Spin-Wave Modes Localized On Isolated Defects In A Two-Dimensional Array Of Dipolarly Coupled Magnetic Nanodots

A comprehensive analytical and numerical study of spin-wave (SW) modes localized on isolated defects in a two-dimensional array of dipolarly coupled magnetic nanodots is presented. Two limiting cases of a defect dot are considered: (i) pointlike defect-a dot having a different eigenfrequency, but the same magnetic moment; (ii) "dipolar defect"-a dot having a different magnetic moment. It is shown, that the appearance of a localized SW mode depends on the peculiarities of the bulk SW spectrum near its bottom or/and top boundaries. In the case of a smooth parabolic spectrum, a localized mode can be created by a defect of a vanishingly small strength, whereas in the case of a spectrum described by a nonanalytic function a localized mode can be created only by a defect of a finite strength, exceeding a certain threshold value. In contrast to the pointlike defects, the dipolar defects may lead to the formation of higher-order localized SW modes. In a case of a complex array having several spin-wave branches (e.g., an array existing in an antiferromagnetic stationary state), the localized SW modes may appear near some (or all) of the SW spectral branches, depending on the structure of the SW spectrum, and on the defect properties.