We carry out a throughout study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and found that the adiabatic approximation still holds for large skyrmions as well as for few atomic size-nanoskyrmions. Finally, we te…
We propose that the non-linear radio-frequency dynamics and nanoscale size of topological magnetic structures associated to their well-defined internal modes advocate for their use as in-materio scalable frequency multipliers for spintronic systems. Frequency multipliers allow for frequency conversion between input and output frequencies, and thereby significantly increase the range of controllably accessible frequencies. In particular, we explore the excitation of eigenmodes of topological magnetic textures by fractions of the corresponding eigenfrequencies. We show via micromagnetic simulati…
We have investigated the nature of surface states in the Bi2Te3 family of three-dimensional topological insulators using first-principles calculations as well as model Hamiltonians. When the surface Dirac cone is warped due to Dresselhaus spin-orbit coupling in rhombohedral structures, the spin acquires a finite out-of-plane component. We predict a novel in-plane spin-texture of the warped surface Dirac cone with spins not perpendicular to the electron momentum. Our k.p model calculation reveals that this novel in-plane spin-texture requires high order Dresselhaus spin-orbit coupling terms.
The anomalous Hall effect is caused by magnetic textures such as skyrmions. We derive an analytical formula of the Hall conductivity on the surface of a topological insulator up to third order in magnetization, $\boldsymbol{M}(\boldsymbol{x})$, based on a perturbative approach. We identify the magnetic textures that contribute to the Hall conductivity up to third order in magnetization and second order in spatial differentiation. We treat magnetization as a perturbation to calculate the Hall conductivity for each magnetic texture based on the linear response theory. Furthermore, we estimate th…
Surface states of three-dimensional topological insulators exhibit the phenomenon of spin-momentum locking, whereby the orientation of an electron spin is determined by its momentum. Probing the spin texture of these states is of critical importance for the realization of topological insulator devices, however the main technique available so far is the spin- and angle-resolved photoemission spectroscopy. Here we reveal a close link between the spin texture and a new kind of magneto-resistance, which depends on the relative orientation of the current with respect to the magnetic field as well a…
We study the planar magnetic textures in an insulating magnetic film coupled to the Dirac surface state of a topological insulator. It is shown that the radial vortex with winding number $w=\pm1$ leads to the confinement of Dirac states, where an exact mapping to the Schrödinger equation of a two-dimensional hydrogen atom is found. The fully spin polarized zero energy bound state resembles the zeroth Landau level of Dirac electrons in a uniform out-of-plane magnetic field. Interestingly, when the hybrid system is proximity coupled to an $s$-wave superconductor, the existence of Majorana zero m…
Spin-transfer torque is one of the important physical quantities to understand for successful application of topological insulators to spintronics. In this paper, we present analytical expressions of the spin-transfer torques on a surface of a magnetic topological insulator by including the higher-order contributions of momentum, $k^2$-term and the hexagonal warping. We obtain six different types of the spin-transfer torque including both the field-like and the damping-like torques; the four of them appear only when the higher-order momentum contributions are included. In addition, we discuss …
The surfaces of antimony are characterized by the presence of spin-split states within the projected bulk band gap and the Fermi contour is thus expected to exhibit a spin texture. Using spin-resolved density functional theory calculations, we determine the spin polarization of the surface bands of Sb(110). The existence of the unconventional spin texture is corroborated by the investigations of the electron scattering on this surface. The charge interference patterns formed around single scattering impurities, imaged by scanning tunneling microscopy, reveal the absence of direct backscatterin…
Collective dynamics of topological magnetic textures can be thought of as a massive particle moving in a magnetic pinning potential. We demonstrate that inside a cavity resonator this effective mechanical system can feel the electromagnetic radiation pressure from cavity photons through the magneto-optical inverse Faraday and Cotton-Mouton effects. We estimate values for the effective parameters of the optomechanical coupling for two spin textures -- a Bloch domain wall and a chiral magnetic soliton lattice. The soliton lattice has magnetic chirality, so that in circularly polarized light it b…
We investigate theoretically the spin torque and magnetization dynamic in a thin ferromagnetic (FM) layer with spatially varying magnetization. The FM layer is deposited on the surface of a topological insulator (TI). In the limit of the adiabatic relaxation of electron spin along the magnetization, the interaction between the exchange interaction and the Rashba-like surface texture of a TI yields a topological gauge field. Under the gauge field and an applied current, spin torque is induced according to the direction of the current. We derived the corresponding effective anisotropy field and …
We present a consistent theory of the topological Hall effect (THE) in 2D magnetic systems with disordered array of chiral spin textures, such as magnetic skyrmions. We focus on the scattering regime when the mean-free path of itinerant electrons exceeds the spin texture size, and THE arises from the asymmetric carrier scattering on individual chiral spin textures. We calculate the resistivity tensor on the basis of the Boltzmann kinetic equation taking into account the asymmetric scattering on skyrmions via the collision integral. Our theory describes both the adiabatic regime, when THE arise…
We investigate the interaction of magnetic vortices and skyrmions with a spin-polarized current. In a square lattice, fixed classical spins and quantum itinerant electrons, evolve according to the coupled Landau-Lifshitz and Schrödinger equations. Changes in the topology occur at microscopic time and length scales, and are shown to be triggered by the nucleation of a nontrivial electron-spin structure at the vortex core.
Helicity-Controlled Hall Transport in Hybrid Topological Magnetic Textures
National Science Center "Kharkiv Institute of Physics and Technology"（国家科学中心“哈尔科夫物理与技术研究所”）；ISQI, Faculty of Physics, Adam Mickiewicz University（亚当·密茨凯维奇大学物理学院ISQI）；School of Physics, The University of New South Wales（新南威尔士大学物理学院）
The surface states of three-dimensional topological insulators exhibit a helical spin texture with spin locked to momentum. To date, however, the direct all-electrical detection of the helical spin texture has remained elusive owing to the lack of necessary spin-sensitive measurements. We here provide a general theory for spin polarized transports of helical Dirac electrons through spin-polarized scanning tunneling microscopy (STM). It is found that different from conventional magnetic materials, the tunneling conductance through the TI surface acquires an extra component determined by the in-…
The unique feature of surface states in topological insulators is the so-called "spin-momentum locking", which means that electron spin is oriented along a fixed direction for a given momentum and forms a texture in the momentum space. In this work, we study spin textures of two typical topological insulators in Hg-Based Chalcogenides, namely HgTe and HgS, based on both the first principles calculation and the eight band Kane model. We find opposite helicities of spin textures between these two materials, originating from the opposite signs of spin-orbit couplings. Furthermore, we reveal that …
Recent observations of topological spin textures brought spintronics one step closer to new magnetic memories. Nevertheless, the existence of Skyrmions, as well as their stabilization, require very specific intrinsic magnetic properties which are usually fixed in magnets. Here we address the possibility to dynamically control their intrinsic magnetic interactions by varying the strength of a high-frequency laser field. It is shown that drastic changes can be induced in the antiferromagnetic exchange interactions and the latter can even be reversed to become ferromagnetic, provided the direct e…
Recently proposed spintronic devices use magnetic skyrmions as bits of information. The reliable detection of those chiral magnetic objects is an indispensable requirement. Yet, the high mobility of magnetic skyrmions leads to their stochastic motion at finite temperatures, which hinders the precise measurement of the topological numbers. Here, we demonstrate the successful training of artificial neural networks to reconstruct the skyrmion number in confined geometries from time-integrated, dimensionally reduced data. Our results prove the possibility to recover the topological charge from a t…
We have designed three-dimensional models of topological insulator thin films, showing a tunability of the odd number of Dirac cones on opposite surfaces driven by the atomic-scale geometry at the boundaries. This enables creation of a single Dirac cone at the $Γ$-point as well as possible suppression of quantum tunneling between Dirac states at opposite surfaces (and gap formation), when opposite surfaces are geometrically differentiated. The spin texture of surface states was found to change from a spin-momentum-locking symmetry to a progressive loss in surface spin polarization upon the int…
Weak topological insulators possess a symmetry related set of Dirac-Weyl cones in the surface Brillouin zone, implying misorientation between the principle axis of the low energy manifold of the bulk and the surface normal. We show that this feature of weak topological insulators comes with a hidden richness of surface spin textures, and that by misorientation a helical texture can become an unusual hyperbolic spin texture. We illustrate this effect by comparison of the $M$-point and $Γ$-point Dirac-Weyl cones on the (111) surface of the crystalline topological insulator SnTe.
Topological phases, van Hove singularities, and spin texture in magic-angle twisted bilayer graphene in the presence of proximity-induced spin-orbit couplings
Topological insulator is a new state of matter which exhibits exotic surface electronic properties. Determining the spin texture of this class of material is of paramount importance for understanding its topological order and can lead to potential applications in spintronics. Here, we have investigated the nature of the surface state of the topological insulator with hexagonal warping subjected to an off-resonant circularly polarized light. The resulting electronic ground state exhibits a novel feature of spin texture breaking the conventional spin-momentum locking present on a topological ins…
Relativistic spin-orbit coupling plays an essential role in the field of topological insulators and quantum spintronics. It gives rise to the topological non-trivial band structure and enables electric manipulation of the spin degree of freedom. Because of the spin-orbit coupling, rich spin-orbital coupled textures can exist both in momentum and in real space. For three dimensional topological insulators in the Bi$_2$Se$_3$ family, topological surface states with p$_z$ orbitals have a left-handed spin texture for the upper Dirac cone and a right-handed spin texture for the lower Dirac cone. In…
We derive the spin texture of a weak topological insulator via a supersymmetric approach that includes the roles of the bulk gap edge states and surface band bending. We find the spin texture can take one of four forms: (i) helical, (ii) hyperbolic, (iii) hedgehog, with spins normal to the Dirac-Weyl cone of the surface state, and (iv) hyperbolic hedgehog. Band bending determines the winding number in the case of a helical texture, and for all textures can be used to tune the spin texture polarization to zero. For the weak topological insulator SnTe, we show that inclusion of band bending is c…
The recent discovery of higher-order topological insulators (HOTIs) has significantly extended our understanding of topological phases of matter. Here, we predict that second-order corner states can emerge in the dipolar-coupled dynamics of topological spin textures in two-dimensional artificial crystals. Taking a breathing honeycomb lattice of magnetic vortices as an example, we derive the full phase diagram of collective vortex gyrations and identify three types of corner states that have not been discovered before. We show that the topological "zero-energy" corner modes are protected by a g…
Topological spin textures, like skyrmions, have significant potential for spintronics applications. The main purpose of this work is to study further the topological spin textures on the discrete lattice with magnetic fields. In this work, we study a classical rotated Heisenberg model with Dzyaloshinskii-Moriya interaction, bond-dependent anisotropy and easy-axis anisotropy on the honeycomb lattice via Monte Carlo simulations. We mainly focus on phase diagrams with magnetic fields, especially on the non-trivial phases only existing with fields. The results demonstrate the emergence of field-in…
The quantum anomalous Hall (QAH) effect has been recently discovered in experiment using thin-film topological insulator with ferromagnetic ordering and strong spin-orbit coupling. Here we investigate the spin degree of freedom of a QAH insulator and uncover a fundamental phenomenon that the edge states exhibit topologically stable spin texture in the boundary when a chiral-like symmetry is present. This result shows that edge states are chiral in both the orbital and spin degrees of freedom, and the chiral edge spin texture corresponds to the bulk topological states of the QAH insulator. We a…
We propose that topological spin currents flowing in topologically non-trivial magnetic textures, such as magnetic skyrmions and vortices, produce an intrinsic non-adiabatic torque of the form ${\bf T}_t\sim [(\partial_x{\bf m}\times\partial_y{\bf m})\cdot{\bf m}]\partial_y{\bf m}$. We show that this torque, which is absent in one-dimensional domain walls and/or non-topological textures, is responsible for the enhanced non-adiabaticity parameter observed in magnetic vortices compared to one-dimensional textures. The impact of this torque on the motion of magnetic skyrmions is expected to be cr…
We show that a semiconductor thin film can acquire a non-trivial spin texture due to the proximity effect induced by a topological insulator. The effect stems from coupling to the topological surface states and is present even when the insulator is doped. We propose a semiconductor/topological insulator heterostructure as a device that allows measuring interface properties and probing surface states in uncompensated samples. We also find that the topological insulator surface modes can be significantly broadened and shifted by the presence of metallic contacts.
Understanding the spin-texture behavior of boundary modes in ultrathin topological insulator films is critically essential for the design and fabrication of functional nano-devices. Here by using spin-resolved photoemission spectroscopy with p-polarized light in topological insulator Bi2Se3 thin films, we report tunneling-dependent evolution of spin configuration in topological insulator thin films across the metal-to-insulator transition. We observe strongly binding energy- and wavevector-dependent spin polarization for the topological surface electrons in the ultra-thin gapped-Dirac-cone lim…
Topological insulators host topology-linked boundary states, whose spin and charge degrees of freedom could be exploited to design topological devices with enhanced functionality. We experimentally observe that dissipationless chiral edge states in a spin-orbit coupled anomalous Floquet topological phase exhibit topological spin texture on boundaries, realized via a two-dimensional quantum walk. Our experiment shows that, for a walker traveling around a closed loop along the boundary in real space, its spin evolves and winds through a great circle on the Bloch sphere, which implies that edge-s…
Using a semiclassical Green's function formalism, we discover the emergence of chiral and topological orbital magnetism in two-dimensional chiral spin textures by explicitly finding the corrections to the orbital magnetization, proportional to the powers of the gradients of the texture. We show that in the absence of spin-orbit coupling, the resulting orbital moment can be understood as the electronic response to the emergent magnetic field associated with the real-space Berry curvature. By referring to the Rashba model, we demonstrate that by tuning the parameters of surface systems the engin…
We demonstrate the generation of high order harmonics in carrier pumping from precessing ferromagnetic or antiferromagnetic orders, excited via magnetic resonance, in the presence of topological antiferromagnetic textures. This results in an enhancement of the carrier dynamics by orders of magnitude. Interestingly, the generation process occurs in an intrinsic manner, and is solely governed by the interplay between the s-d exchange coupling underlying the noncollinear antiferromagnetic order and the dynamical s-d exchange parameter of the magnetic drive. Therefore, the relativistic spin-orbit …
Spin Chern phases and persistent spin texture in a quasi 2D SSH model
National Institute of Science Education and Research（国家科学教育研究中心）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Institute of Physics（物理研究所）；Max-Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
Topological insulators represent a new quantum state of matter that are insulating in the bulk but metallic on the edge or surface. In the Dirac surface state, it is well-established that the electron spin is locked with the crystal momentum. Here we report a new phenomenon of the spin texture locking with the orbital texture in a topological insulator Bi2Se3. We observe light-polarization-dependent spin texture of both the upper and lower Dirac cones that constitutes strong evidence of the orbital-dependent spin texture in Bi2Se3. The different spin texture detected in variable polarization g…
Ever increasing demand of skyrmion manipulation in nanodevices has brought up interesting research to 8 understand the stabilization of these topologically protected chiral structures. To understand the actual shape 9 and size of skyrmion observed experimentally, we have performed micromagnetic simulations to investigate 10 skyrmion stabilization in presence of random anisotropy in magnetic thin film system. Previous experimental 11 reports of skyrmion imaging in thin films depicts that the skyrmion shape is not perfectly circular. Here we 12 show via simulations that the shape of a skyrmion c…
Electrons moving through a noncoplanar magnetic texture acquire a Berry phase, which can be described as an effective magnetic field. This effect is known as the topological Hall effect and has been observed in topological spin textures. Motivated by recent experimental realizations, here we study the Hall effect in a nontopological magnetic texture known as a target skyrmion. We start from a simplified semiclassical picture and show that the Hall signal is a nonmonotonic function of both the electronic energy and target skyrmion radius. That observation carries over to the fully quantum mecha…
Photoinduced nonequilibrium spin structure is examined in the double-exchange model, in which itinerant electrons couple with localized spins through the ferromagnetic Hund coupling. In particular, we focus on the transient spin structure from the initial ferromagnetic metallic state to the steady antiferromagnetic ordered state reported in [Phys. Rev. Lett. 119, 207202 (2017)]. By solving the Schrödinger equation combined with the Landau-Lifshitz-Gilbert equation, we find finite winding number and chirality, which implies emergence of topological chiral spin textures. These observations are r…
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…
Inelastic scattering off magnetic impurities in a spin-chiral two-dimensional electron gas, e.g., the Rashba system, is shown to generate topological changes in the spin texture of the electron waves emanating from the scattering center. While elastic scattering gives rise to a purely in-plane spin texture for an in-plane magnetic scat- tering potential, out-of-plane components emerge upon activation of inelastic scattering processes. This property leads to a possibility to make controlled transitions between trivial and nontrivial topologies of the spin texture.
The energy-momentum relationship of electrons on the surface of an ideal "Hydrogen-Atom" Topological Insulator forms a cone - a Dirac cone, which, when warped and distorted (no longer described by the Dirac equation), can lead to unusual phenomena such as enhanced electronic interference around defects (observed in STM) and a magnetically ordered broken symmetry surface with lost topological protection. A detailed spin-texture and hexagonal warping maps on Bi2Te3 are presented in this context as a Viewpoint on L.Fu, Phys. Rev. Lett. \textbf{103}, 266801 (2009).
Quantum Printing: Laguerre-Gaussian Beam Induced Topological Magnetic Textures
Nordita, Stockholm University（诺迪塔，斯德哥尔摩大学）；KTH Royal Institute of Technology（皇家理工学院）；Department of Physics, IMS, University of Connecticut（康涅狄格大学物理系，物质科学研究所）
We present first principles calculations of the nontrivial surface states and their spin-textures in the topological crystalline insulator SnTe. The surface state dispersion on the [001] surface exhibits four Dirac-cones centered along the intersection of the mirror plane and the surface plane. We propose a simple model of two interacting coaxial Dirac cones to describe both the surface state dispersion and the associated spin-texture. While the out-of-the-plane spin polarization is zero due to the crystalline and time-reversal symmetries, the in-plane spin texture shows helicity with some dis…
Voltage-controlled topological spin textures in the monolayer limit
National Engineering Research Center of Electromagnetic Radiation Control Materials, School of Electronic Science and Engineering, University of Electronic Science and Technology of China（电子科技大学电磁辐射控制材料工程研究中心电子科学与工程学院）；Key Laboratory of Multi Spectral Absorbing Materials and Structures of Ministry of Education, School of Electronic Science and Engineering, University of Electronic Science and Technology of China（教育部多光谱吸收材料与结构重点实验室电子科学与工程学院电子科技大学）；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）；Laboratory of Advanced Materials, Department of Materials Science, Collaborative Innovation Center of Chemistry for Energy Materials(iChEM), Fudan University（复旦大学材料科学系先进材料实验室能源化学协同创新中心）；School of Physics, Zhengzhou University（郑州大学物理学院）；Institute of Quantum Materials and Physics, Henan Academy of Sciences（河南省科学院量子物质与物理研究所）
In recent years, noncollinear topological textures have long gained increasing research attentions for their high values of both fundamental researches and potential applications. The recent discovery of intrinsic orders in magnetic and polar two-dimensional van der Waals materials provides a new ideal platform for the investigation of noncollinear topological textures. Here, we review the theoretical and experimental progresses on noncollinear topological textures in two-dimensional van der Waals materials in very recent years. During these years, magnetic skyrmions of both Bloch and Néel typ…
