Reprogrammability and Scalability of Magnonic Fibonacci Quasicrystals

Magnonic crystals are systems that can be used to design and tune the dynamic properties of magnetization. Here, we focus on one-dimensional Fibonacci magnonic quasicrystals. We confirm the existence of collective spin waves propagating through the structure as well as dispersionless modes; the reprogammability of the resonance frequencies, dependent on the magnetization order; and dynamic spin-wave interactions. With the fundamental understanding of these properties, we lay a foundation for the scalable and advanced design of spin-wave band structures for spintronic, microwave, and magnonic applications.

Figure 1

A sketch of the $S_6$ Fibonacci structure consisting of Py nanowires of different widths separated by air gaps. The static magnetic field is applied along the nanowires.

Figure 2

The normalized MOKE hysteresis loop for the Fibonacci array with two values of stripe widths and the external field applied along the length of the NWs. The red dashed curve represents the first derivative of the lower branch of the loop with respect to the field. The arrows indicate the field range of the parallel (FO) and antiparallel (AFO) alignment of the wider and narrower NW magnetizations. Depending on the field history for an array consisting of 700- and 1400-nm or 350- and 700-nm NWs at $H=+5$ mT or $H=+12.5$ mT, respectively, either an FO or an AFO magnetization orientation is present in the adjacent NWs.

Figure 3

The VNA-FMR spectra of the Fibonacci structures with two sets of wire widths. The field ranges in which ferromagnetic and antiferromagnetic orders are present after saturation in negative field values are separated by the vertical dashed lines and marked by FO and AFO, respectively.

Figure 4

The calculated band structure shown as frequency vs IDOS for structures with $W_N=700$ nm and $W_W=1400$ nm, with ferromagnetic and antiferromagnetic order at $H_{\mathrm{app}}=5$ and $-5$ mT, respectively. The violet (pink) areas represent band gaps for FO (AFO). The dashed green lines mark the frequencies for which the STXM measurements are carried out.

Figure 5

(a) Experimental SW frequencies from BLS data vs wave vector $k$ compared with the band structure obtained from numerical calculations using the finite-element method (FEM, solid lines) shown as frequency vs IDOS for $H_{\mathrm{app}}=+12.5$ mT for structures with $W_N=350$ nm and $W_W=700$ nm in ferromagnetic and antiferromagnetic order. The violet (pink) regions indicate the magnonic band gaps for FO (AFO) from the numerical calculations. (b) Typical experimental BLS spectra measured for $k=0.41\times {10}^7$ rad/m.

Figure 6

(a) Amplitude-phase images from STXM measurements for selected excitation frequencies at 5 mT and $-5$ mT for FO and AFO, respectively, for structures with $W_N=700$ nm and $W_W=1400$ nm. The position of the CPW is marked with transparent gray rectangles and the gaps between the stripes with the dashed white lines. On the right side of each STXM image, experimental profiles of the excitations (blue bars) are plotted and compared with calculated ones (red solid lines). (b) The color codes for the SW amplitude (brightness) and phase (color). (c) A static image of the Fibonacci structure (light gray) with the visible parts of the CPW (dark gray) near the center of the image (the signal line) and at the top and bottom edges of the image (the ground lines).