Topological Localization of FMR Modes by Antidot Arrays Patterned into Permalloy Thin Films

We have observed novel broad-band FMR spectra for 25-nm-thick Permalloy films patterned with square arrays of diamond antidots with axes D$_{x }$= 1430 nm and D$_{y}$ = 860 nm. The y-axis lattice spacing was held constant at d$_{y}$ = 2000 nm, and variable x-axis lattice spacings d$_{x }$= 1730, 2000, 2267 and 2730 nm. The applied DC magnetic field H (in-plane at angle $\theta $ with respect to x-axis) spanned the hysteretic regime $\vert $H$\vert \quad \le $ 150 Oe, to $\vert $H$\vert $ = 3 kOe in the saturated regime, corresponding to mode frequencies f $\approx $ 250 MHz to 14 GHz. In spite of hysteretic evolution of domain walls in the low-field regime, highly reproducible absorption peaks appear at f $<$ 3 GHz. Static and dynamic micromagnetic simulations agree with DC magnetization and FMR dispersion curves, and show domain pinning by the antidot edges is responsible for the reproducible spectra in the hysteretic regime. For H = 1 kOe along the x-axis, we observe two localized modes: one (f = 9 GHz) in a narrow gap between the accute vertices, and another (f = 10.25 GHz) between the oblique vertices, of adjacent diamonds. For $\theta $ = 45$^{\circ}$, one mode (f = 8.7 GHz) extends along the (-1,1) direction with strong angular variation of f, and a standing mode (f = 9.87 GHz) is localized between nearly parallel edges of adjacent antidots.