Figure 1

Sketch of the simulated structures: MC based on a Py waveguide with a periodic variation of its saturation magnetization. The dark blue lines denote the areas where the saturation magnetization has been reduced by a certain percentage.Reuse & Permissions

Figure 2

Spin-wave transmission characteristics for a simple permalloy waveguide as a function of the propagation distance ($x$) from the excitation antenna.Reuse & Permissions

Figure 3

Characteristics of two magnonic crystals with different doping area lengths. The top and the bottom panels correspond to MCs with $d=70$ and 280 nm, respectively. (a), (d) Spin-wave transmission characteristics as a function of the propagation distance ($x$) from the excitation antenna for a magnonic crystal. The vertical dotted lines in panel (a) denote the positions of the areas where the saturation magnetization was decreased. The horizontal dashed white lines in panel (d) represent the frequency band-gap positions for the MC with $d=70$ nm shown above. (b), (e) Spin-wave transmission characteristics obtained by integrating the spin-wave intensity of a period of the magnonic crystal (from 4.35 to 5.35 $\mu$m). The inset frequencies mark the positions of the band gaps. (c), (f) Dispersion relations of the first and the third spin-wave width modes calculated using a saturation magnetization averaged over the entire MC structure. The black and red arrows denote the positions of the band gaps at the corresponding Bragg wavenumbers $k_{\Lambda ,n}$ as they are expected from theory.Reuse & Permissions

Figure 4

(a) Dispersion relations calculated analytically for the first ($n_1$) and the third ($n_3$) width modes for MCs with different widths 4, 2, and 1 $\mu$m, respectively. (b) Difference $\Delta f$ between the frequencies of $n_1$ and of $n_3$ extracted at the Bragg wavenumbers $k_{\Lambda ,n}$ as a function of the magnonic crystal width. The MC parameters used to calculate the dispersions are $d=280$ nm and a 20% reduction of the saturation magnetization.Reuse & Permissions

Figure 5

Snapshot images of the magnetization oscillation pattern with the component $M_z$ color coded recorded for the following cases: MC for a continuous excitation with a frequency of 9.64 GHz (a) and 8.55 GHz (b). (c) Reference waveguide for an excitation frequency of 8.55 GHz.Reuse & Permissions