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We have investigated the properties of the $\beta$-Ga$_2$O$_3$($\bar201$)/HfO$_2$/Cr/Au MOS (metal-oxide-semiconductor) system after annealing (450$^\circ$C) in different ambient conditions (forming gas, N$_2$ and O$_2$). Defect properties have been analyzed using an approach combining experimental impedance measurements with physics-based simulations of the capacitance-voltage (C-V) and conductance-voltage (G-V) characteristics of $\beta$-Ga$_2$O$_3$/HfO$_2$ MOS capacitors. This approach enabled us to detect two defect bands in HfO$_2$ characterized by thermal ionization energies of ~1.1eV (acceptor-like) and ~2eV (donor-like) attributed to a polaronic self-trapping state and an oxygen vacancy in HfO$_2$, respectively. This study demonstrates how thermal treatments affect the energy distributions and densities of the observed defects. The adopted methodology also enabled the extraction of the spatial distribution of defects across the HfO$_2$ thickness and Cr/HfO$_2$ interface. The high concentration of oxygen vacancies close to the Cr/HfO$_2$ interface extracted from experimental and simulated electrical data is confirmed by in-situ XPS analysis which shows how Cr is scavenging oxygen from the HfO$_2$ and creating the donor band confined near the Cr/HfO$_2$ interface. This donor band density is observed to be reduced after annealing as per simulation and unchanged for different annealing conditions. We speculate this may be due to the formation of dense films and polyforms of HfO$_2$ under different ambient as revealed by high-resolution TEM images., Comment: Main article: 23 pages, 6 figures, Supporting information:7 pages, 5 Figures

We theoretically investigate the effect of perpendicular magnetic anisotropy (PMA) on spin wave (SW) dynamics at low magnetic fields. PMA exerts an in-plane torque on magnetization, counteracting exchange, dipolar, and Zeeman torques, thereby significantly transforming SW dynamics. In ultrathin films, sombrero-like dispersion relation facilitates bireflection and negative reflection of SWs, while in thicker films we demonstrate anti-Larmor precession, cowboy-hat-like dispersion relation, and trireflection of SWs. These results open up new opportunities to explore wave phenomena beyond magnonics.

Existing benchmarks for frontier models often test specialized, ``PhD-level'' knowledge that is difficult for non-experts to grasp. In contrast, we present a benchmark based on the NPR Sunday Puzzle Challenge that requires only general knowledge. Our benchmark is challenging for both humans and models, however correct solutions are easy to verify, and models' mistakes are easy to spot. Our work reveals capability gaps that are not evident in existing benchmarks: OpenAI o1 significantly outperforms other reasoning models that are on par on benchmarks that test specialized knowledge. Furthermore, our analysis of reasoning outputs uncovers new kinds of failures. DeepSeek R1, for instance, often concedes with ``I give up'' before providing an answer that it knows is wrong. R1 can also be remarkably ``uncertain'' in its output and in rare cases, it does not ``finish thinking,'' which suggests the need for an inference-time technique to ``wrap up'' before the context window limit is reached. We also quantify the effectiveness of reasoning longer with R1 and Gemini Thinking to identify the point beyond which more reasoning is unlikely to improve accuracy on our benchmark.

Results of extensive combined experimental and theoretical investigations on static and dynamic properties of Ir/Co/Pt multilayer with low uniaxial anisotropy and asymmetric Ir/Co and Co/Pt interfaces responsible for large interfacial Dzyaloshinskii-Moriya interaction (IDMI) are presented. Within longitudinal magneto-optical Kerr effect-based microscopy and magnetic force microscopy studies a complex magnetic configuration was detected: large in-plane magnetized domains of several dozen micrometers size were modulated by a weak stripe domain pattern with periods of about 100 nm. Using Brillouin Light Scattering spectrometry, the hysteresis of the Stokes and anti-Stokes peaks frequencies was observed as a function of the magnetic field. This hysteretic behavior associated with IDMI-induced asymmetry of spin waves dispersion is correlated with switching of the large macro-domains. Using micromagnetic simulations we determine field-dependent magnetization distributions and dispersion relations, proposing an explanation of the observed behavior. The investigated nanostructure can be used as non-volatile spin waves velocity switcher., Comment: Accepted for publication in Physical Rewiev B, https://journals.aps.org/prb/accepted/ce071O5bHbf17c5401c04140b8bb51c940576e842

We show, by means of micromagnetic simulations, inelastic scattering of spin-wave beams on edge-localized spin waves modes. The outcome of the investigated inelastic scattering is creation of new spin-waves beams of frequencies shifted by the edge mode frequencies. We report that inelastically scattered spin-wave beams in both stimulated splitting and confluence processes not only change their direction of propagation, but also undergo lateral shifts along the interface, analogous to the Goos-H\"anchen effect. We report that the lateral shifts of inelastically scattered beams can be much larger than the classical Goos-H\"anchen shifts for reflected spin waves, taking both positive and negative values. In addition, we report the cascade nonlinear excitation of spin-wave leaky modes accompanied by a substantial increase in the value of the lateral shift of the inelastically scattered spin-wave beam in the confluence process. Our results are an important contribution to the understanding of the nonlinear nature of spin waves, which is crucial for spin wave applications.

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

Data races are a notorious problem in parallel programming. There has been great research interest in type systems that statically prevent data races. Despite the progress in the safety and usability of these systems, lots of existing approaches enforce strict anti-aliasing principles to prevent data races. The adoption of them is often intrusive, in the sense that it invalidates common programming patterns and requires paradigm shifts. We propose Capture Separation Calculus (System CSC), a calculus based on Capture Calculus (System CC<:box), that achieves static data race freedom while being non-intrusive. It allows aliasing in general to permit common programming patterns, but tracks aliasing and controls them when that is necessary to prevent data races. We study the formal properties of System CSC by establishing its type safety and data race freedom. Notably, we establish the data race freedom property by proving the confluence of its reduction semantics. To validate the usability of the calculus, we implement it as an extension to the Scala 3 compiler, and use it to type-check the examples in the paper.

We numerically demonstrate the excitation of leaky spin waves (SWs) guided along a ferromagnetic stripe by an obliquely incident SW beam on the thin film edge placed below the stripe. During propagation, leaky waves emit energy back to the layer in the form of plane waves and several laterally shifted parallel SW beams. This resonance excitation, combined with interference effects of the reflected and re-emitted waves, results in the magnonic Woods anomaly and significant increase of the Goos-Hanchen shift magnitude. Hence, we provide a unique platform to control SW reflection and to transfer SWs from a 2D platform into the 1D guiding mode that can be used to form a transdimensional magnonic router.

Many programming languages in the OO tradition now support pattern matching in some form. Historical examples include Scala and Ceylon, with the more recent additions of Java, Kotlin, TypeScript, and Flow. But pattern matching on generic class hierarchies currently results in puzzling type errors in most of these languages. Yet this combination of features occurs naturally in many scenarios, such as when manipulating typed ASTs. To support it properly, compilers need to implement a form of subtyping reconstruction: the ability to reconstruct subtyping information uncovered at runtime during pattern matching. We introduce cDOT, a new calculus in the family of Dependent Object Types (DOT) intended to serve as a formal foundation for subtyping reconstruction. Being descended from pDOT, itself a formal foundation for Scala, cDOT can be used to encode advanced object-oriented features such as generic inheritance, type constructor variance, F-bounded polymorphism, and first-class recursive modules. We demonstrate that subtyping reconstruction subsumes GADTs by encoding $\lambda_{2,G\mu}$, a classical constraint-based GADT calculus, into cDOT., Comment: 46 pages, 11 figures. For the associated mechanized proof of soundness, see https://zenodo.org/record/7079463. This is an extended version of the paper published at OOPSLA'22. v2 fixes typos in Fig. 3, and slightly tweaks some sentences to mirror the formally published version

Type systems usually characterize the shape of values but not their free variables. However, many desirable safety properties could be guaranteed if one knew the free variables captured by values. We describe CCsubBox, a calculus where such captured variables are succinctly represented in types, and show it can be used to safely implement effects and effect polymorphism via scoped capabilities. We discuss how the decision to track captured variables guides key aspects of the calculus, and show that CCsubBox admits simple and intuitive types for common data structures and their typical usage patterns. We demonstrate how these ideas can be used to guide the implementation of capture checking in a practical programming language., Comment: 39 pages

Magnetic multilayers of (Ir/Co/Pt)$_6$ with interfacial Dzyaloshinskii-Moriya interaction (IDMI) were deposited by magnetron sputtering with Co thickness $d=1.8$ nm. Exploiting magneto-optical Kerr effect in longitudinal mode microscopy, magnetic force microscopy, and vibrating sample magnetometry, the magnetic field-driven evolution of domain structures and magnetization hysteresis loops have been studied. The existence of weak stripe domains structure was deduced -- tens micrometers size domains with in-plane "core" magnetization modulated by hundred of nanometers domains with out-of-plane magnetization. Micromagnetic simulations interpreted such magnetization distribution. Quantitative evaluation of IDMI was carried out using Brillouin light scattering (BLS) spectroscopy as the difference between Stokes and anti-Stokes peak frequencies $\Delta f$. Due to the additive nature of IDMI, the asymmetric combination of Ir and Pt covers led to large values of effective IDMI energy density $D_\mathrm{eff}$. It was found that Stokes and anti-Stokes frequencies as well as $\Delta f$, measured as a function of in-plane applied magnetic field, show hysteresis. These results are explained under the consideration of the influence of IDMI on the dynamics of the in-plane magnetized "core" with weak stripe domains.

Efficient numerical methods are required for the design of optimised devices. In magnonics, the primary computational tool is micromagnetic simulations, which solve the Landau-Lifshitz equation discretised in time and space. However, their computational cost is high, and the complexity of their output hinders insight into the physics of the simulated system, especially in the case of multimode propagating wave-based devices. We propose a finite-element modal method allowing an efficient solution of the scattering problem for dipole-exchange spin waves propagating perpendicularly to the magnetisation direction. The method gives direct access to the scattering matrix of the whole system and its components. We extend the formula for the power carried by a magnetostatic mode in the Damon-Eshbach configuration to the case with exchange, allowing the scattering coefficients to be normalised to represent the fraction of the input power transferred to each output channel. We apply the method to the analysis of spin-wave scattering on a basic functional block of magnonic circuits, consisting of a resonator dynamically coupled to a thin film. The results and the method are validated by comparison with micromagnetic simulations., Comment: Revised version

The phase is one of the fundamental properties of a wave that allows to control interference effects and can be used to efficiently encode information. We examine numerically a magnonic resonator of the Gires-Tournois interferometer type, which enables the control of the phase of spin waves reflected from the edges of the ferromagnetic film. The considered interferometer consists of a Py thin film and a thin, narrow Py stripe placed above its edge, both coupled magnetostatically. We show that the resonances and the phase of the reflected spin waves are sensitive for a variation of the geometrical parameters of this bi-layerd part of the system. The high sensitivity to film, stripe, and non-magnetic spacer thicknesses, offers a prospect for developing magnonic metasurfaces and sensors.

Magnonics is a field of science that addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operations in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors that covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with Boolean digital data, unconventional approaches like neuromorphic computing, and the progress towards magnon-based quantum computing. The article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of the current challenges and the outlook of the further development of the research directions., Comment: 74 pages, 57 figures, 500 references

The excitation of high-frequency short-wavelength spin waves is a challenge limiting the application of these propagating magnetization disturbances in information processing systems. We propose a method of local excitation of the high-frequency spin waves using the non-linear nature of magnetization dynamics. We demonstrate with numeric simulations that an edge-localized spin wave can be used to excite plane waves propagating obliquely from the film's edge at a doubled frequency and over twice shorter in wavelength. The excitation mechanism is a direct result of the ellipticity of the magnetic moments precession that is related to the edge-mode propagation. As a consequence, the magnetization component tangential to the equilibrium orientation oscillates with doubled temporal and spatial frequencies, which leads to efficient excitation of the plane spin waves. Threshold-less non-linear process of short-wavelength spin-wave excitation proposed in our study is promising for integration with an inductive or point-like spin-torque source of edge spin waves., Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Appl. Phys. Lett. 118, 062408 (2021) and may be found at https://doi.org/10.1063/5.0041030 or https://aip.scitation.org/doi/abs/10.1063/5.0041030

Spin waves are promising chargeless information carriers for the future, energetically efficient beyond-CMOS systems. Among many advantages there are the ease of achieving nonlinearity, the variety of possible interactions, and excitation types. Although the rapidly developing magnonic research has already yielded impressive realizations, multi-mode nonlinear effects, particularly with the propagating waves and their nanoscale realizations, are still an open research problem. We study theoretically the dynamic interactions of the spin waves confined to the edge of a thin ferromagnetic film with the spin-wave beam incident at this edge. We found the inelastically scattered spin-wave beams at frequencies increased and decreased by the frequency of the edge spin-wave relative to the specularly reflected beam. We observed a strong dependence of the angular shift of the inelastic scattered spin-wave beam on the edge-mode frequency, which allowed us to propose a magnonic demultiplexing of the signal encoded in spin waves propagating along the edge. Since dynamic magnetostatic interactions, which are ubiquitous in the spin-wave dynamics, are decisive in this process, this indicates the possibility of implementing the presented effects, also in other configurations and their use in magnonic systems.

Type systems usually characterize the shape of values but not their free variables. However, there are many desirable safety properties one could guarantee if one could track how references can escape. For example, one may implement algebraic effect handlers using capabilities -- a value which permits one to perform the effect -- safely if one can guarantee that the capability itself does not escape the scope bound by the effect handler. To this end, we study the $\textrm{CF}_{<:}$ calculus, a conservative and lightweight extension of $\textrm{System F}_{<:}$, to track how values and their references can be captured and escape. We show that existing terms in $\textrm{System F}_{<:}$ embed naturally in our calculus, and that many natural problems can be expressed in a system that tracks variable references like we do in $\textrm{CF}_{<:}$. We also give mechanized proofs of the soundness properties of $\textrm{CF}_{<:}$ in Coq. The type system presented in $\textrm{CF}_{<:}$ is powerful enough to reason about safety in the context of many natural extensions of $\textrm{CF}_{<:}$ such as region-based memory-management, non-local returns, and effect handlers., Comment: 23 pages, 11 figures

Using frequency-domain finite element calculations cross-checked with micromagnetic simulations, we demonstrate that the phase of spin waves reflected from an interface between a permalloy film and a bilayer can be controlled by changing dimensions of the bilayer. Treating the bilayer formed by the permalloy film and a ferromagnetic stripe as a segment of a multi-mode waveguide, we show that spin-wave Fabry-Perot resonances of one of its modes are responsible for the high sensitivity of the phase of reflected waves to stripe width and the stripe-film separation. Thus, the system is a unique realization of a fully magnonic Gires-Tournois interferometer based on a two-modes resonator, which can be treated as a magnonic counterpart of a metasurface, since it enables manipulation of the phase of spin waves at subwavelength distances. Knowledge gained from these calculations might be used to design magnonic devices such as flat lenses or magnetic particle detectors.

The increasing demand for ultrahigh data storage densities requires development of 3D magnetic nanostructures. In this regard, focused electron beam induced deposition (FEBID) is a technique of choice for direct-writing of various complex nano-architectures. However, intrinsic properties of nanomagnets are often poorly known and can hardly be assessed by local optical probe techniques. Here, we demonstrate spatially resolved spin-wave spectroscopy of individual circular magnetic elements with radii down to 100 nm. The key component of the setup is a microwave antenna whose microsized central part is placed over a movable substrate with well-separated CoFe-FEBID nanodisks. The circular symmetry of the disks gives rise to standing spin-wave resonances and allows for the deduction of the saturation magnetization and the exchange stiffness of the material using an analytical theory. The presented approach is especially valuable for the characterization of direct-write elements opening new horizons for 3D nanomagnetism and magnonics., Comment: 10 pages, 5 figures

The Talbot effect has been known in optics since XIX century and found various technological applications. In this paper, we demonstrate with the help of micromagnetic simulations this self-imaging phenomenon for spin waves propagating in a thin ferromagnetic film magnetized out-of-plane. We show that the main features of the obtained Talbot carpets for spin waves can be described, to a large extent, by the approximate analytical formulas yielded by the general analysis of the wave phenomena. Our results indicate a route to a feasible experimental realisation of the Talbot effect at low and high frequencies and offer interesting effects and possible applications in magnonics., Comment: 10 pages, 10 figures

We present a method for efficient spin wave guiding within the magnonic nanostructures. Our technique is based on the anomalous refraction in the metamaterial flat slab. The gradual change of the material parameters (saturation magnetization or magnetic anisotropy) across the slab allows tilting the wavefronts of the transmitted spin waves and controlling the refraction. Numerical studies of the spin wave refraction are preceded by the analytical calculations of the phase shift acquired by the spin wave due to the change of material parameters in a confined area. We demonstrate that our findings can be used to guide the spin waves smoothly in curved waveguides, even through sharp bends, without reflection and scattering between different waveguide's modes, preserving the phase -- the quantity essential for wave computing.

The concept of Space-Time Crystals (STC), i.e. translational symmetry breaking in time and space, was recently proposed and experimentally demonstrated for quantum systems. Here, we transfer this concept to magnons and experimentally demonstrate a driven STC at room temperature. The STC is realized by strong homogeneous micro-wave pumping of a micron-sized permalloy (Py) stripe and is directly imaged by Scanning Transmission X-ray Microscopy (STXM). For a fundamental understanding of the formation of the STC, micromagnetic simulations are carefully adapted to model the experimental findings. Beyond the mere generation of a STC, we observe the formation of a magnonic band structure due to back folding of modes at the STC's Brillouin zone boundaries. We show interactions of magnons with the STC that appear as lattice scattering. This results in the generation of ultra short spin waves down to 100 nm wavelength that cannot be described by classical dispersion relations for linear spin wave excitations. We expect that room temperature STCs will be a useful tool to investigate non-linear wave physics, as they can be easily generated and manipulated to control their spatial and temporal band structure.

Spin waves are promising information carriers which can be used in modern magnonic devices, characterized by higher performance and lower energy consumption than presently used electronic circuits. However, before practical application of spin waves, the efficient control over spin wave amplitude and phase needs to be developed. We analyze analytically reflection and refraction of the spin waves at the interface between two ferromagnetic materials. In the model we consider the system consisting of two semi-infinite ferromagnetic media, separated by the ultra-narrow interface region with the magnetic anisotropy. We have found the Goos-Hanchen shift for spin waves in transmission and reflection, and performed detailed investigations of its dependence on the anisotropy at the interface and materials surrounding the interface. We have demonstrated possibility of obtaining Goos-Hanchen shift of several wavelengths in reflection for realistic material parameters. That proves the possibility for change of the spin waves phase in ferromagnetic materials at subwavelength distances, which can be regarded as a metasurface for magnonics., Comment: 6 pages, 3 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

In this paper we show that the phase shift of the spin waves can be controlled in transmission through metasurface represented as an ultra-narrow non-magnetic spacer separating two ferromagnetic films. We design this metasurface to present the focusing of spin waves in an Co thin film. For this purpose we exploit the strength of the interlayer exchange coupling interactions of RKKY type which allows to control the phase of the transmitted and reflected spin waves in the wide range of angles [$-\pi/2$;$\pi/2$]. We combined this phase-shift dependency with the lens equation to demonstrate numerically the lens for spin waves based on ultra-narrow metasurface., Comment: 8 pages, 5 figures

We study azimuthal spin-wave (SW) excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically non-trivial magnetization states, specifically, vortex, Bloch-type skyrmion and N\'eel-type skyrmion states. Continuous mapping of the SW spectrum between these states is realized with gradual change of the out-of-plane magnetic anisotropy and Dzyaloshinskii-Moriya exchange interaction (DMI). Our study shows lifting of the SW frequencies degeneracy and change in systematics of the frequency levels. The change is induced by a geometrical Berry phase, that is present for the dot-edge localized SWs in a vortex state and vanishes in skyrmion states. Furthermore, channeling of the azimuthal SWs localized at the skyrmion edge is present and induces large frequency splitting. This is attributed to DMI induced nonreciprocity, while coupling of the breathing and gyrotropic modes is related to soliton motion. Finally, an efficient coupling of the dynamic magnetization in the skyrmion state to uniform magnetic field in nanodots with non-circular symmetry is shown., Comment: 11 pages, 9 figures

Using analysis of iso-frequency contours of the spin-wave dispersion relation, supported by micromagnetic simulations, we study the propagation of spin-wave (SW) beams in thin ferromagnetic films through the areas of the inhomogeneous refractive index. We compare the transmission and reflection of SWs in areas with gradual and step variation of the SW refractive index. In particular, we show the mirage effect for SWs with narrowing SW beam width, and an application of the gradual modulation of the SWs refractive index as a diverging lens. Furthermore, we study the propagation of SWs in ferromagnetic stripe with modulated refractive index. We demonstrate that the system can be considered as the graded-index waveguide, which preserves the width of the SW beam for a long distance-the property essential for prospective applications of magnonics.

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 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-Eshbach spin wave in 1D magnonic crystals and change of its surface localization with the band number and wavenumber in the first Brillouin zone. The surface property of the spin wave excitation is further exploited by covering plate of the magnonic crystal with conductor. The band structure in 2D magnonic crystals is complex due to additional spatial inhomogeneity introduced by the demagnetizing field. This modifies spin wave dispersion, makes the band structure of magnonic crystals strongly dependent on shape of the inclusions and type of the lattice. The inhomogeneity of the internal magnetic field becomes unimportant for magnonic crystals with small lattice constant, where exchange interactions dominate. For 3D magnonic crystals, characterized by small lattice constant, wide magnonic band gap is found. We show that the spatial distribution of different materials in magnonic crystals can be explored for tailored effective damping of spin waves., Comment: 17 pages, 15 pages, EUs Horizon2020 research and innovation programme under the Marie Sklodowska-Curie GA No644348

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 manipulation of the magnonic band structure of spin waves localized either at the edges of the dots or in matrix material at the edges of grooves. According to the micromagnetic simulations two types of end modes were found. The corresponding frequencies are significantly influenced by the end modes localization region. We also show that, with the use of a single ferromagnetic material, it is possible to design a magnonic crystal preserving properties of bi-component magnonic crystals and magnonic antidot lattices. Finally, the influence of the non-magnetic spacers on the technologically relevant parameters like group velocity and magnonic band width are discussed., Comment: 18 pages, 5 figures

Color filters have important applications in the area of Nano-spectroscopy and ccd imaging applications. Metallic nanostructures provide an efficient way to design and engineer ultrathin color filters. These nanostructures have capability to split the white light into fundamental colors and enable color filters with ultrahigh resolution but their efficiency can be restricted due to high losses in metals especially at the visible wavelengths. In this work, we demonstrate Si nanoantennas based all-dielectric color filters, which are sensitive to incident-wave polarization and, thus, tunable with the aid of polarization angle variation. Two different information can be encoded in two different polarization states in a single physical nanostructure. The nanoantenna based pixels are highly efficient and can provide high quality of colors due to low losses in dielectric at optical frequencies. We experimentally demonstrate that a variety of colors can be achieved by changing the physical size of the nonsymmetric cross-shaped nanoantennas. The proposed devices cover an extended gamut of colors on CIE-1931 chromaticity diagram due to the existence of high quality resonance in Si nanoantennas. The device shows significant tunability of color while operating this color filter device in transmission as well as in reflection mode.

The main object of investigation in magnonics, spin waves (SWs) are promising information carriers. Presently the most commonly studied are plane wave-like SWs and SWs propagating in confined structures, such as waveguides. Here we consider a Gaussian SW beam obliquely incident on an ultra-narrow interface between two identical ferromagnetic materials. We use an analytical model and micromagnetic simulations for an in-depth analysis of the influence of the interface properties, in particular the magnetic anisotropy, on the transmission of the SW beam. We derive analytical formulas for the reflectance, transmittance, phase shift and Goos-Hanchen (GH) shift for beams reflected and refracted by an interface between two semi-infinite ferromagnetic media; the results for the refracted beam are the first to be reported to date. The GH shifts in SW beam reflection and transmission are confirmed by micromagnetic simulations in the thin-film geometry. We demonstrate the dependence of the characteristic properties on the magnetic anisotropy at the interface, the angle of incidence and the frequency of the SWs. We also propose a method for the excitation of high-quality SW beams in micromagnetic simulations.

We present an approach enabling generation of narrow spin wave beams in thin homogeneous ferromagnetic films. The main idea is to match the wave vector of the spin wave with that corresponding to the spectral maximum of the exciting microwave magnetic field only locally, in the region of space from which the beam should be launched. We show that this can be achieved with the aid of a properly designed coplanar waveguide transducer generating a nonuniform microwave magnetic field. The resulting two-dimensional spin wave beams obtained in micromagnetic simulations propagate over distances of several micrometers. The proposed approach requires neither inhomogeneity of the ferromagnetic film nor nonuniformity of the biasing magnetic field, and it can be generalized to yield multiple spin wave beams of different width at the same frequency. Other possible excitation scenarios and applications of spin wave beam magnonics are also discussed.

We study propagation of the Gaussian beam of spin waves and its reflection from the edge of thin yttrium-iron-garnet film with in-plane magnetization perpendicular to this edge. We have performed micromagnetic simulations supported by analytical calculations to investigate influence of the surface magnetic anisotropy present at the film edge on the reflection, especially in the context of the Goos-Hanchen effect. We have shown the appearance of a negative lateral shift between reflected and incident spin wave beams' spots. This shift is particularly sensitive to the surface magnetic anisotropy value and is a result of the Goos-Hanchen shift which is sensitive to the magnitude of the anisotropy and of the bending of spin wave beam. We have demonstrated that the demagnetizing field provide graded increase of the refractive index for spin waves, which is responsible for the bending.

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., Comment: Pacs 75.70.Kw, 75.30.Ds, 75.40.Gb, 75.75.-c, 75.78.Fg