Collective spin-wave excitations in a two-dimensional array of coupled magnetic nanodots

A general theory of collective spin-wave excitations in a two-dimensional array of magnetic nanodots coupled by magnetodipolar interaction is developed. The theory allows one to analytically calculate spectra, damping rates, excitation efficiencies, and other characteristics of spin waves in both periodic and aperiodic ground states of an array. It is demonstrated that all the properties of collective spin waves in an array existing in any spatially periodic ground state (e.g., ferromagnetic or chessboard antiferromagnetic) are determined by the same state-independent array's demagnetization tensor ̂ \^F_k, which is determined by the spin-wave wave vector k, the size and shape of the array's elements (nanodots), and the geometry of the array's lattice. The applications of the developed general theory are illustrated on particular examples: (i) spin waves in ferromagnetic and chessboard antiferromagnetic states of a square array, and (ii) localized spin-wave excitations associated with an isolated ``defect'' in a uniform ferromagnetic ground state of a square array.