The spin-wave band structure of a two-dimensional bicomponent magnonic crystal, consisting of Co nanodisks partially embedded in a Permalloy thin film, is experimentally investigated along a high-symmetry direction by Brillouin light scattering. The eigenfrequencies and scattering cross sections are interpreted using plane wave method calculations and micromagnetic simulations. At the boundary of both the first and the second Brillouin zones, we measure a forbidden frequency gap whose width depends on the magnetic contrast between the constituent materials. The modes above and below the gap exhibit resonant spin-precession amplitudes in the complementary regions of periodically varying magnetic parameters. Our findings are key to advance both the physics and the technology of band gap engineering in magnonics.

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.

A chain of resonant cavities in a photonic crystal can form a periodic waveguide that supports propagating modes of energy values within the photonic gap. Due to the periodicity of the waveguide, the allowed energy levels are grouped in bands, beyond which single levels are found, corresponding to surface states localized at the chain ends. We have analyzed the conditions of existence of Tamm and Shockley surface states in a two-band tight-binding model. The two types of states are shown to localize at both surfaces of a symmetric chain, in which Tamm and Shockley state coexistence is found to be excluded. In an asymmetric chain, Tamm and Shockley states can occur at the same model parameter values, and each is localized at one surface only.

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