  Relaxation of linear magnetization dynamics is well described by the viscous
Gilbert damping processes. However, for strong excitations, nonlinear damping
processes such as the decay via magnon-magnon interactions emerge and trigger
additional relaxation channels. Here, we use space- and time-resolved
microfocused Brillouin light scattering spectroscopy and micromagnetic
simulations to investigate the nonlinear relaxation of strongly driven
propagating spin waves in yttrium iron garnet nanoconduits. We show that the
nonlinear magnon relaxation in this highly quantized system possesses
intermodal features, i.e., magnons scatter to higher-order quantized modes
through a cascade of scattering events. We further show how to control such
intermodal dissipation processes by quantization of the magnon band in
single-mode devices, where this phenomenon approaches its fundamental limit.
Our study extends the knowledge about nonlinear propagating spin waves in
nanostructures which is essential for the construction of advanced spin-wave
elements as well as the realization of Bose-Einstein condensates in scaled
systems.
