Complete wave vector mapping of a two-dimensional Magnonic Crystal consisting of square array of NiFe disks -- Presentazione poster by R. Zivieri - Conferenza internazionale

A complete mapping of the spin wave band structure of a two-dimensional magnonic crystal (MC) consisting of a square array of interacting nanodisks, has been performed by Brillouin light scattering (BLS) by measuring the spin wave frequency dispersion along the principal highsymmetry directions of the first Brillouin Zone (BZ), i.e. Gamma X, Gamma Y, Gamma M, XM and YM. The samples is formed by a dense array of 50 nm thick NiFe disks having a diameter d=600 nm and arranged in a square matrix with interdot separation 55 nm (period a = 655 nm). This corresponds to a square first BZ of side 2 Pi/a=2x4.8 x10^4 rad/cm. Note that the Gamma-X and Gamma Y directions correspond to the Magnetostatic Backward Volume Wave (MSBVW) geometry and Magnetostatic Surface Wave (MSSW) geometry, respectively. The experimental data are compared to calculations of the band diagram performed by means of the dynamical matrix method extended to include the dipolar interaction between the disks. A very good agreement between experimental frequencies and calculated curves has been obtained. The detected modes can be labeled depending on the number m (n) of nodes perpendicular (parallel) to the direction of the magnetization as Backward-like modes m-BA (Damon-Eshbach-like n-DE); modes with mixed character m-BAx n- DE are also found. In addition, the mode with no nodes is classified as fundamental mode (F), while modes with dynamic magnetization localized at the ends of the particle are labeled n-EM, depending on the number of nodes n. Since the width of each magnonic band is proportional to the mean square dynamic magnetization inside a single dot, the largest dispersion has been observed for the F mode. For higher order modes, instead, the amplitude of the magnonic band rapidly decreases by increasing the number of oscillations within the single dot. The behaviour of dispersion curves can be explained introducing an effective wave vector keff. The effective wavevector describes the overall oscillation of the magnetization on the array, because it takes into account both the oscillation within the dot due to the mode character and the changing between adjacent dots due to the Bloch wave vector. In disks coupled by dynamic dipolar interaction, the frequency dispersion as a function of keff exhibits a behaviour analogous to that of the continuous film, where mode frequency increases (decreases), when the modulus of the wavevector increases in a direction perpendicular (parallel) to the applied magnetic field. For example, the F mode at Gamma has keff=0 (no nodes), while at Y, |kx eff|=0 and |ky eff|=Ky=Pi/a: hence, from Gamma to Y, |ky eff| increases and this implies a frequency increase. Conversely, from Gamma to X, |kx eff| increases and this implies a frequency decrease, because keff is now parallel to H. It is interesting to notice that the measured and calculated dispersion of F mode along the Gamma-M high-symmetry direction has less pronounced amplitude with respect to that measured along the XM and YM high-symmetry directions. This is due to a compensation frequency effect associated to the fact that moving from Gamma to M, there is a simultaneous increment of the two in-plane components of the spin wave wavevector and an opposite behavior of the frequency mode. A different behavior is observed for the 1-DE and 1-BA modes whose frequency oscillation amplitudes are more pronounced with respect to those measured in the XM and YM. In such a case, the increase of wavevector either in the MSBVW or in the MSSW scattering configuration, has the same effect, i.e. an increase of frequency for 1-BA, a decrease of frequency for 1-DE: hence, the joint increase along Gamma M results in an amplification of those trends. -- Presentazione poster by R. Zivieri - Conferenza internazionale