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 simulations that low-frequency perturbations to the system can efficiently excite bounded modes with a higher amplitude. For example, we excited the eigenmodes of isolated ferromagnetic skyrmions by applying half, a third and a quarter of the corresponding eigenfrequency. We predict that the frequency multiplication via magnetic structures is a general phenomenon which is independent of the particular properties of the magnetic texture, and works also for magnetic vortices, droplets and other topological textures.
We study correlations and magnetic textures of localized spins, doped in three-dimensional Dirac semimetals. An effective field theory for magnetic moments is constructed by integrating out the fermionic degrees of freedom. The spin correlation shows a strong anisotropy, originating from spin-momentum locking of Dirac electrons, in addition to the conventional Heisenberg-like ferromagnetic correlation. The anisotropic spin correlation allows topologically nontrivial magnetic excitation textures such as a transient hedgehog state, as well as the ferromagnetic ground state. The spin-wave dispers…
In this article an analytical and numerical study of superconducting thin film with ferromagnetic textures of elliptical geometries in close proximity is presented. The screening currents induced in the superconductor due to the magnetic texture are calculated. Close to the superconducting transition temperature $T_c$ the spontaneous creation of superconducting vortices becomes energy favorable depending on the value of the magnetization and the geometrical quantities of the magnetic texture. The creation of vortices by elliptic dots is more energy favorable than those created by circular ones…
We propose a Hamiltonian dynamics formalism for the current and magnetic field driven dynamics of ferromagnetic and antiferromagnetic domain walls in one dimensional systems. To demonstrate the power of this formalism, we derive Hamilton equations of motion via Poisson brackets based on the Landau-Lifshitz-Gilbert phenomenology, and add dissipative dynamics via the evolution of the energy. We use this approach to study current induced domain wall motion and compute the drift velocity. For the antiferromagnetic case, we show that a nonzero magnetic moment is induced in the domain wall, which in…
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…
The magnetic textures on nanoscale possess topological features due to the continuity of the magnetization vector field and its boundary conditions. In thin planar nanoelements, where the dependence of the magnetization across the thickness is inessential, the textures can be represented as a soup of 2-d topological solitons, corresponding to magnetic vortices and antivortices, which are the solutions of Skyrme's model. Topology of the element (of the boundary conditions) then imposes the restrictions on properties and locations of these objects. Periodic arrays of magnetic antidots have topol…
The control of recently observed spintronic effects in topological-insulator/ferromagnetic-metal (TI/FM) heterostructures is thwarted by the lack of understanding of band structure and spin texture around their interfaces. Here we combine density functional theory with Green's function techniques to obtain the spectral function at any plane passing through atoms of Bi$_2$Se$_3$ and Co or Cu layers comprising the interface. In contrast to widely assumed but thinly tested Dirac cone gapped by the proximity exchange field, we find that the Rashba ferromagnetic model describes the spectral functio…
In this paper, by the use of the topological current theory, the topological structures and the dynamic processes in thin-film ferromagnetic systems are investigated directly from viewpoint of topology. It is found that the topological charge of a thin-film ferromagnetic system can be changed by annihilation or creation processes of opposite polarized vortex-antivortex pairs taking place at space-time singularities of the normalized magnetization vector field of the system, the variation of the topological charge is integer and can further be expressed in terms of the Hopf indices and Brouwer …
The spin-helical surface states in three-dimensional topological insulator (TI), such as Bi2Se3, are predicted to have superior efficiency in converting charge current into spin polarization. This property is said to be responsible for the giant spin-orbit torques observed in ferromagnetic metal/TI structures. In this work, using first-principles and model tight-binding calculations, we investigate the interface between the topological insulator Bi2Se3 and 3d-transition ferromagnetic metals Ni and Co. We find that the difference in the work functions of the topological insulator and the ferrom…
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…
In this paper, we study the zero temperature persistent current in a ferromagnetic Kondo lattice model in the strong coupling limit. In this model, there are spontaneous spin textures at some values of the external magnetic flux. These spin textures contribute a geometric flux, which can induce an additional spontaneous persistent current. Since this spin texture changes with the external magnetic flux, we find that there is an anomalous persistent current in some region of magnetic flux: near Phi/Phi_0=0 for an even number of electrons and Phi/Phi_0=1/2 for an odd number of electrons.
We provide a general procedure to calculate the current-induced spin-transfer torque which acts on a general steep magnetic texture due to the exchange interaction with an applied spin-polarized current. As an example, we consider a one-dimensional ferromagnetic quantum wire and also include a Rashba spin-orbit interaction. The spin-transfer torque becomes generally spatially non-local. Likewise, the Rashba spin-orbit interaction induces a spatially nonlocal field-like nonequilibrium spin-transfer torque. We also find a spatially varying nonadiabaticity parameter and markedly different domain …
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 …
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…
We predict frequency multiplication of surface acoustic waves in dielectric substrates via the ferromagnetic resonance of adjacent magnetic transducers when driven by microwaves. We find pure second harmonic generation (SHG) without any linear and third harmonic components by a magnetic nanowire. The SHG and linear phonon pumping are switched by varying the saturated magnetization direction of the wire, or resolved directionally when pumped by magnetic nano-disc. We address the high efficiency of SHG with comparable magnitude to that of linear response, as well as unique non-reciprocal phonon …
Magnetic excitations in ferromagnetic systems with a noncollinear ground state magnetization experience a fictitious magnetic field due to the equilibrium magnetic texture. Here, we investigate how such fictitious fields lead to thermal Hall effects in two-dimensional insulating magnets in which the magnetic texture is caused by spin-orbit interaction. Besides the well-known geometric texture contribution to the fictitious magnetic field in such systems, there exists also an equally important contribution due to the original spin-orbit term in the free energy. We consider the different possibl…
It is shown that in antiferromagnetic open or closed corrals of magnetic adatoms grown on surfaces, the attachment of a single extra adatom anywhere in the corral impacts on the geometrical topology of the nanosystem and generates complex magnetic structures when a magnetic field is applied or a magnetic coupling to a ferromagnetic substrate exists. The spin configuration of the corral can be tuned to a non-planar state or a planar non-collinear or ferrimagnetic state by adjusting its number of sites, the location of the extra adatom or the strength of the coupling to the ferromagnetic substra…
The magnetotransport properties of disordered ferromagnetic kagome layers are investigated numerically. We show that a large domain-wall magnetoresistance or negative magnetoresistance can be realized in kagome layered materials (e.g. Fe$_3$Sn$_2$, Co$_3$Sn$_2$S$_2$, and Mn$_3$Sn), which show the quantum anomalous Hall effect. The kagome layers show a strong magnetic anisotropy and a large magnetoresistance depending on their magnetic texture. These domain-wall magnetoresistances are expected to be robust against disorder and observed irrespective of the domain-wall thickness, in contrast to c…
Recent theoretical and experimental attemps have been successful in finding magnetic Weyl semimetal phases, which show both nodal-point structure in the electronic bands and magnetic orders. Beyond uniform ferromagnetic or antiferromagnetic orders, nonuniform magnetic textures, such as domain walls and skyrmions, may even more enrich the properties of the Weyl electrons in such materials. This article gives a topical review on interplay between Weyl electrons and magnetic textures in those magnetic Weyl semimetals. The basics of magnetic textures in non-topological magnetic metals are reviewed…
Coupling of the spin and orbital degrees of freedom on the surface of a strong three-dimensional insulator, on the one hand, and textured magnetic configuration in an adjacent ferromagnetic film, on the other, is studied using a combination of transport and thermodynamic considerations. Expressing exchange coupling between the localized magnetic moments and Dirac electrons in terms of the electrons' out-of-plane orbital and spin magnetizations, we relate the thermodynamic properties of a general ferromagnetic spin texture to the physics in the zeroth Landau level. Persistent currents carried b…
Topological Hall Effect Induced by Chiral Spin Textures at the Ferroelectric/Ferromagnetic Interface
National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University（南京大学物理学院固态微结构国家重点实验室，先进微结构协同创新中心）；Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所，北京凝聚态物理国家研究中心）
Magnetic skyrmions are topological magnetization textures that are characterized by the homotopy group of two dimensional spheres. Despite years of intensive research on skyrmions, the fundamental problem of the inertia of a skyrmion in driven motion remains unresolved. By properly taking into account a direct coupling between skyrmion motion and the correspondingly excited magnons, we identify a dynamical mass for the skyrmion in motion. The direct coupling between skyrmion motion and magnons can be employed to engineer skyrmion dynamics with magnons through ingenious material and geometry de…
The bilayer heterostructures composed of an ultrathin ferromagnetic metal (FM) and a material hosting strong spin-orbit (SO) coupling are principal resource for SO torque and spin-to-charge conversion nonequilibrium effects in spintronics. We demonstrate how hybridization of wavefunctions of Co layer and a monolayer of transition metal dichalcogenides (TMDs)---such as semiconducting MoSe$_2$ and WSe$_2$ or metallic TaSe$_2$---can lead to dramatic transmutation of electronic and spin structure of Co within some distance away from its interface with TMD, when compared to the bulk of Co or its su…
Momentum-space topology of electrons under strong spin-orbit coupling contributes to the electrically induced torques exerting on magnetic textures insensitively to disorder or thermal fluctuation. We present a direct connection between band topology and the torques by classifying the whole torques phenomenologically. As well as the intrinsic anomalous Hall effect, the torques also emerge intrinsically from the anomalous velocity of electrons regardless of a nonequilibrium transport current. We especially point out the intrinsic contribution arising exclusively in magnetic textures, which we c…
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 …
We consider the edge dynamics of a compact, fully spin polarized state at filling factor $ν=1$. We show that there are two sets of collective excitations localized near the edge: the much studied, gapless, edge magnetoplasmon but also an additional edge spin wave that splits off below the bulk spin wave continuum. We show that both of these excitations can soften at finite wave-vectors as the potential confining the system is softened, thereby leading to edge reconstruction by spin texture or charge density wave formation. We note that a commonly employed model of the edge confining potential …
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…
The properties of surface Dirac Fermions on a 3D topological insulator in proximity to a magnetic insulator with spatially textured magnetization are considered. We present an exact analytical treatment of the spectrum, the bound states and the domain wall resistance for an extended generic domain wall with in-plane and out-of-plane magnetizations. In the latter case, we find oscillations in the domain wall resistance as a function of the wall width and for certain widths a complete absence of reflections for all incoming momenta. The surprising occurrence of oscillations and the reflectionles…
Cubic chiral magnets, such as Cu$_{2}$OSeO$_{3}$, exhibit a variety of non-collinear spin textures, including a trigonal lattice of spin whirls, so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at GHz frequencies, we probe the ferromagnetic resonance modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS-FMR, is car…
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 …
Coherent exchange between photons and different matter excitations (like qubits, acoustic surface waves or spins) allows for the entanglement of light and matter and provides a toolbox for performing fundamental quantum physics. On top of that, coherent exchange is a basic ingredient in the majority of quantum information processors. In this work, we develop the theory for coupling between magnetic textures (vortices and skyrmions) stabilized in ferromagnetic nanodiscs and photons generated in a circuit. In particular, we show how to perform broadband spectroscopy of the magnetic textures by s…
In most ferromagnets the magnetization rotates from one domain to the next with no preferred handedness. However, broken inversion symmetry can lift the chiral degeneracy, leading to topologically-rich spin textures such as spin-spirals and skyrmions via the Dzyaloshinskii-Moriya interaction (DMI). Here we show that in ultrathin metallic ferromagnets sandwiched between a heavy metal and an oxide, the DMI stabilizes chiral domain walls (DWs) whose spin texture enables extremely efficient current-driven motion. We show that spin torque from the spin Hall effect drives DWs in opposite directions …
The spin-transfer torque is a fundamental physical quantity to operate the spintronics devices such as racetrack memory. We theoretically study the spin-transfer torque and analyze the dynamics of the magnetic domain walls in magnetic Weyl semimetals. Owing to the strong spin-orbit coupling in Weyl semimetals, the spin-transfer torque can be significantly enhanced, because of which they can provide a more efficient means of controlling magnetic textures. We derive the analytical expression of the spin-transfer torque and find that the velocity of the domain wall is one order of magnitude great…
Spontaneous symmetry breaking is ubiquitous in physics. Its spectroscopic signature consists in the softening of a specific mode upon approaching the transition from the high symmetry side and its subsequent splitting into a zero-frequency "Goldstone" mode and a non-zero-frequency "Higgs" mode. Although they determine the whole system dynamics, these features are difficult to address in practice because of their vanishing coupling to most experimental probes and/or their strong interaction with other fluctuations. In this work, we consider a periodic magnetic modulation occurring in a ferromag…
The large spin orbit coupling in topological insulators results in helical spin-textured Dirac surface states that are attractive for topological spintronics. These states generate an efficient spin-orbit torque on proximal magnetic moments at room temperature. However, memory or logic spin devices based upon such switching require a non-optimal three terminal geometry, with two terminals for the writing current and one for reading the state of the device. An alternative two terminal device geometry is now possible by exploiting the recent discovery of a unidirectional spin Hall magnetoresista…
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…
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…
Adiabatic dynamics of conduction electrons in antiferromagnetic (AFM) materials with slowly varying spin texture is developed. Quite different from the ferromagnetic (FM) case, adiabaticity in AFM texture does not imply perfect alignment of conduction electron spins with background profile, instead, it introduces an internal dynamics between degenerate bands. As a result, the orbital motion of conduction electrons becomes spin-dependent and is affected by two emergent gauge fields: one of them is the non-Abelian version of what has been discovered in FM systems; the other leads to an anomalous…
Achieving control over magnon spin currents in insulating magnets - where dissipation due to Joule heating is highly suppressed - is an active area of research that could lead to energy-efficient spintronics applications. However, magnon spin currents supported by conventional systems with uniform magnetic order have proven hard to control. An alternative approach that relies on topologically protected magnonic edge states of spatially periodic magnetic textures has recently emerged. A prime example of such textures is the ferromagnetic skyrmion crystal which hosts chiral edge states providing…
Spin-orbit coupling in inversion-asymmetric magnetic crystals and structures has emerged as a powerful tool to generate complex magnetic textures, interconvert charge and spin under applied current, and control magnetization dynamics. Current-induced spin-orbit torques mediate the transfer of angular momentum from the lattice to the spin system, leading to sustained magnetic oscillations or switching of ferromagnetic as well as antiferromagnetic structures. The manipulation of magnetic order, domain walls and skyrmions by spin-orbit torques provides evidence of the microscopic interactions bet…
Antiferromagnetic materials present us with rich and exciting physics, which we can exploit to open new avenues in spintronic device applications. We explore perpendicularly magnetized exchange biased systems of Pt/Co/IrMn and Pt/Co/FeMn, where the crossover from paramagnetic to antiferromagnetic behavior in the IrMn and FeMn layers is accessed by varying the thickness. We demonstrate, through magneto-optical imaging, that the magnetic domain morphology of the ferromagnetic Co layer is influenced by the N${é}$el order of the antiferromagnet (AFM) layers. We relate these variations to the aniso…
Effective dynamics of conduction electrons in antiferromagnetic (AFM) materials with slowly varying spin texture is developed via non-Abelian gauge theory. Quite different from the ferromagnetic (FM) case, the spin of a conduction electron does not follow the background texture even in the adiabatic limit due to the accumulation of a SU(2) non-Abelian Berry phase. Correspondingly, it is found that the orbital dynamics becomes spin-dependent and is affected by two emergent gauge fields. While one of them is the non-Abelian generalization of what has been discovered in FM systems, the other lead…
We study current-induced dynamics of spin textures in thin magnetic nanowires. We derive effective equations of motion describing the dynamics of the domain-wall soft modes associated with topological defects. Because the magnetic domain walls are topological objects, these equations are universal and depend only on a few parameters. We obtain spin spiral domain-wall structure in ferromagnetic wires with Dzyaloshinskii-Moriya interaction and critical current dependence on this interaction. We also find the most efficient way to move the domain walls by resonant current pulses and propose a pro…
We investigate one-dimensional (1D) Majorana bound states (MBSs) realized in terms of the helical edge states of a 2D quantum spin-Hall insulator (QSHI) in a heterostructure with a superconducting substrate and two ferromagnetic insulators (FIs). By means of Bogoliubov-de Gennes approach we demonstrate that there is a helical spin texture in the MBS wave function with a pitch proportional to the Fermi momentum of the helical edge states of QSHI. Moreover, simultaneous detection on local density of states by scanning tunneling microscopy and spectroscopy at a position close to one FI edge and a…
Advanced vector imaging techniques provide us with 3D maps of magnetization fields in which topological concepts can be directly applied to describe real-space experimental textures in non-ideal geometries. Here, the 3D magnetization of a low symmetry permalloy microstructure is obtained by X-ray vector magnetic tomography and analysed in detail in terms of topological charges and emergent fields. A central asymmetric domain wall with a complex 3D structure is observed in which magnetization chirality transitions are mediated by Bloch points arranged in several dipoles and a triplet. The ideal…
Antiferromagnets with vanishingly small (or zero) magnetization are interesting candidates for spintronics applications. In the present paper we propose two models for description of the current-induced phenomena in antiferromagnetic textures. We show that the magnetization that originates from rotation or oscillations of antiferromagnetic vector can, via $sd$-exchange coupling, polarize the current and give rise to adiabatic and nonadiabatic spin torques. Due to the Lorentz-type dynamics of antiferromagnetic moments (unlike the Galilenian-like dynamics in ferromagnets), the adiabatic spin tor…
