Multipole magnetostatic interactions and collective vortex excitations in dot pairs,chains, and two-dimensional arrays

摘要

The multipole expansion of magnetostatic interaction energy between nonuniformly magnetized ferromagnetic particles is developed and applied for calculation of the gyrotropic frequencies of the coupled vortex state dots. A pair of coupled dots in a vortex state is considered as a model system, and then the calculations are extended to lateral arrays of the interacting vortex state dots [one- and two-dimensional (2D) square and hexagonal lattices]. The odd rank multipole moments (dipolar, octupolar, etc.) play the main role in the interdot magnetostatic interaction. The vortex collective frequencies and group velocities are calculated within the pole-free and rigid vortex models and compared with the experimental observations of the dynamics by broadband ferromagnetic resonance and x-ray imaging. The cases of different vortex core polarizations are considered, and their strong influence on the excitation spectra is shown. Frequency bandwidths of the vortex gyrotropic modes for dense 2D square and hexagonal arrays can exceed 1 /3 of the eigenfrequency of an isolated dot. The group velocity for transferring the total microwave magnetic energy from one dot to another is found to be proportional to the dot thickness and inversely proportional to the squared lattice period.