Spin-wave bound modes in a circular array of magnetic inclusions embedded into a metallized ferromagnetic thin-film matrix

A general theory of forward volume magnetostatic spin-wave multiple scattering by a finite two-dimensional ensemble of cylindrical magnetic inclusions in a ferromagnetic film (matrix) metallized from both sides is developed. It is predicted that bound spin-wave modes are excited around these inclusions. The set of self-consistent equations for spin-wave multiple scattering inside the matrix with inclusions is obtained by using an invariant addition theorem for the cylindrical wave functions. This set of equations is solved by an iterative process. We derive simple expressions for eigenmodes (bound modes) in a form of Bloch-like spin waves propagating along the inclusion circular array. The theory is illustrated on practically significant examples: (i) bound-mode excitation by propagating spin waves; (ii) helix components of the spin-wave-scattered field around magnetic inclusions; and (iii) a high-quality spin-wave resonator based on a small number of magnetic inclusions.