Magnonics addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operation 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 current challenges and the outlook of further development for each research direction.

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.The possibility to use spin-waves (SW) to excite, transmit, store, and retrieve electric signals as well as to perform logical operations has fueled a new spectrum of research in the wavebased signal processing technology [1-4]. Usually, magnonic crystals (MC), i.e. arrays of macroscopic magnetic stripes [5], dots [6], antidots [7], etched grooves or pits[1], periodic variations of the internal magnetic field [9] and saturation magnetization by ion implantation [10], are employed to control the flow of SWs. Magnetostatic surface SWs or the Damon-Eshbach (DE) SW modes, which propagate perpendicular to the in-plane (IP) magnetization direction, are promising in this context because of their large group velocities (vg) and low attenuation.Consequently, significant progress has been made towards the practical realization of magnonic devices in terms of the on-chip generation, directional channeling, detection and manipulation of SWs. However, to realize the experimental geometry, a large magnetic field has to be applied to enforce the magnetization perpendicular to the SW propagation direction. This is a major obstacle to the implementation of a MC into a practical device. A way out is to use the Oersted field generated from an underlying current-carrying stripe [11][12], which is still plagued by the problem of generation of waste heat which increases with increasing data processing speed. Moreover, the fabrication of periodic nanostructures involves high-precision electron-beam lithography which is very complex and expensive. An alternative approach to overcome these fundamental drawbacks is to take recourse to the spin dynamics in the remanent state, which is more suitable for nanoscale device applications, as it does not require any stand-by power once initialized.In the literature, only few reports exist on the magnetization dynamics for systems with an inhomogeneous magnetization distribution containing domains and domain walls. Most commonly studied is a periodic or non-periodic distribution of magnetic units of up and down domains (parallel, labyrinthine, bubble-like domains) [13][14][15][16][17][18][19], separated by negligibly thin, onedimensional domain walls. Such domains appear in magnetic thin films with a perpendicular anisotropy smaller than the demagnetizing energy if the film thickness is higher than a critical value tc, which is, in turn, dependent on the perpendicular anisotropy constant, saturation magnetization and the exc...

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.

For magnon spintronic applications, the detailed knowledge of spin wave (SW) beam dispersion, transmission (reflection) of SWs passing through (reflected from) interfaces, or borders or the scattering of SWs by inhomogeneities is crucial. These wave properties are decisive factors on the usefulness of a particular device. Here, we demonstrate, using micromagnetic simulations supported by an analytical model, that the Goos-Hänchen (GH) shift exists for SW reflecting from thin film edge and that with the effect becomes observable. We show that this effect will exist for a broad range of frequencies in the dipole-exchange range, with the magnetization degree of pinning at the film edge as the crucial parameter, whatever its nature. Moreover, we have also found that the GH effect can be accompanied or even dominating by a bending of the SW beam due to the inhomogeneity of the internal magnetic field. This inhomogeneity, created by demagnetizing field taking place at the film edge, causes gradual change of SWs refractive index. The refraction of the SW beams by the non-uniformity of the magnetic field enables the exploration of graded index magnonics and metamaterial properties for the transmission and processing of information at nanoscale.

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 the influence of the surface magnetic anisotropy present at the film edge on the reflection, especially in the context of the Goos-Hänchen 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-Hänchen shift which is sensitive to the magnitude of the anisotropy and of the bending of the 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.PACS numbers: 75.30.Ds, 75.30.Gw, 75.70.Rf, 75.78.Cd In recent years magnetic nanostructures with controlled magnetization dynamics have been considered as candidates for design of new miniaturized devices with enhanced performance and functionality for various applications, e.g. heat transport, energy conversion, magnetic field sensing, information storage and processing. 1-3 Spin waves (SWs), being propagating collective excitations of the magnetization are also regarded as information carriers, which can be exploited for information processing in devices potentially competitive with standard CMOS systems. 4,5 Thus, understanding of SW properties in nanostructures is crucial in designing magnonic units and this is one of the main goal in the research field called magnonics. 6,7 It is expected that magnonic devices allow energy-efficient processing of information which will combine the advantages of photonics (high frequency and wide band) and electronics (miniaturization) in a single unit. 8 One of the basic phenomena connected with wave propagation is the wave transmission and reflection. [9][10][11] The reflection of SWs is determined by magnetic properties of the film and boundary conditions at the border of the ferromagnetic material. The reflection of SWs has already been investigated in theoretical and experimental papers 10,12 where SWs were treated as plane waves. Use of wave beams, instead of the plane waves or spherical waves, in many cases, can be much more useful and opens new possibilities due to its coherence and low divergence. The known example of the wave beam is a light beam emitted by laser. Usually, its intensity profiles can be described by Gaussian distribution (beams with such property are called Gaussian beams). However, in magnonics the idea of SW beams is unexplored, with only a few theoretical and experimental studies considering formation of SW beams at low frequencies due to the caustic or nonlinear effects. [13][14][15][16][17][18][19] An interesting phenomenon characteristic for the reflection of beam is a possibility for occurrence of a lateral shift of the beam spot along the interface between...