We describe the features of magnonic crystals based upon antiferromagnetic elements. Our main results are that with a periodic modulation of either magnetic fields or system characteristics, such as the anisotropy, it is possible to tailor the spin wave spectra of antiferromagnetic systems into a band-like organization that displays a segregation of allowed and forbidden bands. The main features of the band structure, such as bandwidths and bandgaps, can be readily manipulated. Our results provide a natural link between two steadily growing fields of spintronics: antiferromagnetic spintronics and magnonics.
We investigate the nonequilibrium spin polarization due to a temperature gradient in antiferromagnetic insulators, which is the magnonic analogue of the inverse spin-galvanic effect of electrons. We derive a linear response theory of a temperature-gradient-induced spin polarization for collinear and noncollinear antiferromagnets, which comprises both extrinsic and intrinsic contributions. We apply our theory to several noncentrosymmetric antiferromagnetic insulators, i.e., to a one-dimensional antiferromagnetic spin chain, a single layer of kagome noncollinear antiferromagnet, e.g., $\text{KFe…
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…
The magnonic band gaps of the two types of planar one-dimensional magnonic crystals comprised of the periodic array of the metallic stripes on yttrium iron garnet (YIG) film and YIG film with an array of grooves was analyzed experimentally and theoretically. In such periodic magnetic structures the propagating magnetostatic surface spin waves were excited and detected by microstripe transducers with vector network analyzer and by Brillouin light scattering spectroscopy. Properties of the magnonic band gaps were explained with the help of the finite element calculations. The important influence…
In this work, the rich ground-state structure of orthogonally-coupled symmetric all-antiferromagnetic junctions with easy-plane anisotropy is reported. Spin reorientation process rather than the traditional spin flop (SF) occurs, resulting in a novel phase in which Néel vectors preserve the mirror-reflection symmetry (termed as ``MRS phase"). The phase transitions between SF and MRS phases can be either the first- or second-order. After disturbed by external stimuli, magnons with different parities emerge. For in-plane dc fields, no couplings between magnons occur. When dc fields become obliqu…
Magnons - the quanta of spin waves - propagating in magnetic materials with wavelengths at the nanometer-scale and carrying information in the form of an angular momentum, can be used as data carriers in next-generation, nano-sized low-loss information processing systems. In this respect, artificial magnetic materials with properties periodically varied in space, known as magnonic crystals, are especially promising for controlling and manipulating the magnon currents. In this article, different approaches for the realization of static, reconfigurable, and dynamic magnonic crystals are presente…
We present the concept of Zak phase for spin waves in planar magnonic crystals and discuss the conditions for the existence of interface modes localized on the boundary between two magnonic crystals with centrosymmetric unit cells. Using the symmetry criterion and the calculated logarithmic derivative of the Bloch function we study the interface modes to demonstrate the bulk-edge correspondence. Our theoretical results are verified numerically for structures in the exchange and exchange-dipolar regimes and extended to the case in which one of the magnonic crystals has an arbitrary unit cell. M…
We have investigated theoretically band structure of spin waves in magnonic crystals with periodicity in one-(1D), two- (2D) and three-dimensions (3D). We have solved Landau-Lifshitz equation with the use of plane wave method, finite element method in frequency domain and micromagnetic simulations in time domain to find the dynamics of spin waves and spectrum of their eigenmodes. The spin wave spectra were calculated in linear approximation. In this paper we show usefulness of these methods in calculations of various types of spin waves. We demonstrate the surface character of the Damon-Eshbac…
An electric current controlled spin-wave logic gate based on a width-modulated dynamic magnonic crystal is realized. The device utilizes a spin-wave waveguide fabricated from a single-crystal Yttrium Iron Garnet film and two conducting wires attached to the film surface. Application of electric currents to the wires provides a means for dynamic control of the effective geometry of the waveguide and results in a suppression of the magnonic band gap. The performance of the magnonic crystal as an AND logic gate is demonstrated.
A new type of magnonic crystals, curvature induced ones, is realized in ferromagnetic nanowires with periodically deformed shape. A magnon band structure of such crystal is fully determined by its curvature: the developed theory is well confirmed by simulations. An application to nanoscale spintronic devises with the geometrically tunable parameters is proposed, namely, to filter elements.
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 gy…
Multiferroics offer an elegant means to implement voltage-control and on the fly reconfigurability in microscopic, nanoscaled systems based on ferromagnetic materials. These properties are particularly interesting for the field of magnonics, where spin waves are used to perform advanced logical or analogue functions. Recently, the emergence of nano-magnonics {\color{black} is expected to} eventually lead to the large-scale integration of magnonic devices. However, a compact voltage-controlled, on demand reconfigurable magnonic system has yet to be shown. Here, we introduce the combination of m…
In this paper, we theoretically study the influence of a non-magnetic spacer between ferromagnetic dots and ferromagnetic matrix on the frequency dispersion of the spin wave excitations in two-dimensional bi-component magnonic crystals. By means of the dynamical matrix method we investigate structures inhomogeneous across the thickness represented by square arrays of Cobalt or Permalloy dots in a Permalloy matrix. We show that the introduction of a non-magnetic spacer significantly modifies the total internal magnetic field especially at the edges of the grooves and dots. This permits the mani…
We study the effect of surface-induced Dzyaloshinskii-Moriya interaction (DMI) on the ferromagnetic resonance (FMR) spectrum of thickness-modulated one-dimensional magnonic crystals and isolated stripes. The DMI is found to substantially increases the intensity of absorption peaks and shifts the frequencies of the laterally quantized modes. The role of the DMI is determined by analyzing the amplitude and phase distributions of dynamic magnetic excitations calculated with frequency- and time-domain calculation methods. We propose experimentally realizable magnonic crystals and confined structur…
We investigate spin-wave propagation in a microstructured magnonic-crystal waveguide fabricated by localized ion implantation. The irradiation caused a periodic variation in the saturation magnetization along the waveguide. As a consequence, the spin-wave transmission spectrum exhibits a set of frequency bands, where spin-wave propagation is suppressed. A weak modification of the saturation magnetization by 7% is sufficient to decrease the spin-wave transmission in the band gaps by a factor of 10. These results evidence the applicability of localized ion implantation for the fabrication of eff…
By means of the plane wave method we study spin wave dynamics in two-dimensional bi-component magnonic crystals based on a squeezed hexagonal lattice and consist of a permalloy thin film with cobalt inclusions. We explore the dependence of a spin wave frequency on the external magnetic field, especially in weak fields where the mode softening takes place. For considered structures, the mode softening proves to be highly non-uniform on both the mode number and the wave vector. We found this effect to be responsible for the omnidirectional band gap opening. Moreover, we show that the enhancement…
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…
Magnonic crystals are magnetic metamaterials, that provide a promising way to manipulate magnetodynamic properties by controlling the geometry of the patterned structures. Here, we study the magnetodynamic properties of 1D magnonic crystals consisting of parallel NiFe strips with different strip widths and separations. The strips couple via dipole-dipole interactions. As an alternative to experiments and/or micromagnetic simulations, we investigate the accuracy of a simple macrospin model. For the case of simple strips, a model with a single free parameter to account for an overestimation of t…
We demonstrate a microscopic magnonic-crystal waveguide produced by nano-patterning of a 20 nm thick film of Yttrium Iron Garnet. By using the phase-resolved micro-focus Brillouin light scattering spectroscopy, we map the intensity and the phase of spin waves propagating in such a periodic magnetic structure. Based on these maps, we obtain the dispersion and the attenuation characteristics of spin waves providing detailed information about the physics of spin-wave propagation in the magnonic crystal. We show that, in contrast to the simplified physical picture, the maximum attenuation of spin …
The influence of the Dzyaloshinskii-Moriya interaction in ultra-thin ferromagnetic films and chiral magnonic crystals on the behavior of spin waves is reviewed. During the last decade, it has been shown, both theoretically and experimentally, that this anisotropic exchange interaction produces non-reciprocal features on the spin-wave spectrum of a magnetic system, a phenomenon that occurs both for bulk and interfacial Dzyaloshinskii-Moriya coupling. More recently, the concept of a chiral magnonic crystal has been introduced, where the interfacial Dzyaloshinskii-Moriya interaction is periodic. …
Strongly-interacting nanomagnetic systems are pivotal across next-generation technologies including reconfigurable magnonics and neuromorphic computation. Controlling magnetisation state and local coupling between neighbouring nanoelements allows vast reconfigurable functionality and a host of associated functionalities. However, existing designs typically suffer from an inability to tailor inter-element coupling post-fabrication and nanoelements restricted to a pair of Ising-like magnetisation states. Here, we propose a new class of reconfigurable magnonic crystal incorporating nanodisks as t…
We discuss several aspects of chiral optomagnonics in antiferromagnetic insulators by considering common symmetries between the electromagnetic field and spin excitations. This approach allows us to look at optical and magnetic materials from similar perspectives, and discuss useful analogies between them. We show that spin waves in collinear antiferromagnets and the electromagnetic field in vacuum are both invariant under the same eight-dimensional algebra of symmetry transformations. By such analogy, we can extend the concept of optical chirality to antiferromagnetic insulators, and demonstr…
Strongly-interacting nanomagnetic arrays are crucial across an ever-growing suite of technologies. Spanning neuromorphic computing, control over superconducting vortices and reconfigurable magnonics, the utility and appeal of these arrays lies in their vast range of distinct, stable magnetisation states. Different states exhibit different functional behaviours, making precise, reconfigurable state control an essential cornerstone of such systems. However, few existing methodologies may reverse an arbitrary array element, and even fewer may do so under electrical control, vital for device integ…
We demonstrate the use of the magnetic-field-dependence of highly spatially confined, GHz-frequency ferromagnetic resonances in a ferromagnetic nanostructure for the detection of adsorbed magnetic nanoparticles. This is achieved in a large area magnonic crystal consisting of a thin ferromagnetic film containing a periodic array of closely spaced, nano-scale anti-dots. Stray fields from nanoparticles within the anti-dots modify resonant dynamic magnetisation modes in the surrounding magnonic crystal, generating easily measurable resonance peak shifts. The shifts are comparable to the resonance …
A nano-scale reconfigurable magnonic crystal is designed using voltage-controlled perpendicular magnetic anisotropy (PMA) in ferromagnetic-dielectric hetero-structures. A periodic array of gate metallic stripes is placed on top of a MgO/Co structure in order to apply a periodic electric field and to modify the PMA in Co. It is numerically demonstrated that the application of the voltage to the gate stripes modifies the spin-wave propagation and leads to the formation of band gaps in the spin-wave spectrum. The band gaps are dynamically controllable, i.e. it is possible to switch band gaps on a…
The Stern-Gerlach (SG) effect is well known as the spin-dependent splitting of a beam of atoms carrying magnetic moments by a magnetic-field gradient, leading to the concept of electron spin. Antiferromagnets can accommodate two magnon modes with opposite spin polarizations, which is equivalent to the spin property of electrons. Here, we propose the existence of an all-magnonic SG effect in antiferromagnetic magnonic system, where a linearly polarized spin-wave beam is deflected by a straight Dzyaloshinskii-Moriya interaction (DMI) interface into two opposite polarized spin-wave beams propagat…
The one-dimensional planar magnonic crystals are usually fabricated as a sequence of stripes intentionally or accidentally separated by non-magnetic spacers. The influence of spacers on shaping the spin wave spectra is complex and still not completely clarified. We performed the detailed numerical studies of the one-dimensional single- and bi-component magnonic crystals comprised of a periodic array of thin ferromagnetic stripes separated by non-magnetic spacers. We showed that the dynamic dipolar interactions between the stripes mediated by non-magnetic spacer, even ultra-narrow, significantl…
We present a theoretical investigation of the Goos-Hänchen effect, i.e., the lateral shift of the light beam transmitted through one-dimensional biperiodic multilayered photonic systems consisting of equidistantmagnetic layers separated by finite size dielectric photonic crystals. We show that the increase of the number of periods in the photonic-magnonic structure leads to increase of the Goos-Hänchen shift in the vicinity of the frequencies of defect modes located inside the photonic band gaps. Presence of the linear magnetoelectric coupling in the magnetic layers can result in a vanishing o…
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…
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 …
Topological phases have been explored in various fields in physics such as spintronics, photonics, liquid helium, correlated electron system and cold-atomic system. This leads to the recent foundation of emerging materials such as topological band insulators, topological photonic crystals and topological superconductors/superfluid. In this paper, we propose a topological magnonic crystal which provides protected chiral edge modes for magnetostatic spin waves. Based on a linearized Landau-Lifshitz equation, we show that a magnonic crystal with the dipolar interaction acquires spin-wave volume-m…
We have investigated surface spin wave states in one-dimensional planar bi-component magnonic crystals, localized on the surfaces resulting from the breaking of the periodic structure. The two systems have been considered: the magnonic crystal with periodic changes of the anisotropy field in exchange regime and the magnonic crystal composed of Fe and Ni stripes in dipolar regime with exchange interactions included. We chose the symmetric unit cell for both systems to implement the symmetry related criteria for existence of the surface states. We investigated also the surface states induced by …
We present a theoretical investigation of the polarization plane rotation at light transmission - Faraday effect, through one-dimensional multilayered magneto-photonic systems consisting of periodically distributed magnetic and dielectric layers. We calculate Faraday rotation spectra of photonic-magnonic crystals, where cell (or supercell) is composed of magnetic layer and dielectric layer (or section of dielectric photonic crystal). We found that the Faraday rotation of p-polarized incident light is increasing in the transmission band with the number of magnetic supercells. The increase of Fa…
A theory of three-dimensional (3D) hypothetical magnonic crystal (conceived as the magnetic counterpart of the well-known photonic crystal) is developed and applied to explain the existence of a spin-wave frequency gap recently revealed in low-doped manganites $La_{1-x}Ca_{x}MnO_{3}$ by neutron scattering. A successful confrontation with the experimental results allows us to formulate a working hypothesis that certain manganites could be regarded as 3D magnonic crystals existing in nature.
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 …
The discovery of the ultrafast magnetization dynamics twenty years ago has led to a broad variety of experimental techniques to explore phenomena in magnetic materials with high temporal resolution. In the present article we present a study dealing with broadband excitation of spin-wave packets at different magnonic crystal continuous magnetic film interfaces. Similar to protected conducting states on the surfaces of topological band insulators, these interfaces exhibit surface spin-wave modes that propagate out of the crystal into the continuous film. The propagation distance depends on the d…
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…
We propose an alternative micromagnetic approach to determine the spin wave dispersion relations in magnonic structures. Characteristic of the method is that a limited area of the system is continuously excited with a spatially uniform oscillating field, tuned at a given frequency. After a transitory time, the regime magnetization dynamics is collected and a spatial Fourier analysis on it determines the frequency vs wave vector relation. Combining several simulations in any predetermined range of frequencies, at any resolution, we investigate the dispersion relations for different kinds of mag…
When the crystalline symmetries that protect a higher-order topological phase are not preserved at the boundaries of the sample, gapless hinge modes or in-gap corner states cannot be stabilized. Therefore, careful engineering of the sample termination is required. Similarly, magnetic textures, whose quantum fluctuations determine the supported magnonic excitations, tend to relax to new configurations that may also break crystalline symmetries when boundaries are introduced. Here we uncover that antiskyrmion crystals provide an experimentally accessible platform to realize a magnonic topologica…
Spin-wave modes are studied under the gradual transition from a flat thin film to a 'full' (one-dimensional) magnonic crystal. For this purpose, the surface of a pre-patterned 36.8 nm thin permalloy film was sequentially ion milled resulting in magnonic hybrid structures, referred to as surface-modulated magnonic crystals, with increasing modulation depth. After each etching step, ferromagnetic resonance measurements were performed yielding the spin-wave resonance modes in backward-volume and Damon-Eshbach geometry. The spin-wave spectra of these hybrid systems reveal an even larger variety of…
We introduce a new type of binary magnonic crystal, where Ni$_{80}$Fe$_{20}$ nanodots of two different sizes are diagonally connected forming a unit and those units are arranged in a square lattice. The magnetization dynamics of the sample is measured by using time-resolved magneto-optical Kerr effect microscope with varying magnitude and in-plane orientation ($ϕ$) of the bias magnetic field. Interestingly, at $ϕ=0^{\circ}$, the spin-wave mode profiles show frequency selective spatial localization of spin-wave power within the array. With the variation of $ϕ$ in the range $0^{\circ}<ϕ\leq 45^{…
We present the results of a systematic micromagnetic study of the effect of the Dzyaloshinskii-Moriya interaction (DMI) on the spin wave band structure of two one-dimensional magnonic crystals (MCs), both with the same periodicity p=300 nm, but different implementation of the DMI modulation. In the first system the artificial periodicity was achieved by modulating the interfacial DMI constant D, while in the second system also the sample morphology was modulated. Due to the folding property of the band structure in the dispersion relations of the magnonic crystals it is possible to extend the …
By means of the plane wave method, we study nonuniform, i.e., mode- and k-dependent, effects in the spin-wave spectrum of a two-dimensional bicomponent magnonic crystal. We use the crystal based on a hexagonal lattice squeezed in the direction of the external magnetic field wherein the squeezing applies to the lattice and the shape of inclusions. The squeezing changes both the demagnetizing field and the spatial confinement of the excitation, which may lead to the occurrence of an omnidirectional magnonic band gaps. In particular, we study the role played by propagational effects, which allows…
Using spatial light interference of ultrafast laser pulses, we generate a lateral modulation in the magnetization profile of an otherwise uniformly magnetized film, whose magnetic excitation spectrum is monitored via the coherent and resonant interaction with elastic waves. We find an unusual dependence of the magnetoelastic coupling as the externally applied magnetic field is angle- and field-tuned relative to the wave vector of the magnetization modulation, which can be explained by the emergence of spatially inhomogeneous spin-wave modes. In this regard, the spatial light interference metho…
The potential to control the number of the spin-wave band gaps of a magnonic crystal (MC) by variation of its geometry is investigated by numerical simulations. The magnonic crystal is represented by a micro-sized planar ferromagnetic waveguide with periodically variable width. By choosing a step-like or sinusoidal variation of the width, the magnonic crystal reveals multiple or single band gaps, respectively. This allows for additional degrees of freedom in the design of MC based microwave filters and phase shifters with desired characteristics. The MCs band gaps have been studied in the spac…
We present a semiclassical formalism for antiferromagnetic (AFM) magnonics which promotes the central ingredient of spin wave chirality, encoded in a quantity called magnonic isospin, to a first-class citizen of the theory. We use this formalism to unify results of interest from the field under a single chirality-centric formulation. Our main result is that the isospin is governed by unitary time evolution, through a Hamiltonian projected down from the full spin wave dynamics. Because isospin is SU(2)-valued, its dynamics on the Bloch sphere are precisely rotations - which, in general, do not …
We demonstrate a real-space imaging of a heterodyne signal of light that is produced as a result of the Brillouin light scattering by coherently driven magnons in magnetostatic modes. With this imaging technique, we characterize surface magnetostatic modes (Damon-Eshbach modes) in a one-dimensional magnonic crystal, which is formed by patterned aluminum strips deposited on the ferromagnetic film. The modified band structures of the magnonic crystal are deduced from the Fourier transforms of the real-space images. The heterodyne imaging provides a simple and powerful method to probe magnons in …
Hybrid systems combining magnons and superconducting quantum circuits have attracted increasing interest in recent years. Magnonic crystals (MCs) are one of the building blocks of room-temperature magnonics and can be used to create devices with an engineered band structure. These devices, exhibiting tunable frequency selectivity and the ability to store travelling excitations in the microwave regime, may form the basis of a set of new tools to be used in the context of quantum information processing. In order to ascertain the feasibility of such plans, MCs must be demonstrated to work at the …
Transmission of microwave spin waves through a microstructured magnonic crystal in the form of a permalloy waveguide of a periodically varying width was studied experimentally and theoretically. The spin wave characteristics were measured by spatially-resolved Brillouin light scattering microscopy. A rejection frequency band was clearly observed. The band gap frequency was controlled by the applied magnetic field. The measured spin-wave intensity as a function of frequency and propagation distance is in good agreement with a model calculation.
Using Brillouin spectroscopy, the first observation has been made of the band structures of nanostructured defect magnonic crystals. The samples are otherwise one-dimensional periodic arrays of equal-width Ni80Fe20 and cobalt nanostripes, where the defects are stripes of a different width. A dispersionless defect branch emerges within the bandgap with a frequency tunable by varying the defect stripe width, while the other branches observed are similar to those of a defect-free crystal. Micromagnetic and finite-element simulations performed unveil additional tiny bandgaps and the frequency-depe…
Magnonic crystals with locally alternating properties and specific periodicities exhibit interesting effects, such as a multitude of different spin-wave states and large band gaps. This work aims for demonstrating and understanding the key role of local demagnetizing fields in such systems. To achieve this, hybrid structures are investigated consisting of a continuous thin film with a stripe modulation on top favorable due to the adjustability of the magnonic effects with the modulation size. For a direct access to the spin dynamics, a magnonic crystal was reconstructed from `bottom-up', i.e.,…
