We investigate theoretically skyrmion magnonic crystal, i.e., the dynamics of the magnetization in a chain of the ferromagnetic nanodots being in skyrmion magnetic configuration. We show that collective excitations are possible to be observed in the structure. We present the dispersion relation of the coupled skyrmions. It exhibit a periodical property in dependence on wave vector, characteristic feature of the band structure in magnonic crystals. Spatial analysis of the magnetization amplitude associated with the magnonic bands confirms type of the excited modes, as breathing and clockwise gyrotropic dynamical skyrmions. These high and low frequency excitations, propagate with negative and positive group velocity, respectively, and can be explored for study fundamental properties and technological applications in spintronics and magnonics.
The presence of interfacial Dzyaloshinskii-Moriya interaction (DMI) may lead to the appearance of Néel skyrmions in ferromagnetic films. These topologically protected structures, whose diameter is as small as a few nanometers, can be nowadays stabilized at room temperature and have been proposed for the realization of artificial magnonic crystals and new spintronic devices, such as racetrack memories. In this perspective, it is of utmost importance to analyze their dynamical properties in the GHz range, i.e. in the operation range of current communication devices. Here we exploited the softwar…
Spin torque nano-oscillator has been extensively studied both theoretically and experimentally in recent decades due to its potential applications in future microwave communication technology and neuromorphic computing. In this work, we present a skyrmion-based spin torque nano-oscillator driven by a spatially uniform direct current, where the skyrmion is confined by two pinning sites. Different from other skyrmion-based oscillators that arise from the circular motion or the breathing mode of a skyrmion, the steady-state oscillatory motions are produced by the periodic deformation of an elonga…
We study the motion of magnetic skyrmions in a nanowire induced by a spin-wave current $J$ flowing out of a driving layer close to the edge of the wire. By applying micromagnetic simulation and an analysis of the effective Thiele equation, we find that the skyrmion trajectory is governed by an interplay of both forces due to the magnon current and the wire boundary. The skyrmion is attracted to the driving layer and is accelerated by the repulsive force due to the wire boundary. We consider both cases of a driving longitudinal and transverse to the nanowire, but a steady-state motion of the sk…
Magnetic materials hosting correlated electrons play an important role for information technology and signal processing. The currently used ferro-, ferri- and antiferromagnetic materials provide microscopic moments (spins) that are mainly collinear. Recently more complex spin structures such as spin helices and cycloids have regained a lot of interest. The interest has been initiated by the discovery of the skyrmion lattice phase in non-centrosymmetric helical magnets. In this review we address how spin helices and skyrmion lattices enrich the microwave characteristics of magnetic materials. W…
Various latest experiments have proven the theoretical prediction that domain walls in planar magnetic structures can channel spin waves as outstanding magnonic waveguides, establishing a superb platform for building magnonic devices. Recently, three-dimensional nanomagnetism has been boosted up and become a significant branch of magnetism, because three-dimensional magnetic structures expose a lot of emerging physics hidden behind planar ones and will inevitably provide broader room for device engineering. Skyrmions and antiSkyrmions, as natural three-dimensional magnetic configurations, are …
Antiferromagnetic skyrmion crystals are magnetic phases predicted to exist in antiferromagnets with Dzyaloshinskii-Moriya interactions. Their spatially periodic noncollinear magnetic texture gives rise to topological bulk magnon bands characterized by nonzero Chern numbers. We find topologically-protected chiral magnonic edge states over a wide range of magnetic fields and Dzyaloshinskii-Moriya interaction values. Moreover, and of particular importance for experimental realizations, edge states appear at the lowest possible energies, namely, within the first bulk magnon gap. Thus, antiferromag…
An optical frequency comb consists of a set of discrete and equally spaced frequencies and has found wide applications in the synthesis over broad spectral frequencies of electromagnetic wave and precise optical frequency metrology. Despite the analogies between magnons and photons in many aspects, the analogue of optical frequency comb in magnonic system has not been reported. Here, we theoretically study the magnon-skyrmion interaction and find that magnonic frequency comb (MFC) can be generated above a threshold of driving amplitude, where the nonlinear scattering process involving three ma…
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…
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…
We theoretically study the thermal Hall effect by magnons in skyrmion crystal phases of ferrimagnets in the vicinity of the angular momentum compensation point (CP). To this end, we start by deriving the equation of motion for magnons in the background of an arbitrary equilibrium spin texture, which gives rise to the fictitious electromagnetic field for magnons. As the net spin density varies, the resultant equation of motion interpolates between the relativistic Klein-Gordon equation at CP and the nonrelativistic Schr{ö}dinger-like equation away from it. In skyrmion crystal phases, the right-…
We propose a new method to generate magnetic skyrmions through spin-wave focusing in chiral ferromagnets.A lens is constructed to focus spin waves by a curved interface between two ferromagnetic thin films with different perpendicular magnetic anisotropies. Based on the principle of identical magnonic path length, we derive the lens contour that can be either elliptical or hyperbolical depending on the magnon refractive index. Micromagnetic simulations are performed to verify the theoretical design. It is found that under proper condition magnetic skyrmions emerge near the focus point of the l…
We present the observation of a complete bandgap and collective spin wave excitation in two-dimensional magnonic crystals comprised of arrays of nanoscale antidots and nanodots, respectively. Considering that the frequencies dealt with here fall in the microwave band, these findings can be used for the development of suitable magnonic metamaterials and spin wave based signal processing. We also present the application of a numerical procedure, to compute the dispersion relations of spin waves for any high symmetry direction in the first Brillouin zone. The results obtained from this procedure …
We propose a method to generate magnetic skyrmions by focusing spin waves totally reflected by a curved film edge. Based on the principle of identical magnonic path length, we derive the edge contour that is parabolic and frequency-independent. Micromagnetic simulations are performed to verify our theoretical design. It is found that under proper conditions, magnetic droplet first emerges near the focal point where the spin-wave intensity has been significantly enhanced, and then converts to magnetic skyrmion accompanied by a change of the topological charge. The phase diagram about the amplit…
Lattice vibration modes are collective excitations in periodic arrays of atoms or molecules. These modes determine novel transport properties in solid crystals. Analogously, in periodical arrangements of magnetic vortex-state disks, collective vortex motions have been predicted. Here, we experimentally observe wave modes of collective vortex gyration in one-dimensional (1D) chains of periodic disks using time-resolved scanning transmission x-ray microscopy. The observed modes are interpreted based on micromagnetic simulation and numerical calculation of coupled Thiele equations. Dispersion of …
Magnonic crystals are prototype magnetic metamaterials designed for the control of spin wave propagation. Conventional magnonic crystals are composed of single domain elements. If magnetization textures, such as domain walls, vortices and skyrmions, are included in the building blocks of magnonic crystals, additional degrees of freedom over the control of the magnonic band structure can be achieved. We theoretically investigate the influence of domain walls on the spin wave propagation and the corresponding magnonic band structure. It is found that the rotation of magnetization inside a domain…
We study the spin waves of the triangular skyrmion crystal that emerges in a two dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii-Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic ba…
Using a particle-based model, we examine the collective dynamics of skyrmions interacting with a funnel potential under dc driving as the skyrmion density and relative strength of the Magnus and damping terms are varied. For driving in the easy direction, we find that increasing the skyrmion density reduces the average skyrmion velocity due to jamming of skyrmions near the funnel opening, while the Magnus force causes skyrmions to accumulate on one side of the funnel array. For driving in the hard direction, there is a critical skyrmion density below which the skyrmions become trapped. Above t…
The emergence of a topologically nontrivial vortex-like magnetic structure, the magnetic skyrmion, has launched new concepts for memory devices. There, extensive studies have theoretically demonstrated the ability to encode information bits by using a chain of skyrmions in one-dimensional nanostripes. Here, we report the first experimental observation of the skyrmion chain in FeGe nanostripes by using high resolution Lorentz transmission electron microscopy. Under an applied field normal to the nanostripes plane, we observe that the helical ground states with distorted edge spins would evolves…
Graphene exhibits quantum Hall ferromagnetism in which an approximate SU(4) symmetry involving spin and valley degrees of freedom is spontaneously broken. We construct a set of integer and fractional quantum Hall states that break the SU(4) spin/valley symmetry, and study their neutral and charged excitations. Several properties of these ferromagnets can be evaluated analytically in the SU(4) symmetric limit, including the full collective mode spectrum at integer fillings. By constructing explicit wave functions we show that the lowest energy skyrmion states carry charge $\pm 1$ for {\em any} …
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. …
Spin waves are the low-energy excitations of magnetically ordered materials. They are key elements in the stability analysis of the ordered phase and have a wealth of technological applications. Recently, we showed that spin waves of a magnetic nanowire may carry a definite amount of orbital angular momentum components along the propagation direction. This helical, in addition to the chiral, character of the spin waves is related to the spatial modulations of the spin wave phase across the wire. It, however, remains a challenge to generate and control such modes with conventional magnetic fiel…
We study spin-wave excitation modes of $kπ$ skyrmion in a magnetic nanodot under an external magnetic field along $z$-direction using micromagnetic simulations based on Landau-Lifshitz-Gilbert equation. We find that a transition of $kπ$ skyrmion to other skyrmion-like structures appears under some critical external field, the corresponding spin-wave spectra are simulated for each state in the process of applying magnetic field. For skyrmion, the frequencies of excitation modes increases and then decreases with the low frequency modes splitting at a critical magnetic field. In addition to the w…
Engineering a driven-dissipative bath of altermagnetic quantum magnons for controlling classical dynamics of spins hosting spin waves, domain walls, or skyrmions
Here we study the effect of an additional interfacial spin-transfer torque, as well as the well established spin-orbit torque and bulk spin-transfer torque, on skyrmion collections - group of skyrmions dense enough that they are not isolated from on another - in ultrathin heavy metal / ferromagnetic multilayers, by comparing modelling with experimental results. Using a skyrmion collection with a range of skyrmion diameters and landscape disorder, we study the dependence of the skyrmion Hall angle on diameter and velocity, as well as the velocity as a function of diameter. We show the experimen…
Antiferromagnetic Skyrmion Scattering Revealed by Direct Time-Resolved Imaging of Collective Dynamics
Institute of Physics, Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学物理研究所）；Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University（东北大学电气通信研究所纳米电子与自旋电子学实验室）；Singulus Technologies AG（辛古卢斯科技有限公司）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Helmholtz-Zentrum Berlin für Materialien und Energie GmbH（柏林亥姆霍兹材料能源中心有限公司）
Skyrmion crystals (SkX) are periodic alignment of magnetic skyrmions, i.e., a type of topologically protected spin textures. Compared with ordinary crystals, they can be drastically deformed under anisotropic effects because they are composed of field patterns whose deformation does not cause any bond-breaking. This exotic ductility of SkX bring about great tunability of its collective excitations called emergent phonons, which are vital for magnonics application. The question is how to quantitatively determine the emergent phonons of distorted SkX. Here we systematically study the long wavele…
The magnetization dynamics in nanostructures has been extensively studied in the last decades, and nanomagnetism has evolved significantly over that time, discovering new effects, developing numerous applications, and identifying promising new directions. This includes magnonics, an emerging research field oriented on the study of spin-wave dynamics and their applications. In this context, thin ferromagnetic films with perpendicular magnetic anisotropy (PMA) offer interesting opportunities to study spin waves, in particular, due to out-of-plane magnetization in remanence or at relatively weak …
Spin waves (SW) are the excitation of the spin system in a ferromagnetic condensed matter body. They are collective excitations of the electron system and, from a quasi-classical point of view, can be understood as a coherent precession of the electrons' spins. Analogous to photons, they are also referred to as magnons indicating their quasi-particle character. The collective nature of SWs is established by the short-range exchange interaction as well as the non-local magnetic dipolar interaction, resulting in coherence of SWs from mesoscopic to even macroscopic length scales. As one consequen…
We present a minimal one-dimensional model of collective spin excitations in itinerant ferromagnetic superlattices within the regime of parabolic spin-carrier dispersion. We discuss the cases of weakly and strongly modulated magnetic profiles finding evidences of antiferromagnetic correlations for long-wave magnons (especially significant in layered systems), with an insight into the ground state properties. In addition, the presence of local minima in the magnonic dispersion suggests the possibility of (thermal) excitation of spin waves with a relatively well controlled wave length. Some of t…
Spin waves in antiferromagnetic materials have great potential for next-generation magnonic technologies. However, their properties and their dependence on the type of ground-state antiferromagnetic structure are still open questions. Here, we investigate theoretically spin waves in one- and two-dimensional model systems with a focus on noncollinear antiferromagnetic textures such as spin spirals and skyrmions of opposite topological charges. We address in particular the nonreciprocal spin excitations recently measured in bulk antiferromagnet $α$--$\text{Cu}_2\text{V}_2\text{O}_7$ utilizing in…
We use particle-based simulations to examine the static and driven collective phases of skyrmions interacting with random quenched disorder. We show that non-dissipative effects due to the Magnus term reduce the depinning threshold and strongly affect the skyrmion motion and the nature of the dynamic phases. The quenched disorder causes the Hall angle to become drive-dependent in the moving skyrmion phase, while different flow regimes produce distinct signatures in the transport curves. For weak disorder, the skyrmions form a pinned crystal and depin elastically, while for strong disorder the …
We investigated the lifetime of spin wave eigenmodes in periodic and quasiperiodic sequences of Py and Co wires. Those materials differ significantly in damping coefficients, therefore, the spatial distribution of the mode amplitude within the structure is important for the lifetime of collective spin wave excitations. Modes of the lower frequencies prefer to concentrate in Py wires, because of the lower FMR frequency for this material. This inhomogeneous distribution of amplitude of modes (with lower amplitude in material of higher damping and with higher amplitude in material of lower dampin…
The two-dimensional electron gas in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor nu=1 even in the absence of tunneling between the layers. This system has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor nu =1 a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling (Delta_SAS), Zeeman coupling (Delta_Z) or electrical bias (Delta_b), these textured crystal states can involve spin, pseud…
The large arrays of magnetic dots are the building blocks of magnonic crystals and the emerging bit patterned media for future recording technology. In order to fully utilize the functionalities of high density magnetic nanodots, a method for the selective reversal of a single nanodot in a matrix of dots is desired. We have proposed a method for magnetization reversal of a single nanodot with microwave excitation in a matrix of magneto-statically interacting dots. The method is based on the excitation of collective modes and the spatial anomaly in the microwave power absorption. We perform num…
Collective excitation modes in solid state systems play a central role in circuit quantum electrodynamics, cavity optomechanics, and quantum magnonics. In the latter, quanta of collective excitation modes in a ferromagnet, called magnons, interact with qubits to provide the nonlinearity necessary to access quantum phenomena in magnonics. A key ingredient for future quantum magnonics systems is the ability to probe magnon states. Here we observe individual magnons in a millimeter-sized ferromagnet coherently coupled to a superconducting qubit. Specifically, we resolve magnon number states in sp…
In the last decades, collinear magnetic insulating systems have emerged as promising energy-saving information carriers. Their elementary collective spin excitations, i.e., magnons, can propagate for long distances bypassing the Joule heating effects that arise from electron scattering in metal-based devices. This tutorial article provides an introduction to theoretical and experimental advances in the study of magnonics in collinear magnetic insulating systems. We start by outlining the quantum theory of spin waves in ferromagnetic and antiferromagnetic systems and we discuss their quantum st…
We study the collective dynamics of the Skyrmion crystal (SkX) in thin films of ferromagnetic metals resulting from the nontrivial Skyrmion topology. We show that the current-driven motion of the crystal reduces the topological Hall effect and the Skyrmion trajectories bend away from the direction of the electric current (the Skyrmion Hall effect). We find a new dissipation mechanism in non-collinear spin textures that can lead to a much faster spin relaxation than Gilbert damping, calculate the dispersion of phonons in the SkX, and discuss effects of impurity pinning of Skyrmions.
Magnons are the quanta of collective spin excitations in magnetically-ordered systems and manipulation of magnons for computing and information processing has witnessed the development of ``magnonics". A magnon corresponds to an excitation of the magnetic system from its ground state and the creation of a magnon thus increases the total energy of the system. In this perspective, we introduce the antiparticle of a magnon, dubbed the antimagnon, as an excitation that lowers the magnetic energy. We investigate the stability and thermal occupation of antimagnons and verify our theory by micromagne…
Magnetic materials in which it is possible to control the topology of their magnetic order in real space or the topology of their magnetic excitations in reciprocal space are highly sought-after as platforms for alternative data storage and computing architectures. Here we show that multiferroic insulators, owing to their magneto-electric coupling, offer a natural and advantageous way to address these two different topologies using laser fields. We demonstrate that via a delicate balance between the energy injection from a high-frequency laser and dissipation, single skyrmions -- archetypical …
We investigate the propagation of magnetic skyrmions on elastically deformable geometries by employing imaginary time quantum field theory methods. We demonstrate that the Euclidean action of the problem carries information of the elements of the surface space metric, and develop a description of the skyrmion dynamics in terms of a set of collective coordinates. We reveal that novel curvature-driven effects emerge in geometries with non-constant curvature, which explicitly break the translational invariance of flat space. In particular, for a skyrmion stabilized by a curvilinear defect, an ine…
We show that periodic magnetic nanostructures (magnonic crystals) represent an ideal system for studying excitations on disordered periodical lattices because of the possibility of controlled variation of the degree of disorder by varying the applied magnetic field. Ferromagnetic resonance (FMR) data collected inside minor hysteresis loops for a periodic array of Permalloy nanowires of alternating width and magnetic force microscopy images of the array taken after running each of these loops were used to establish convincing evidence that there is a strong correlation between the type of FMR r…
In the developing field of magnonics,it is very important to achieve tailoring of spin wave propagation by both a proper combination of materials with different magnetic properties and their nanostructuring on the submicrometric scale. We have exploited deep ultra-violet lithography, in combination with tilted shadow deposition technique, to fabricate arrays of closely spaced bi-layer nanowires (NWs), with separation d=100 nm and periodicity a=440 nm, having bottom and top layers made of Permalloy and Iron, respectively. The NWs have either rectangular cross section (bottom and upper layers of…
We study the nucleation and collective dynamics of Shankar skyrmions [R. Shankar, Journal de Physique 38, 1405 (1977)] in the class of frustrated magnetic systems described by an SO(3) order parameter, including multi-lattice antiferromagnets and amorphous magnets. We infer the expression for the spin-transfer torque that injects skyrmion charge into the system and the Onsager-reciprocal pumping force that enables its detection by electrical means. The thermally-assisted flow of topological charge gives rise to an algebraically decaying drag signal in nonlocal transport measurements. We contra…
Quantum magnonics is a new and active research field, leveraging the strong collective coupling between microwaves and magnetically ordered spin systems. To date work in quantum magnonics has focused on transition metals and almost entirely on ferromagnetic resonances in yttrium iron garnet (YIG). Antiferromagnetic systems have gained interest as they produce no stray field, and are therefore robust to magnetic perturbations and have narrow, shape independent resonant linewidths. Here we show the first experimental evidence of ultrastrong-coupling between a microwave cavity and collective anti…
Magnetic skyrmions are topological quasiparticles with great potential for applications in future information storage and processing devices because of their nanoscale size, high stability, and large velocity. Recently, the high-frequency properties of skyrmions have been explored for magnon nanodevices. Here we systematically study the dynamics of an isolated skyrmion under voltage excitation through the voltage-controlled magnetic anisotropy effect in a circular thin film. A theoretical model considering the demagnetization energy, which has often been neglected or treated superficially in p…
Recent experiments have established a qualitative difference between the magnetization temperature-dependences $M(T)$ of quantum Hall ferromagnets at integer and fractional filling factors. We explain this difference in terms of the relative energies of collective magnon and particle-hole excitations in the two cases. Analytic calculations for hard-core model systems are used to demonstrate that, in the fractional case, interactions suppress the magnetization at finite temperatures and that particle-hole excitations rather than long-wavelength magnons control $M(T)$ at low $T$.
A spin-polarized current in a nanocontact to a magnetic film can create collective magnetic oscillations by compensating the magnetic damping. In particular, in materials with uniaxial magnetic anisotropy, droplet solitons have been observed a self-localized excitation consisting of partially reversed magnetization that precesses coherently in the nanocontact region. It is also possible to generate topological droplet solitons, known as \emph{dynamical skyrmions}. Here we study the conditions that promote either droplet or dynamical skyrmion formation and describe their stability in magnetic f…
Excitations of two-dimensional skyrmion lattice are theoretically studied based on a collective coordinate description. Starting from the representation of skyrmion lattice in terms of three helices, we identify the canonical coordinates describing low energy excitations as phasons. The phason excitation spectra turn out to have one gapless mode with a quadratic dispersion and one massive mode, in agreement with previous studies. We will show that there is another collective mode governing the topological nature and the stability of skyrmion lattice and that the fluctuation of this mode leads …
The techniques of microwave quantum optics are applied to collective spin excitations in a macroscopic sphere of ferromagnetic insulator. We demonstrate, in the single-magnon limit, strong coupling between a magnetostatic mode in the sphere and a microwave cavity mode. Moreover, we introduce a superconducting qubit in the cavity and couple the qubit with the magnon excitation via the virtual photon excitation. We observe the magnon-vacuum-induced Rabi splitting. The hybrid quantum system enables generation and characterization of non-classical quantum states of magnons.
