  The concept of Space-Time Crystals (STC), i.e. translational symmetry
breaking in time and space, was recently proposed and experimentally
demonstrated for quantum systems. Here, we transfer this concept to magnons and
experimentally demonstrate a driven STC at room temperature. The STC is
realized by strong homogeneous micro-wave pumping of a micron-sized permalloy
(Py) stripe and is directly imaged by Scanning Transmission X-ray Microscopy
(STXM). For a fundamental understanding of the formation of the STC,
micromagnetic simulations are carefully adapted to model the experimental
findings. Beyond the mere generation of a STC, we observe the formation of a
magnonic band structure due to back folding of modes at the STC's Brillouin
zone boundaries. We show interactions of magnons with the STC that appear as
lattice scattering. This results in the generation of ultra short spin waves
down to 100 nm wavelength that cannot be described by classical dispersion
relations for linear spin wave excitations. We expect that room temperature
STCs will be a useful tool to investigate non-linear wave physics, as they can
be easily generated and manipulated to control their spatial and temporal band
structure.
