Title: Dynamic self-organisation and pattern formation by magnon-polarons

Abstract: Nonlinear dynamics can give rise, via the processes of self-organisation and pattern formation, to the spontaneous manifestation of order in open and complex systems far from equilibrium. Self-organising systems, transforming the inflow of energy into information, are ubiquitously found in current topical areas of science ranging from brainwave entrainment and neuromorphic computing to energy-efficient data storage technologies. In the latter, magnetic materials play a pivotal role combining very fast switching with permanent retention of information. However, it has been shown that, at very short time scales, magnetisation dynamics become chaotic due to internal instabilities, resulting in incoherent spin-wave excitations that ultimately destroy magnetic ordering. Here, contrary to all expectations, we show that such chaos gives rise to a periodic pattern of reversed magnetic domains, with a feature size far smaller than the spatial extent of the excitation. We explain this pattern as a result of phase-synchronisation of magnon-polaron waves, driven by strong coupling of magnetic and elastic modes. Our results reveal not only the peculiar formation and evolution of magnon-polarons at short time-scales, but also present a novel mechanism of magnetization reversal driven by coherent packets of short-wavelength quasiparticles.