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Waveguides are fundamental components for signal transmission in integrated wave-based processing systems. In this paper, we address the challenges associated with designing magnonic waveguides and propose a novel type with promising properties. Specifically, we study a magnonic waveguide formed within a uniform ferromagnetic layer (Co$_{20}$Fe$_{60}$B$_{20}$) through surface anisotropy applied in stripe regions, creating Bragg mirror structures. The proposed waveguide enables the propagation of high-frequency spin waves with high velocities in the ferromagnetic layer while avoiding static demagnetizing effects. Using finite element simulations, we calculate the dispersion relation of the waveguide modes and analyze their spatial profiles. Additionally, we evaluate the group velocity and localization characteristics, providing a comprehensive understanding of the waveguide's performance.

This study investigates the nucleation, dynamics, and stationary configurations of Abrikosov vortices in hybrid superconductor-ferromagnetic nanostructures exposed to inhomogeneous magnetic fields generated by a ferromagnetic nanodot. Using time-dependent Ginzburg-Landau simulations and Maxwell's equations, we observe and provide an explanation for the evolution of curved vortex structures that undergo creep-like deformation while reaching a steady state. Spatial variations in the Lorentz force, along with the interaction between geometric constraints and vortex interactions, give rise to unusual stationary vortex configurations that gradually change with increasing field strength, a behavior not seen in homogeneous magnetic fields. These findings reveal complex pinning mechanisms, providing valuable insights for the optimization and further advancement of nanoscale superconducting systems.

One of the most intriguing properties of magnonic systems is their reconfigurability, where an external magnetic field alters the static magnetic configuration to influence magnetization dynamics. In this paper, we present an alternative approach to tunable magnonic systems. We studied theoretically and numerically a magnonic crystal induced within a uniform magnetic layer by a periodic magnetic field pattern created by the sequence of superconducting strips. We showed that the spin-wave spectrum can be tuned by the inhomogeneous stray field of the superconductor in response to a small uniform external magnetic field. Additionally, we demonstrated that modifying the width of superconducting strips and separation between them leads to the changes in the internal field which are unprecedented in conventional magnonic structures. The paper presents the results of semi-analytical calculations for realistic structures, which are verified by finite-element method computations.

Eddy currents in a superconductor shield the magnetic field in its interior and are responsible for the formation of a magnetic stray field outside of the superconducting structure. The stray field can be controlled by the external magnetic field and affect the magnetization dynamics in the magnetic system placed in its range. In the case of a hybrid system consisting of a superconducting strip placed over a magnetic layer, we predict theoretically the confinement of spin waves in the well of the static stray field. The number of bound states and their frequencies can be controlled by an external magnetic field. We have presented the results of semi-analytical calculations complemented by numerical modeling., Comment: 12 pages, 5 figures

Confined spin-wave modes are a promising object for studying nonlinear effects and future quantum technologies. Here, using micromagnetic simulations, we use a microwave magnetic field from a coplanar waveguide (CPW) to pump a standing spin-wave confined in the cavity of magnonic crystal. We find that the frequency of the fundamental cavity mode is equal to the ferromagnetic resonance frequency of the plane film and overlaps with the magnonic bandgap, allowing high magnetic field tunability. Multi-frequency harmonics of the cavity mode are generated once the microwave amplitude surpasses a certain threshold. Specifically, the second and third harmonics at 0.5 T equate to 48.6 and 72.9 GHz with wavelengths of 44 and 22 nm respectively, which propagate into the crystal. This effect reaches saturation when the CPW covers the entire cavity, making the system feasible for realization. These processes show potential for the advancement of magnonics at high-frequencies and very short-wavelengths., Comment: 8 pages, 5 figures

A planar square dot is one of the simplest structures confined to three dimensions. Despite its geometrical simplicity, the description of the spin wave modes in this structure is not trivial due to the competition of dipolar and exchange interactions. An additional factor that makes this description challenging are the boundary conditions depend both on non-local dipolar interactions and local surface parameters such as surface anisotropy. In the presented work, we showed how the surface anisotropy applied at the lateral faces of the dot can tune the frequency of fundamental mode in the planar CoFeB dot, magnetized in an out-of-plane direction. Moreover, we analyzed the spin wave profile of the fundamental mode and the corresponding dynamic stray field. We showed that the asymmetric application of surface anisotropy produces an asymmetric profile of dynamic stray field for square dot and can be used to tailor inter-dot coupling. The calculations were performed with the use of the finite-element method., Comment: 4 pages, 4 figures

We demonstrate that the spin wave Cherenkov effect can be used to design the unidirectional spin wave emitter with tunable frequency and switchable direction of emission. In our numerical studies, we propose to use a pair of traveling profiles of the magnetic field which generate the spin waves, for sufficiently large velocity of their motion. In the considered system, the spin waves of shorter (longer) wavelengths are induced at the front (back) of the moving profiles and interfere constructively or destructively, depending on the velocity of the profiles. Moreover, we showed that the spin waves can be confined between the pair of traveling profiles of the magnetic field. This work opens the perspectives for the experimental studies in hybrid magnonic-superconducting systems where the magnetic vortices in a superconductor can be used as moving sources of the magnetic field driving the spin waves in the ferromagnetic subsystem., Comment: 4 pages, 3 figures

Lieb lattice is one of the simplest bipartite lattices where compact localized states (CLS) are observed. This type of localisation is induced by the peculiar topology of the unit cell, where the modes are localized only on one sublattice due to the destructive interference of partial waves. The CLS exist in the absence of defects and are associated with the flat bands in the dispersion relation. The Lieb lattices were successfully implemented as optical lattices or photonic crystals. This work demonstrates the possibility of magnonic Lieb lattice realization where the flat bands and CLS can be observed in the planar structure of sub-micron in-plane sizes. Using forward volume configuration, we investigated numerically (using the finite element method) the Ga-dopped YIG layer with cylindrical inclusions (without Ga content) arranged in a Lieb lattice of the period 250 nm. We tailored the structure to observe, for the few lowest magnonic bands, the oscillatory and evanescent spin waves in inclusions and matrix, respectively. Such a design reproduces the Lieb lattice of nodes (inclusions) coupled to each other by the matrix with the CLS in flat bands.

We report on the evolution of the spin-wave spectrum under structural disorder introduced intentionally into one-dimensional magnonic quasicrystal. We study theoretically a system composed of ferromagnetic strips arranged in a Fibonacci sequence. We considered several stages of disorder in the form of phasonic defects, where different rearrangements of strips are introduced. By transition from the quasiperiodic order towards disorder, we show a gradual degradation of spin-waves fractal spectra and closing of the frequency gaps. In particular, the phasonic defects lead to the disappearance of the van Hove singularities at the frequency gap edges by moving modes into the frequency gaps and appearing new modes inside the frequency gaps. These modes disperse and eventually can close the gap, with increasing disorder levels. The work reveals how the the presence of disorder modifies the intrinsic spin wave localization existing in undefected magnonic quasicrystals. The paper contributes to the knowledge of magnonic Fibonacci quasicrystals and opens the way to study of the phasonic defects in two-dimensional magnonic quasicrystals.

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. Moreover, we show that by shifting the unit cell the interface modes can be caused to traverse the bandgap edges.

Magnonics is seen nowadays as a candidate technology for energy-efficient data processing in classical and quantum systems. Pronounced nonlinearity, anisotropy of dispersion relations and phase degree of freedom of spin waves require advanced methodology for probing spin waves at room as well as at mK temperatures. Yet, the use of the established optical techniques like Brillouin light scattering (BLS) or magneto optical Kerr effect (MOKE) at ultra-low temperatures is forbiddingly complicated. By contrast, microwave spectroscopy can be used at all temperatures but is usually lacking spatial and wavenumber resolution. Here, we develop a variable-gap propagating spin-wave spectroscopy (VG-PSWS) method for the deduction of the dispersion relation of spin waves in wide frequency and wavenumber range. The method is based on the phase-resolved analysis of the spin-wave transmission between two antennas with variable spacing, in conjunction with theoretical data treatment. We validate the method for the in-plane magnetized CoFeB and YIG thin films in $k\perp B$ and $k\parallel B$ geometries by deducing the full set of material and spin-wave parameters, including spin-wave dispersion, hybridization of the fundamental mode with the higher-order perpendicular standing spin-wave modes and surface spin pinning. The compatibility of microwaves with low temperatures makes this approach attractive for cryogenic magnonics at the nanoscale., Comment: 9 pages, 5 figures

The use of spin waves as a signal carrier requires developing the functional elements allowing for multiplexing and demultiplexing information coded at different wavelengths. For this purpose, we propose a system of thin ferromagnetic layers dynamically coupled by a rectangular ferromagnetic resonator. We show that a single and double, clockwise and counter-clockwise, circulating modes of the resonator offer a wide possibility of control of propagating waves. Particularly, at frequency related to the double-clockwise circulating spin-wave mode of the resonator, the spin wave excited in one layer is transferred to the second one where it propagates in the backward direction. Interestingly, the wave excited in the second layer propagates in the forward direction only in that layer. This demonstrates add-drop filtering, as well as circulator functionality. Thus, the proposed system can become an important part of future magnonic technology for signal routing., Comment: 6 pages, 4 figures

By combining Brillouin Light Scattering and micromagnetic simulations we studied the spin-wave dynamics of a Co/Pd thin film multilayer, features a stripe domain structure at remanence. The periodic up and down domains are separated by cork-screw type domain walls. The existence of these domains causes a scattering of the otherwise bulk and surface spin-wave modes, which form mode families, similar to a one dimensional magnonic crystal. The dispersion relation and mode profiles of spin waves are measured for transferred wave vector parallel and perpendicular to the domain axis., Comment: 18 pages, 3 figures

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 Faraday rotation is observed also in vicinity of the band-gap modes localized in magnetic layers but the maximal polarization plane rotation angles are reached at minimal transmittivity. We show that presence of linear magneto-electric interaction in the magnetic layers leads to significant increase of the Faraday rotation angles of s-polarized incident light in the vicinity of the fine-structured modes inside the photonic-band-gap., Comment: 7 pages

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., Comment: 10 pages, 6 figures

The microstrip of modulated width is a realization of a one-dimensional photonic crystal operating in the microwave regime. Like any photonic crystal, the periodic microstrip is characterised by the presence of frequency bands and band gaps that enable and prohibit wave propagation, respectively. The frequency bands for microstrip of symmetric unit cell can be distinguished by $0$ or $\pi$ Zak phase. The sum of these topological parameters for all bands below a given frequency gap determines the value of the surface impedance and whether or not edge modes are present at the end of the microstrip. We demonstrate that edge modes are absent in a finite microstrip terminated at both ends in the centres of unit cells, but they can be induced by adding the defected cells. Edge modes present at both ends of the microstrip enable microwave tunneling with high transitivity in the frequency gap with or without a change in phase. This has been demonstrated experimentally and developed in detail using numerical simulations and model calculations. The investigated system, with a doublet of edge modes in the frequency gap, can be considered as a narrow passband filter of high selectivity., Comment: 13 pages, 6 figures

Hartman effect for spin waves tunnelling through a barrier in a thin magnetic film is considered theoretically. The barrier is assumed to be created by a locally increased magnetic anisotropy field. The considerations are focused on a nanoscale system operating in the exchange-dominated regime. We derive the formula for group delay $\tau_{gr}$ of spin wave package and show that $\tau_{gr}$ saturates with increasing barrier width, which is a signature of the Hartman effect predicted earlier for photonic and electronic systems. In our calculations we consider the general boundary exchange conditions which take into account different strength of exchange coupling between the barrier and its surrounding. As a system suitable for experimental observation of the Hartman effect we propose a CoFeB layer with perpendicular magnetic anisotropy induced by a MgO overlayer.

We studied the effect of collimation for monochromatic beams of spin waves, resulting from the refraction at the interface separating two magnetic half-planes. The collimation was observed in broad range of the angles of ncidence for homogenous Co and Py half-planes, due to significant intrinsic anisotropy of spin wave propagation in these materials. The effect exists for the sample saturated by in plane magnetic field tangential to the interface. The collimation for all possible angles of incidence was found in the system where the incident spin wave is refracted on the interface between homogeneous and periodically patterned layers of YIG. The refraction was investigated by the analysis of isofrequency dispersion contours of both pairs materials, i.e., uniform YIG/patterned YIG and Co/Py, which are calculated with the aid of the plane wave method. Besides, the refraction in Co/Py system was studied using micromagnetic simulations.

We consider the planar magnonic waveguide with a periodic sequence of antidots forming zig-zag pattern, where two neighboring antidots are shifted towards the opposite edges of the waveguide. This system has a complex base with two antidots in one unit cell. The Brillouin zone is here two-times narrower than the Brillouin zone for the waveguide without displacement of antidots. We have shown that for dispersion relation folded into narrower Brillouin zone, new frequency gap can be opened and their width can be controlled by the shift of the antidots. We found that, the different strength of spin wave pinning at the edges of the periodic waveguide (and their antidots)determines the dependence of the width of gap on the shift of antidots. For the systems with completely free or ideally pinned magnetization, these dependencies are qualitatively different. We have found an optimum shift of antidot for maximzing the width of the gap for the system with pinned magnetization. More interestingly, we notice that for this kind of geometry of the structure, majority of the modes are doubly degenerate at the edge of Brillouin zone and have a finite group velocity at the very close vicinity of the edge of Brillouin zone, for larger values of antidot shift. This empowers us to design magnonic waveguide to steer the spin waves.

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 were arranged in quasiperiodic Pernose-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 distictive 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 SW eingenmodes resulting from the quasipeiodicity of the structure.