Size Effects on Spin-wave Modes in Ferromagnetic Antidot Lattices -- Presentazione orale by R. Zivieri - Congresso nazionale

The size effects on frequencies of collective modes in two-dimensional arrays of periodic circular antidots (ADs) (holes) embedded into a ferromagnetic Permalloy material are investigated. The study is performed by determining the frequency behaviour as a function of the intensity H of the external magnetic field applied in the plane of the system along the y-direction for vanishing Bloch wave vector. The AD periodicity is a = 420 nm, the thickness is L = 30 nm, whereas the diameters of the holes are d1 = 260 nm, d2 = 220 nm and d3= 180 nm, respectively [1]. The two relevant modes having an appreciable scattering cross-section are: 1) the resonant mode of the spectrum, the so-called Fundamental (F) mode, whose spatial profile is confined in the channels; 2) the equivalent mode mainly localized in the horizontal rows of ADs, the Floc mode. Frequencies of spin modes monotonically increase with increasing the external field. More specifically, the frequencies of each spin mode are proportional to the mean internal field. However, at a fixed external field: a) the F mode frequencies increase by decreasing hole diameter b) the Floc frequencies decrease by decreasing hole diameter. In order to explain this opposite behaviour, it is necessary to make a qualitative analysis of the trend of the mean internal field, whose magnitude is given by the sum of H and the mean demagnetizing field <Hdem>. Due to the presence of magnetic surface charges on the external edges of ADs, the mean demagnetizing field experienced by the F mode is anti-parallel to the external field and almost homogeneous, while for the Floc mode it is parallel and strongly inhomogeneous. By increasing the diameter of the holes, the channels reduce and, as a consequence, <Hdem> increases negatively leading to a decrease of the F mode frequencies. Instead, the larger is the diameter of the holes, the more is the mean demagnetizing field felt by the Floc mode in correspondence of the ADs yielding to an increase of the corresponding frequencies. [1] J. Ding, D. Tripathy and A. O. Adeyeye, J. Appl. Phys. 109, 07D304 (2011).