From Gardner Nonlinear Dynamics to Nano-Hillock Morphology: Linking Solitary Waves to Measurable Nanostructures

A nonlinear plasma-dynamic model has been proposed to describe the formation of nano-hillocks on the yttrium iron garnet surface due to the bombardment of energetic C60 ions. Localized energy deposition is thought to generate a transient multicomponent plasma, described in the framework of the multi-fluid model and eventually reduced to the Gardner equation by means of the reductive perturbation technique. Unlike the traditional electrostatic analysis, the model proposed in this paper connects the Gardner solution with measurable parameters of the surface, which provides a possibility to interpret the amplitude and spatial scale of the Gardner solution as the height and width of the nano-hillocks. The results obtained turn out to be in agreement with the observed morphology, indicating that the Gardner nonlinear evolution can be applied to the real spatial characteristics of the nanostructure obtained as a result of the irradiation. The reductive-perturbation derivation of a Gardner equation is a standard nonlinear-plasma procedure and is not claimed here as the principal novelty. The new step is the dimensional mapping of the Gardner solitary-wave solution to the measured nano-hillock morphology and its quantitative comparison with the digitized scanning-force-microscopy profile. The plasma-dynamic interpretation is conditional: the Gardner reduction is applied only after the prompt electronic cascade, and its validity requires the remaining source/sink, charge-changing, and heavy-particle collisional times to be longer than the nonlinear evolution time.