For instance, Zhang et al. [7] and Maznev [15, 16] attributed the origin of the gaps they observed in film-substrate samples to the avoided crossings of the RW and zone-folded Sezawa modes. Also, hybridization bandgaps in Si and SiO2 gratings [13, 14] were ascribed to the mixing of the RW and the longitudinal resonance, also referred to as the high-frequency pseudo-surface
wave. It is noteworthy Ceritinib mw that the phonon dispersion spectrum of Py/BARC differs substantially from those of the 1D Py/Fe(Ni) arrays of [7]. For instance, the measured gap opening of 1.0 GHz at the BZ boundary of the former, is much wider than the first bandgap of 0.4 GHz observed for the latter. This is primarily due to the elastic and density contrasts between two metals (Fe
or Ni and Py) being much lower than that between the polymer BARC and the BMS-777607 concentration metal Py. The 4.8 GHz center of this gap opening is also higher than those (≈ 3.4 GHz) of Py/Fe(Ni). This is expected as the 350-nm period of our Py/BARC is shorter than the 500-nm one of Py/Fe(Ni). Another reason is that our Py/BARC is directly patterned on a Si substrate, while the Py/Fe(Ni) samples contain an 800-nm-thick SiO2 sub-layer between the patterned arrays and the Si substrate which has the effect of red shifting the SAW frequencies. Another notable difference is that the 2.2-GHz bandgap is considerably larger than those of the Py/Fe(Ni) arrays, whose maximum gap is only 0.6 GHz. One explanation for this is the high elastic and density contrasts between the materials in Py/BARC. We now discuss the dispersion of spin waves in Py/BARC. The magnon band structure (Figure 3a) and mode profiles of the dynamic magnetization (Figure 3b) were calculated by solving the coupled linearized Landau-Lifshitz equation and Maxwell’s equations in the magnetostatic approximation using O-methylated flavonoid a finite element approach [10]. As Py has negligible magnetic anisotropy, the free-spin boundary condition [28] is imposed on the Py surface. The Bloch-Floquet boundary
condition is applied along the periodic direction. Parameters used for Py are the saturation magnetization M S = 7.3 × 105 A/m, the exchange stiffness A = 1.2 × 10-11 J/m, and the gyromagnetic ratio γ = 190 GHz/T. The relative BLS intensities I of the magnon modes [11] were estimated from I ∝ | ∫ 0 a m z (x)exp(−iqx) dx|2. The dispersion curves of the more intense modes are indicated by bold solid lines while those of weaker ones by dotted lines in Figure 3a, which reveals generally good agreement between experiment and simulations. Aside from the fundamental mode branch, labeled M1 in Figure 3a (see below), the other branches are rather flat. The magnon eigenmodes of a single isolated Py stripe having the same dimensions as those of a Py stripe in Py/BARC were also calculated using the above approach. Their calculated frequencies are indicated by blue bars in Figure 3a.