Spin wave band structure of a two-dimensional ferromagnetic antidot array -- Presentazione orale by R. Zivieri - Conferenza internazionale

The spin wave band structure of a two-dimensional square array of NiFe circular antidots (ADs) has been investigated both experimentally and theoretically by using Brillouin light scattering (BLS) technique and micromagnetic calculations, carried out by means of the dynamical matrix method (DMM) with implemented periodic boundary conditions [1]. Sample consists of 22 nm NiFe film with etched circular having diameter of 120 nm and periodicity of 800 nm. As depicted in the inset to Fig.1, the external magnetic field is applied along y direction, while the transferred wave vector is along x direction. Both the experimental measurements and the calculated spin wave dispersion provide evidence for either extended or localized magnonic modes having a propagative nature. Extended modes spreading in the “horizontal” channels comprised between adjacent rows of ADs have a non-vanishing precession amplitude also along the horizontal rows of holes. These spin-wave modes are labelled as DEnBZ (black curves) where nBZ denotes a given Brillouin zone with n=1,2,.. Instead, the other kind of spin-wave modes, mainly localized along the horizontal rows of antidots, the so-called localized modes [2], are labelled as DElocnBZ (red curves). Both families of modes exhibit bandgaps at Brillouin zone boundaries predicted by the DMM calculations. Opening of bandgaps is interpreted in terms of Bragg diffraction of spin waves from the AD lattice and a quantitative explanation of this effect is given by studying the behavior of the mean internal field. The calculated mean internal field experienced by the two kind of modes is strongly inhomogeneous and is larger in correspondence of ADs. The DE2BZ mode exhibits its maximum precession amplitude where the internal field is larger (smaller) and has thus a larger (smaller) frequency. Band gaps are also calculated within the analytical model according to a perturbation approach. The eigenfunctions representing frequency modes at the BZs boundaries belonging to n-th and (n+1)-th band (sin (k π / a) x and cos (k π / a) x with k = 1,2,.., respectively) are interchanged with respect to those of electrons in electronic bands studied within the nearly-free electron model. This can be understood taking into account that the periodic mean internal field has its maxima in correspondence of ADs, while the periodic electronic potential is minimum close to the nuclei and vice versa. A comparison between the bandgap measured by BLS and the values calculated by means of the analytical model and by using the DMM is shown in Table 1. According to the analytical model, it is found that the relevant scattering potential for Bragg reflection is not provided by the holes themselves, but by the concomitant internal field inhomogeneity between holes [3]. This is in contrast to antidots in photonics and electronics where the back-reflection is directly caused by the presence of holes. The results of this study are important also for the potential applications of these patterned structures that can be used in magnonic devices. Indeed, AD behaves not only as waveguide for spin waves, but the presence of bandgaps permits to filter the frequency of travelling excitations. In this way, AD can be used also as a filter for spin waves. The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement n228673 (MAGNONICS). [1] L. Giovannini, F. Montoncello, and F. Nizzoli, Phys. Rev. B 75, 024416 (2007) [2] S. Tacchi, M. Madami, G. Gubbiotti, G. Carlotti, A.O. Adeyeye, S. Neusser, B. Botters, and D. Grundler, IEEE Trans. Magn. 46, 172 (2010) [3] R. Zivieri, S. Tacchi, F. Montoncello, L. Giovannini, F. Nizzoli, M. Madami, G. Gubbiotti, G. Carlotti, S. Neusser, G. Duerr, and D. Grundler, “Bragg diffraction of spin waves from a two dimensional antidot lattice ”, in press in Physical Review B -- Presentazione orale by R. Zivieri - Conferenza internazionale