Magnonic Gaps Research Articles

Topological Phase Transitions of Dirac Magnons in Honeycomb Ferromagnets.

The study of the magnonic thermal Hall effect in magnets with Dzyaloshinskii-Moriya interaction (DMI) has recently drawn attention because of the underlying topology. Topological phase transitions may arise when there exist two or more distinct topological phases, and they are often revealed by a gap-closing phenomenon. In this work, we consider the magnons in honeycomb ferromagnets described by a Heisenberg Hamiltonian containing both an out-of-plane DMI and a Zeeman interaction. We demonstrate that the magnonic system exhibits temperature (or magnetic field) driven topological phase transitions due to magnon-magnon interactions. Specifically, when the temperature increases, the magnonic energy gap at Dirac points closes and reopens at a critical temperature, T_{c}. By showing that the Chern numbers of the magnonic bands are distinct above and below T_{c}, we confirm that the gap-closing phenomenon is indeed a signature for the topological phase transitions. Furthermore, our analysis indicates that the thermal Hall conductivity in the magnonic system exhibits a sign reversal at T_{c}, which can serve as an experimental probe of its topological nature. Our theory predicts that in CrI_{3} such a phenomenon exists and is experimentally accessible.

Photonic Signatures of Spin-Driven Ferroelectricity in Multiferroic Dielectric Oxides.

We study the dispersion and scattering properties of electromagnetic modes coupled to a helically ordered spin lattice hosted by a dielectric oxide with a ferroelectric polarization driven by vector spin chirality. Quasianalytical approaches and full-fledged numerics evidence the formation of a chiral magnonic photonic band gap and the presence of gate-voltage dependent circular dichroism in the scattering of electromagnetic waves from the lattice. Gating couples to the emergent ferroelectric polarization and hence, to the underlying vector-spin chirality. The theory relies on solving simultaneously Maxwell's equations coupled to the driven localized spins taking into account their spatial topology and spatial anisotropic interactions. The developed approach is applicable to various settings involving noncollinear spins and multiferroic systems with potential applications in noncollinear magnetophotonics.

Anisotropic spin-wave propagation in asymmetric width modulated Ni80Fe20 nanostripes

Nanoscale magnonic waveguides have attracted significant attention due to their potential applications in on-chip GHz frequency signal communication and processing. Here, we report a strongly anisotropic magnonic band structure and band gap in an asymmetric sawtooth shaped width modulated Ni80Fe20 nanostripe array using Brillouin light scattering spectroscopy. The experimental observation is reproduced numerically by using plane-wave method. Further, micromagnetic simulations underpin that the shape anisotropy of the nanostripe and the continuous variation of spin configuration with bias magnetic field orientation play crucial roles in steering the anisotropic spin-wave propagation in this structure. Based on the observed spin-wave anisotropy, we numerically propose frequency dependent XNOR and XOR logic gates intended for integrated spin-based nanocircuits.

Frequency Filtering with a Magnonic Crystal Based on Nanometer-Thick Yttrium Iron Garnet Films

Magnonics rely on the wave nature of the magnetic excitations to process information, an approach that is common to many fields such as photonics, phononics, and plasmonics. Nevertheless, magnons, the quanta of spin-wave excitations, have the unique advantage to be at frequencies that are lying between a few GHz to tens of GHz, that is, in the technologically relevant radio-frequency bands for 4G and 5G telecommunications. Furthermore, their typical wavelengths are compatible with on-chip integration. Here, we demonstrate radio-frequency signal filtering by a micron-scale magnonic crystal (MC) based on a nanopatterned 20 nm-thick film of yttrium iron garnet with a minimum feature size of 100 nm where the Bragg vector is set to be kB = 2.1 μm–1. We map the intensity and the phase of spin waves (SWs) propagating in the periodic magnetic structure using phase-resolved microfocus Brillouin light-scattering spectroscopy. Based on these maps, we obtain the SW dispersion and the attenuation characteristics. Efficient filtering is obtained with a frequency selectivity of 20 MHz at an operating frequency of 4.9 GHz. The results are analyzed by performing time- and frequency-resolved full-scale micromagnetic simulations of the MC that reproduce quantitatively the complexity of the harmonic response across the magnonic band gap and allow the identification of the relevant SW-quantized modes, thereby providing an in-depth insight into the physics of SW propagation in periodically modulated nanoscale structures.

2D Surface Spin Waves in Dynamic Magnonic Crystals Created by a Surface Acoustic Wave in YIG Films

Some results of the study of 2D propagation of surface magnetostatic spin waves (SMSW) in dynamic magnonic crystals (DMC) created by a surface acoustic wave (SAW) in a structure with a yttrium-iron garnet (YIG) film are presented. Such studies are interesting from the practical point of view of creating real relatively complex devices on spin waves when they propagate in different directions, and not only in the 1D case. The methods of experimental research are presented, in particular, the features of the method of excitation of SAW in the structure that do not lead to the appearance of additional magnetic anisotropy in it, a method for measuring the angular dependencies of SMSW using mobile antenna–probes is presented. The angular dependences of the magnonic band gap frequencies are measured. It is established that the transmission bands with the transformation of the reflected SMSW into other types of magnetostatic waves (MSW) exist at any angle values, while the intervals in which there are no SMSW transformations during reflections occur in a certain narrower range of angles. The angles of the directions of the wave vectors and the Poynting vector of the reflected SMSW were also measured. A satisfactory agreement was obtained with the calculation performed using the method of isofrequency curves and the laws of inelastic scattering SMSW on SAW.

Spin-texture driven reconfigurable magnonics in chains of connectedNi80Fe20submicron dots

Topological magnonics has attracted intense interest for application in energy efficient computational devices. Here, we show reconfigurable magnonic band structure and band gap by a bias-field controlled spin texture in chains of connected ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ submicron dots. Particularly for an identical field value, we achieve both ``$S$'' and shifted-core vortex states based on magnetic history leading to a drastic change in magnonic band structure. A first-order phase transition from the saturation to vortex state drives this change, as opposed to a continuous change from the saturation to $S$ state.

Reversible tuning of omnidirectional band gaps in two-dimensional magnonic crystals by magnetic field and in-plane squeezing

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 us to explain the k-dependent softening of modes. The effects we found enabled us not only to design the width and position of magnonic band gaps, but also to plan their response to a change in the external magnetic field magnitude. This allows the reversible tuning of magnonic band gaps, and it shows that the studied structures are promising candidates for designing magnonic devices that are tunable during operation.

Use of Dynamic Magnonic Crystals for Measuring the Parameters of Surface Magnetostatic Waves

The use of dynamic magnonic crystals created by a surface acoustic wave (SAW) for measuring the parameters of a surface magnetostatic wave in a film of yttrium iron garnet (YIG) on a gallium gadolinium garnet (GGG) substrate is described. A method for measuring the dispersion characteristics of a surface magnetostatic spin wave (SMSW) and results of such measurements are presented. The method is based on measuring reflected SMSWs at frequencies of forbidden magnonic gaps using the same antenna for the excitation of incident SMSWs and the detection of reflected SMSWs. The attenuation parameter of the SMSW is determined by measuring the frequency width of reflected SMSW signals. The dispersion curves have been measured for several angles between the direction of the magnetic field and the wave vector in the plane of YIG film and for two thicknesses of the YIG film at wave numbers ranging up to 1000 cm–1. Results of measurements of the attenuation parameter are also presented.

Dynamic magnonic crystals for measurements of parameters of surface spin waves in yttrium-iron garnet films

Abstract The application of dynamic magnonic crystals, created by a surface acoustic wave, to measure the parameters of surface magnetostatic waves in YIG – GGG structures is considered. The methods and results of measuring the dispersion characteristics of surface magnetostatic spin waves (SMSW) at different angles between the magnetic field direction and the wave vector in the YIG film plane are described. The method is based on measurements of reflected SMSWs at frequencies of forbidden magnonic gaps, using the same antenna for exciting incident waves and registrations of reflected ones. Measurements of the frequency width of these reflected SMSW permit to determine its attenuation parameter. The results of measurements of the dispersion curves at several angles between the magnetic field direction and the wave vector in the YIG film plane are presented as well as the measurement results on attenuation parameters.

Magnons in a Quasicrystal: Propagation, Extinction, and Localization of Spin Waves in Fibonacci Structures

Magnonic quasicrystals exceed the possibilities of spin wave (SW) manipulation offered by regular magnonic crystals, because of their more complex SW spectra with fractal characteristics. Here, we report the direct x-ray microscopic observation of propagating SWs in a magnonic quasicrystal, consisting of dipolarly coupled permalloy nanowires arranged in a one-dimensional Fibonacci sequence. SWs from the first and second band as well as evanescent waves from the band gap between them are imaged. Moreover, additional mini-band gaps in the spectrum are demonstrated, directly indicating an influence of the quasiperiodicity of the system. The experimental results are interpreted using numerical calculations and we deduce a simple model to estimate the frequency position of the magnonic gaps in quasiperiodic structures. The demonstrated features of SW spectra in one-dimensional magnonic quasicrystals allows utilizing this class of metamaterials for magnonics and makes them an ideal basis for future applications.

Nonuniform Spin-Wave Softening in Two-Dimensional Magnonic Crystals as a Tool for Opening Omnidirectional Magnonic Band Gaps

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 of the demagnetizing field caused by the squeezing of the structure is of crucial importance for the non-uniform mode softening. This allows us to employ this mechanism to design magnonic gaps with different sensitivity for the tiny change of the external field. The effects we have found should be useful in designing and optimization of spin wave filters highly tunable by a small external magnetic field.

Electrical detection of magnonic band gaps for metallic one-dimensional magnetic crystals

We investigated metallic magnonic crystals (MCs) of the permalloy (Py) strips with periodic grooves. The pronounced dips in the transmitted spectra of magnetostatic surface spin waves were observed using an antenna method. The frequencies of the dips were in good agreement with the ones of the magnonic band gaps obtained by micromagnetic simulation. Furthermore, we demonstrated the band gap frequency was modified by varying the lattice constant of MCs. The success of the electrical detection of the magnonic band gaps for the Py MCs opens up a route for the development of novel magnonic devises based on metallic MCs.

Magnonic band gap and mode hybridization in continuous permalloy films induced by vertical dynamic coupling with an array of permalloy ellipses

We investigate magnonic band structure in thin homogeneous permalloy film decorated with periodic array of elliptically shaped permalloy dots and separated by non-magnetic Pt spacer. We demonstrated experimentally formation of the magnonic band structure for Damon-Eshbach wave propagating in permalloy film with the band gap opened at the Brillouin zone border and band splitting at smaller wavenumbers, due to the Bragg interference and interaction of propagating wave of the continuous film with a standing resonant mode of the nano-ellipses, respectively. The shape anisotropy of the permalloy nanodots allows to control the spin wave dynamics through the switch between two states of the magnetization with respect to the underneath film magnetization, thus enabling magnonic band structure reprogrammability. With numerical analysis we show, that predominant role in formation of the magnonic band structure is played by a vertical dynamic coupling between propagating wave in the film and magnetization oscillations in the nanodots.

Spin-wave dynamics in artificial anti-spin-ice systems: Experimental and theoretical investigations

Reversed structures of artificial spin-ice systems, where elongated holes with elliptical shape (antidots) are arranged into a square array with two orthogonal sublattices, are referred to as anti-squared spin-ice. Using Brillouin light scattering spectroscopy and plane wave method calculations, we investigate the spin wave propagation perpendicular to the applied field direction for two 20 nm thick Permalloy nanostructures which differ by the presence of single and double elliptical antidots. For the spin waves propagation along the principal antidot lattice axis, the spectrum consists of flat bands separated by several frequency gaps which are the effect of spin wave amplitude confinement in the regions between antidots. Contrarily, for propagation direction at 45 degrees with respect to the antidot symmetry axis, straight and narrow channels of propagation are formed, leading to broadening of bands and closing of the magnonics gaps. Interestingly, in this case, extra magnonic band gaps occur due to the additional periodicity along this direction. The width and the position of these gaps depend on the presence of single or double antidots. In this context, we discuss possibilities for the tuning of spin wave spectra in anti-squared spin ice structures.

Symmetry and localization properties of defect modes in magnonic superlattices

Symmetry and localization properties of defect modes of a one-dimensional bi-component magnonic superlattice are theoretically studied. The magnonic superlattice can be seen as a periodic array of nanostripes, where stripes with different width, termed as defect stripes, are periodically introduced. By controlling the geometry of the defect stripes, a transition from dispersive to practically flat spin-wave defect modes can be observed inside the magnonic band gaps. It is shown that the spin-wave profile of the defect modes can be either symmetric or antisymmetric, depending on the geometry of the defect. Due to the localized character of the defect modes, a particular magnonic superlattice is proposed, wherein the excitation of either symmetric or antisymmetric flat magnonic modes is enabled at the same time. Also, it is demonstrated that the relative frequency position of the antisymmetric mode inside the band gap does not significantly change with the application of an external field, while the symmetric modes move to the edges of the frequency band gaps. The results are complemented by numerical simulations, where an excellent agreement is observed between both methods. The proposed theory allows exploring different ways to control the dynamic properties of the defect modes in metamaterial magnonic superlattices, which can be useful for applications on multifunctional microwave devices operating over a broad frequency range.

Dipolar interaction induced band gaps and flat modes in surface-modulated magnonic crystals

Theoretical results for the magnetization dynamics of a magnonic crystal formed by grooves on the surface of a ferromagnetic film, called a surface-modulated magnonic crystal, are presented. For such a system, the role of the periodic dipolar field induced by the geometrical modulation is addressed by using the plane-wave method. The results reveal that, under the increasing of the depth of the grooves, zones with magnetizing and demagnetizing fields act on the system in such a way that magnonic band gaps are observed in both Damon-Eshbach and backward volume geometries. Particularly, in the backward volume configuration, high-frequency band gaps and low-frequency flat modes are obtained. By taking into account the properties of the internal field induced by the grooves, the flattening of the modes and their shift towards low frequencies are discussed and explained. To test the validity of the model, the theoretical results of this work are confirmed by micromagnetic simulations, and good agreement between both methods is achieved. The theoretical model allows for a detailed understanding of the physics underlying these kinds of systems, thereby providing an outlook for potential applications on magnonic devices.

Nonlinear spin waves in dynamic magnonic crystals created by surface acoustic waves in yttrium iron garnet films

Experimental results on the influence of the intensity of surface magnetostatic spin wave (SMSW) on its propagation in the dynamic magnonic crystals (MCs) created by surface acoustic waves (SAW) propagating in yttrium iron garnet (YIG) film on the gallium gadolinium garnet (GGG) substrate are presented. The shift of the resonant frequency of the SMSW reflections (frequency of the magnonic gap) and widening of the resonant reflection curves (increasing the width of the magnonic band gap) from their former meanings (3730 MHz and 5.25 MHz, respectively) were observed at 20 MHz SAW of 20 mW in biasing magnetic field of 640 Oe at input microwave power exceeding the threshold value of −5 dBm. At the input power of 10 dBm, the deviations of the magnonic gap frequency and of the width of the SMSW resonant reflected curves reach the values of 5 MHz and 2 MHz, respectively. At a frequency of 3730 MHz, a decrease in the reflection coefficient of the SMSW was observed at the input powers above the threshold. These results may be useful in investigations of MC and for creating new nonlinear signal processing devices.

Magnonic crystals based on ferrite and multiferroic periodic structures

A comparison of spectrum characteristics of ferrite and multiferroic magnonic crystals has been made for the first time. It is shown that ferrite-ferroelectric magnonic crystal band gaps shift in the low frequencies against ferrite magnonic crystal. Theoretical and experimental results are in good agreement.

Pseudo-One-Dimensional Magnonic Crystals for High-Frequency Nanoscale Devices

Periodically patterned composite ferromagnetic nanostructures known as magnonic crystals (MCs) are promising for spintronic and other spin-based technologies, as they manipulate spin waves in analogy to photonic crystals' manipulation of light. The authors create an array of asymmetric sawtooth waveguides that presents two different one-dimensional MCs in perpendicular directions, yet not a two-dimensional MC. Its magnonic band structure and gap are tuned by rotating the applied magnetic field, and its edge modes may also be controlled, to yield, say, a GHz-frequency nanoscale filter.

Spin waves in planar quasicrystal of Penrose tiling

We investigated two-dimensional magnonic structures which are the counterparts of photonic quasicrystals forming Penrose tiling. We considered the slab composed of Ni (or Py) disks embedded in Fe (or Co) matrix. The disks are arranged in quasiperiodic Penrose-like structure. The infinite quasicrystal was approximated by its rectangular section with periodic boundary conditions applied. This approach allowed us to use the plane wave method to find the frequency spectrum of eigenmodes for spin waves and their spatial profiles. The calculated integrated density of states shows more distinctive magnonic gaps for the structure composed of materials of high magnetic contrast (Ni and Fe) and relatively high filling fraction. This proves the impact of quasiperiodic long-range order on the spectrum of spin waves. We also investigated the localization of spin wave eingenmodes resulting from the quasiperiodicity of the structure.