Extended Data Fig. 1: TDGL simulations of vortex dynamics upon magnon generation.

a, I-V curves for a superconducting strip without magnon radiation and for two symmetries of the eddy currents (‘vortex lattice’ and ‘vortex stripes’) accompanied by a reconfiguration of the vortex lattice. b, Snapshots of the superconducting order parameter ∣Δ∣ at points 1-9 in the I-V curves in panel a. c, Development of the magnon Shapiro step in the I-V curve of the superconductor with increase of the amplitude dA_m of eddy currents upon magnon generation. With an increase in the eddy currents’ amplitude, a constant-voltage step is developed in the I-V curve, panel c. This is accompanied by a dynamic ordering of the vortex lattice, as concluded from the snapshots of the superconducting order parameter, panel b. Without magnon generation, the flow of vortices ordered in a nearly hexagonal vortex lattice (snapshot 1) loses its long-range order (snapshot 2) in the regime of nonlinear conductivity II. As the transport current increases, areas with a suppressed order parameter are nucleated at the edge where the vortices enter the superconductor, forming ‘vortex rivers’ (snapshot 3) and leading to an avalanche-like transition of the sample to the normal state. When the excitation of magnons is modelled with a resonance-like enhancement of the eddy currents, the I-V curve becomes flattened, and the motion of vortices ordered in a hexagonal lattice (snapshots 4, 5 and 6) or stripes (snapshots 7, 8, and 9) persists up to larger currents. With a further current increase, the vortex stripes hinder the development of vortex rivers such that an ordered vortex-stripe state is preserved up to yet larger transport currents (snapshots 8 and 9) as compared to the case of a hexagonal vortex lattice. A hallmark of the stripe symmetry is that the vortex lattice maintains its stripe-like ordering in a broad range of transport currents despite the same amplitude of the eddy currents.