FMR Study of Quasicrystalline Arrays of Antidots in Permalloy Films

We have used electron beam lithography to pattern permalloy films of thickness 25 nm with \textbf{\textit{quasiperiodic, }}five-fold rotationally symmetric Penrose tilings of antidots (AD). Two samples were fabricated with AD kites and darts having long (d$_{\mathrm{1}})$ and short edges (d$_{\mathrm{2}})$ equal to 1620 nm or 810 nm, and 1000 nm or 500 nm, respectively, with fixed Py line width of 100 nm. We have studied broad-band (RF frequencies 10 MHz \textless f \textless 15 GHz, DC applied fields -3.5 kOe \textless H \textless 3.5 kOe) and narrow-band FMR (f $=$ 9.7 GHz, 0 \textless H \textless 8 kOe) for various angles between the in-plane DC field and the array edge. BBFMR spectra for f \textless 4 GHz exhibit rich, highly reproducible structure, in spite of low-field (\textbar H\textbar \textless 500 Oe) hysteresis, including a \textbf{\textit{frequency-independent}} (implying localized) mode near H $=$ 0 Oe. Both low-field FMR data and dynamic simulations exhibit two-fold rotational symmetry instead of the expected five-fold symmetry, which we attribute to an unsaturated state. Higher-field (\textbar H\textbar \textless 12 kOe) simulations exhibit ten-fold rotational symmetry, which we attribute to the symmetry of the demagnetization fields.