  The interfacial Dzyaloshinskii-Moriya Interaction can modify the topology of
droplets excited by a localized spin-polarized current. Here, we show that, in
addition to the stationary droplet excitations with skyrmion number either one
(topological) or zero (non-topological), there exists, for a fixed current, an
excited mode with a non-stationary time behavior. We call this mode "instanton
droplet", which is characterized by time domain transitions of the skyrmion
number. These transitions are coupled to an emission of incoherent spin-waves
that can be observed in the frequency domain as a source of noise. Our results
are interesting from a fundamental point of view to study spin-wave emissions
due to a topological transition in current-driven systems, and could open the
route for experiments based on magnetoresistance effect for the design of a
further generation of nanoscale microwave oscillators.
