  Excitation of magnetization dynamics by pure spin currents has been recently
recognized as an enabling mechanism for spintronics and magnonics, which allows
implementation of spin-torque devices based on low-damping insulating magnetic
materials. Here we report the first spatially-resolved study of the dynamic
modes excited by pure spin current in nanometer-thick microscopic insulating
Yttrium Iron Garnet disks. We show that these modes exhibit nonlinear
self-broadening preventing the formation of the self-localized magnetic bullet,
which plays a crucial role in the stabilization of the single-mode
magnetization oscillations in all-metallic systems. This peculiarity associated
with the efficient nonlinear mode coupling in low-damping materials can be
among the main factors governing the interaction of pure spin currents with the
dynamic magnetization in high-quality magnetic insulators.
