FMR Study of an Eightfold Artificial Quasicrystal*

We have performed DC magnetization, and broad-band and narrowband FMR measurements on eightfold-rotationally-symmetric artificial quasicrystals. Permalloy films of thickness 25 nm were patterned with 1$^{\mathrm{st}}$ and 4$^{\mathrm{th}}$ generation \textbf{\textit{Ammann tilings}} (AT) [1] using standard electron beam lithography. The AT can be viewed as an antidot lattice of squares and rhombi whose edges are film segments of length 1000 nm (7 $\mu $m), and width 130 nm (910 nm), respectively, in 4$^{\mathrm{th}}$ (1$^{\mathrm{st}})$ generation AT. In spite of clear DC magnetization hysteresis in the low-field regime, we observed remarkably sharp and reproducible FMR spectra (including both the low-field-reversal and the saturated regimes) that strongly reflected the geometry of the AT. The applied DC field \textbf{H} could be oriented in-plane at an angle $\varphi $ with respect to a AT reference axis. Our FMR spectra exhibit the expected eight-fold symmetry of the AT for experimentally accessible RF frequencies (7 to 18.5 GHz). Static and dynamic micromagnetic simulations were in good agreement with our experimental FMR spectra. \\[4pt] [1] B. Gr\"{u}nbaum and G. C. Shephard, \textit{Tilings and Patterns} (Freemann, New York, 1986).