Eigenmodes of two-dimensional conservative droplet soliton

Droplet solitons are strongly nonlinear, dynamic structures in ferromagnets with perpendicular magnetic anisotropy. For experimental observation of such structures a nanocontact spin torque oscillator (NC-STO) where spin polarized currents act as a gain source to counteract magnetic damping is utilized. We analyze eigenmode of this droplet excitations in a simplest case of conservative droplet solitons, when both Gilbert damping in magnetic films and energy gain due to spin-polarized current can be neglected. As a result of such analysis eigenmode frequencies of conservative droplet are obtained. Among main features of conservative droplet eigenmode is azimuthal degeneration of mods and localization of mode frequencies in a finite region.