We found from analytical derivations and micromagnetic numerical simulations that there exist two distinct normal modes in apparently complex vortex gyrotropic motions in two dipolar-coupled magnetic nanodisks. The normal modes have characteristic higher and lower single angular eigenfrequencies with their own elliptical orbits elongated along the x (bonding axis) and y axes, respectively. The superposition of the two normal modes results in coupled vortex gyrations, which depend on the relative vortex-state configuration in a pair of dipolar-coupled disks. This normal-mode representation is a simple means of understanding the observed complex vortex gyrations in two or more dipolar-interacting disks of various vortex-state configurations.
@article{arxiv.1102.0519,
title = {Normal modes of coupled vortex gyration in two spatially separated magnetic nanodisks},
author = {Ki-Suk Lee and Hyunsung Jung and Dong-Soo Han and Sang-Koog Kim},
journal= {arXiv preprint arXiv:1102.0519},
year = {2015}
}