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Approximate electrodynamic boundary conditions are derived for an array of dipolarly coupled magnetic elements. It is assumed that the elements' thickness is small compared to the wavelength of an electromagnetic wave in a free space. The boundary conditions relate electric and magnetic fields existing at the top and bottom sides of the array through the averaged uniform dynamic magnetization of the array. This dynamic magnetization is determined by the collective dynamic eigen-excitations (spin wave modes) of the array and is found using the external magnetic susceptibility tensor. The problem of oblique scattering of a plane electromagnetic wave on the array is considered to illustrate the use of the derived boundary conditions. [ABSTRACT FROM AUTHOR]

A general theory of collective spin-wave edge modes in semi-infinite and finite periodic arrays of magnetic nanodots having uniform dynamic magnetization (macrospin approximation) is developed. The theory is formulated using a formalism of multivectors of magnetization dynamics, which allows one to study edge modes in arrays having arbitrarily complex primitive cells and lattice structure. The developed formalism can describe spin-wave edge modes localized both at the physical edges of the array and at the internal "domain walls" separating the 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 the edge modes and to describe 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 the spectra of nonreciprocal spin-wave edge modes, including the modes at the physical edges of an array and modes at the domain walls inside the array; and (iii) study of the influence of the domain wall modes on the FMR spectrum of an array existing in a nonideal chessboard antiferromagnetic ground state. [ABSTRACT FROM AUTHOR]