Topological defects such as magnetic solitons, vortices and skyrmions have started to play an important role in modern magnetism because of their extraordinary stability 1 , which can be exploited in the production of memory devices. Recently, a type of antisymmetric exchange interaction, namely the Dzyaloshinskii-Moriya interaction (DMI; refs 2,3), has been uncovered and found to influence the formation of topological defects [4][5][6][7] . Exploring how the DMI a ects the dynamics of topological defects is therefore an important task. Here we investigate the dynamics of the magnetic domain wall (DW) under a DMI by developing a real time DW detection scheme. For a weak DMI, the DW velocity increases with the external field and reaches a peak velocity at a threshold field, beyond which it abruptly decreases. For a strong DMI, on the other hand, the velocity reduction is completely suppressed and the peak velocity is maintained constant even far above the threshold field. Such a distinct trend of the velocity can be explained in terms of a magnetic soliton, the topology of which is protected during its motion. Our results therefore shed light on the physics of dynamic topological defects, which paves the way for future work in topology-based memory applications.The magnetic domain wall (DW) has received significant attention because of the academic interest it inspires, as well as its potential applications in data storage and logic devices [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] . The dynamics of the DW consists of unique, nonlinear behaviour in response to an external magnetic field. In one-dimensional wires, the DW velocity increases linearly with the external magnetic field up to a threshold, beyond which it abruptly decreases. The abrupt reduction of DW velocity is due to the onset of precessional DW motion, which causes a periodic change in the helicity of the DW (Fig. 1a and Supplementary Fig. 5). This is a wellknown phenomenon in field-driven DW dynamics, and is referred to as the Walker breakdown (WB; refs 8,15). An actual DW, however, may have two-dimensional configurations, where the coherent precessional motion of the DW above the threshold field (hereafter the Walker field) should be replaced by the nucleation and propagation of vertical Bloch lines (VBLs; Fig. 1b) 8 . The VBL, a magnetic curling structure that divides the DW, is considered to be a topological defect as its stability can be determined on the basis of a topological argument. The VBL has four-fold degeneracy that depends on the magnetic charge (Q = ±1) and chirality (C = ±1/2). Here, the topological charge corresponds to the sign of magnetic charge at the centre of the VBL-that is to say, Q = +1 for head-to-head spin alignment and Q = −1 for tail-to-tail spin alignment. Positive (negative) chirality is defined as clockwise (anticlockwise) rotation of the spin. The half-integer feature of the chirality indicates the half-cycle of the spin rotation (so called π-VBL). We define the four degenerate state...

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We report the experimental observation of Snell's law for magneto-static spin waves in thin ferromagnetic Permalloy films by imaging incident, refracted and reflected waves. We use a thickness step as the interface between two media with different dispersion relation. Since the dispersion relation for magneto-static waves in thin ferromagnetic films is anisotropic, deviations from the isotropic Snell's law known in optics are observed for incidence angles larger than 25°with respect to the interface normal between the two magnetic media. Furthermore, we can show that the thickness step modifies the wavelength and the amplitude of the incident waves. Our findings open up a new way of spin wave steering for magnonic applications.

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.