Size effects on magnonic mode dynamics in 2D ferromagnetic antidot lattices -- Presentazione poster by R. Zivieri -- Conferenza nazionale

The size effects on frequencies of collective modes in two-dimensional (2D) arrays of periodic circular antidots (holes) embedded into a ferromagnetic Permalloy material are investigated. The study is performed by calculating 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 antidot periodicity is a = 420 nm, the thickness is L = 30 nm, whereas the diameters of the holes are d1 = 140 nm, d2 = 180 nm, d3= 220 nm and d4= 260 nm, respectively [1]. The two relevant modes, having an appreciable calculated 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 antidots, the Floc mode. Frequencies of collective modes monotonically increase with increasing the mean internal field. However, at a fixed external field the frequencies of F and Floc mode have on opposite behavior as a function of the hole size as shown in Figure 1. Indeed, the mean demagnetizing field experienced by the F mode is anti-parallel to the external field lowering the mean internal field, while for the Floc mode it is parallel and has the effect to increase the internal field. Moreover, at the centre of the first Brillouin zone, the two lowest spin-wave mode frequencies, namely the edge mode (EM) localized at the antidot borders [2] and the F mode, become soft at a given critical field showing a deep minimum. The intensity of the critical field depends on the hole size and both soft modes do exhibit a finite gap. The softening mechanism is strictly related to the rotation of the static magnetization from the hard to the easy axis marking a reorientational and continuous phase transition. A phenomenological model based on an Hamiltonian density including the different density energy contributions and describing the continuous phase transition is developed. According to this model, the critical field turns out to be equal to the first-order mean demagnetizing field. The mean demagnetizing field was determined according to micromagnetic calculations by averaging over the micromagnetic cells corresponding to the antidot separation. The results of the calculations compare well with experimental data obtained by means of Brillouin light scattering technique for all the diameters investigated [3]. [1] J. Ding, D. Tripathy, A. O. Adeyeye, J. Appl. Phys. 109, (2011) 07D304-1-3. [2] S. Tacchi, M. Madami, G. Gubbiotti, G. Carlotti, A.O. Adeyeye, S. Neusser, B. Botters, D. Grundler, IEEE Trans. Magn. 46, (2010) 172-178. [3] R. Zivieri et al., “Soft magnonic modes in two-dimensional permalloy antidot lattices”, J. of Physics: Condens. Matter 25, (2013) 336002-1-7.