Controlled Magnetic Reversal in Permalloy Films Patterned into Artificial Quasicrystals

We have patterned novel Permalloy thin films with quasicrystalline Penrose $P2$ tilings and measured their dc magnetization and ferromagnetic resonance absorption. Reproducible anomalies in the hysteretic, low-field data signal a series of abrupt transitions between ordered magnetization textures, culminating in a smooth evolution into a saturated state. Micromagnetic simulations compare well to experimental dc hysteresis loops and ferromagnetic resonance spectra and indicate that systematic control of magnetic reversal and domain wall motion can be achieved via tiling design, offering a new paradigm of magnonic quasicrystals.

Figure 1

SEM image of third-generation pattern of sample III134E. Bright (dark) regions correspond to permalloy (Si substrate). Segment lengths are $d_1=810\mathrm{nm}$ and $d_2=500\mathrm{nm}$, and the width $W=85\mathrm{nm}$. An applied dc field $\mathit{H}$ makes polar angle $\varphi$ with respect to the $\widehat{x}$ axis shown (defined as $\varphi =0°$) parallel to a decahedral base.

Figure 2

(a) Horizontal dc magnetization $M_X$ normalized to saturation value $M_S$ vs applied dc magnetic field $H$ for samples III130C (8th gen.), III133C (12th gen.), and III133E (3rd gen.) at temperature $T=310\mathrm{K}$. Inset shows first knees encountered in a negative field sweep. (b) $M_X/M_S$ for sample III134E vs $H$ for $T=310$ and 5 K, compared with the simulated magnetization (black line) at $T=0\mathrm{K}$. Knees in simulated $M(H)$ are indicated by arrows.

Figure 3

(a) Simulated dc magnetization map for $H=-0.46\mathrm{kOe}$. The arrow denotes dc field direction, and the color scale indicates individual pixel polarization. Arrows indicate average direction of $\approx {10}^2$ pixels. Horizontal (0°, red) segments begin switching (to 180°, turquoise) at $H=-0.29\mathrm{kOe}$ [14]. (b) Simulated absorbed power (squared spin tipping amplitude) vs frequency $f$ for $H=-0.46\mathrm{kOe}$. A red arrow marks a peak (that first emerges for $H\approx -0.3\mathrm{kOe}$ and $f\approx 13.4\mathrm{GHz}$) that corresponds to the appearance of the first large knee in $M(H)$ in Fig. 2b and the first flipped 0° segment [14]. (c) Simulated power absorption map for $H=-0.46\mathrm{kOe}$ and $f=13.72\mathrm{GHz}$, corresponding to (a) and (b). Color scale indicates power amplitude (red is greatest). Note the correlation between locations of switched (turquoise) segments in (a) and resonant (red) segments with several orientations.

Figure 4

(a) Experimental FMR absorption of sample III129A for frequency $f=13\mathrm{GHz}$ and temperature $T=310\mathrm{K}$. Note reproducible, symmetric spectra for dc fields $|H|>1\mathrm{kOe}$; arrows mark an asymmetric mode that only occurs on one side of the field origin near $|H|=50\mathrm{Oe}$. (b) Simulated global power vs frequency $f$ in applied field $\mathit{H}=(3\mathrm{kOe})$ $\widehat{x}$ and $T=0\mathrm{K}$ for a third-generation P2T with segment dimensions shown. Data in (a) suggest that the modes for $H=3\mathrm{kOe}$ are symmetric. (c) Simulated power absorption map for $f=15.2\mathrm{GHz}$ and $\mathit{H}=(3.0\mathrm{kOe})$ $\widehat{x}$, corresponding to a symmetric mode peak [red arrow in (b)]. The color scale indicates that magnetization tipping amplitude (red is greatest) is concentrated in extended chains of segments oriented at $\varphi =\pm 72°$ and $\pm 108°$.

Figure 5

FMR frequency $f$ vs dc field $H$ for sample III129A. Numbers denote mode branches; 10 and 11 correspond to asymmetric modes such as those shown in Fig. 3c. Note that two additional branches (not numbered) appear below $f=12\mathrm{GHz}$. Associations of branches with particular dc magnetization and power maps are detailed in the Supplemental Material [14].

Figure 6

FMR absorption derivative vs applied dc magnetic field $H$ of sample III129A in negative field sweeps at $T=300\mathrm{K}$ for frequency $f=15.5\mathrm{GHz}$. Colors correspond to different angles $0°\le \varphi \le 40°$ between the decagon base and $\mathit{H}$ (see Fig. 1). Adjacent curves correspond to angular increments $\Delta \varphi =4°$. Note tenfold rotational symmetry (black and blue curves reproduce for $\Delta \varphi =36°$).