Dynamics of nano-scale magnetic vortices in ferromagnetic dot arrays

We investigate analytically and numerically the dynamics of magnetostatically coupled vortices in ferromagnetic dot arrays. Eigenfrequencies of rotational motion of vortex core in two nano-dots are calculated by using the rigid vortex model and Thiele's equation where collective degrees of freedom describe the motion of each vortex core. We further extend the model to array of magnetostatically coupled NxN dots in two-dimensional tetragonal lattice, which is found to exhibit characteristic dispersion relation for eigenfrequencies