A general theory of edge spin wave excitations in semi-infinite and finite periodic arrays of magnetic nanodots existing in a spatially uniform magnetization ground state is developed. The theory is formulated using a formalism of multi-vectors of magnetization dynamics, which allows one to study edge excitations in arrays having arbitrary complex primitive cells and lattice geometry. The developed formalism can describe edge excitations localized both at the physical edges of the array and at the internal domain walls separating array regions existing in different static magnetization states. Using a perturbation theory in the framework of the developed formalism it is possible to calculate damping of edge modes and their excitation by external variable magnetic fields. The theory is illustrated on the following practically important examples: (i) calculation of the FMR absorption in a finite nanodot array having the shape of a right triangle, (ii) calculation of nonreciprocal spin wave spectra of edge modes, including modes at the physical edges of an array and modes at the domain walls inside an array, (iii) study of the influence of the domain wall modes on the FMR spectrum of an array existing in a non-ideal chessboard antiferromagnetic ground state.
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