A general theory of edge spin wave excitations in semi-infinite and finiteperiodic arrays of magnetic nanodots existing in a spatially uniformmagnetization ground state is developed. The theory is formulated using aformalism of multi-vectors of magnetization dynamics, which allows one to studyedge excitations in arrays having arbitrary complex primitive cells and latticegeometry. The developed formalism can describe edge excitations localized bothat 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 ispossible to calculate damping of edge modes and their excitation by externalvariable magnetic fields. The theory is illustrated on the followingpractically important examples: (i) calculation of the FMR absorption in afinite nanodot array having the shape of a right triangle, (ii) calculation ofnonreciprocal spin wave spectra of edge modes, including modes at the physicaledges of an array and modes at the domain walls inside an array, (iii) study ofthe influence of the domain wall modes on the FMR spectrum of an array existingin a non-ideal chessboard antiferromagnetic ground state.
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