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Driving condensed matter systems with periodic electromagnetic fields can result in exotic states not found in equilibrium. Termed Floquet engineering, such periodic driving applied to electronic systems can tailor quantum effects to induce topological band structures and control spin interactions. However, Floquet engineering of magnon band structures in magnetic systems has proven challenging so far. Here, we present a class of Floquet states in a magnetic vortex that arise from nonlinear interactions between the vortex core and microwave magnons. Floquet bands emerge through the periodic oscillation of the core, which can be initiated by either driving the core directly or pumping azimuthal magnon modes. For the latter, the azimuthal modes induce core gyration through nonlinear interactions, which in turn renormalizes the magnon band structure. This represents a self-induced mechanism for Floquet band engineering and offers new avenues to study and control nonlinear magnon dynamics.

Parametric spin wave excitation allows studying a variety of nonlinear phenomena, such as magnon scattering. In patterned micro- and nanostructures the magnon spectra is discrete and translational symmetry is broken, which means allowable scattering channels differ from those in continuous films. An example is non-degenerate scattering by which high-power transverse field pumping creates two magnons with distinct frequencies around half the pumping frequency. Through micromagnetics simulations, we show under certain conditions that combining two pumping frequencies generates new magnon modes through a process of stimulated magnon scattering. Such processes are found to depend on the film geometry and sequence of the pumping fields., Comment: 6 pages, 5 figures

We present a computational study of the parametric excitation of spin waves in thin film disks with a mode-resolved approach. The method involves projecting out the time-dependent magnetization, computed using micromagnetics simulations, onto the spatial profile of the eigenmodes that are obtained from the linearization of the equations of motion. Unlike spectral analysis in the frequency domain, the projection allows for the analysis of transient mode dynamics under parametric excitation. We apply this method to parallel pumping of quantized spin wave modes in in-plane magnetized thin-film disks, where phenomena such as frequency pulling, mutual phase locking, and higher-order magnon scattering processes are identified., Comment: 12 pages, 11 figures

Magnons are elementary excitations in magnetic materials and undergo nonlinear multimode scattering processes at large input powers. In experiments and simulations, we show that the interaction between magnon modes of a confined magnetic vortex can be harnessed for pattern recognition. We study the magnetic response to signals comprising sine wave pulses with frequencies corresponding to radial mode excitations. Three-magnon scattering results in the excitation of different azimuthal modes, whose amplitudes depend strongly on the input sequences. We show that recognition rates above 95\% can be attained for four-symbol sequences using the scattered modes, with strong performance maintained with the presence of amplitude noise in the inputs.

The spectral signatures of magnetic skyrmions under microwave field excitation are of fundamental interest and can be an asset for high frequency applications. These topological solitons can be tailored in multilayered thin films, but the experimental observation of their spin wave dynamics remains elusive, in particular due to large damping. Here, we study Pt/FeCoB/AlO$_x$ multilayers hosting dense and robust skyrmion lattices at room temperature with Gilbert damping of $\sim 0.02$. We use magnetic force microscopy to characterise their static magnetic phases and broadband ferromagnetic resonance to probe their high frequency response. Micromagnetic simulations reproduce the experiments with accuracy and allow us to identify distinct resonant modes detected in the skyrmion lattice phase. Low ($<$ 2 GHz) and intermediate frequency ($2-8$ GHz) modes involve excitations localised to skyrmion edges in conjunction with precession of the uniform background magnetisation, while a high frequency ($>$ 12 GHz) mode corresponds to in-phase skyrmion core precession emitting spin waves into uniform background with wavelengths in the 50--80 nm range commensurate with the lattice structure. These findings could be instrumental in the investigation of room temperature wave scattering and the implementation of novel microwave processing schemes in reconfigurable arrays of solitons., Comment: Main text and supplemetary information, 31 pages in total, 18 figures