Nonlinear oscillations of magnetization for ferromagnetic particles in the vortex state and their ordered arrays

The dynamics of magnetization oscillations with a considerable amplitude and a radial symmetry in small ferromagnetic particles in the form of a thin disk with a magnetic vortex has been investigated. The collective variables that describe radially symmetric oscillations of the magnetization dynamics for particles in the vortex state are introduced, and the dependence of the particle energy is studied as a function of these variables. The analytical expressions describing the frequency of magnetization oscillations with a radial symmetry, including nonlinear oscillations, are derived using the collective variables. It is shown that the presence of a magnetic field oriented perpendicular to the particle plane reduces the oscillation frequency and can lead to hybridization of this mode with other modes of spin oscillations, including the mode of translational oscillations of the vortex core. The soliton solutions describing the propagation of collective oscillations along the chain of magnetic particles are found.