Orientation-dependent two-dimensional magnonic crystal modes in an ultralow-damping ferrimagnetic waveguide containing repositioned hexagonal lattices of $\mathrm{Cu}$ disks

Two-dimensional (2D) hexagonal lattices of $\mathrm{Cu}$ disks are shown to induce orientation-dependent magnonic crystal (MC) modes for propagating forward volume spin waves in a single-crystal yttrium iron garnet (YIG) film. The width and depth of the magnonic band gaps are 0.022 GHz and –15.2 dB at the frequency of 1.815 GHz. Integrating differently oriented lattices on the same YIG film and positioning them between the microwave antenna surrounded by magnon absorbers consisting of $\mathrm{Au}$ films, we clearly resolve a characteristic frequency shift of the magnonic band gap by altering the incident angle of the spin waves to the 2D MC. The shift amounts to approximately 10 MHz when the incident angle is changed between 10° and 30°. The obtained results show a good agreement with calculations using the finite integration technique and are a step toward complete band-gap investigations in YIG of ultralow spin-wave damping.

Figure 1

(a) Sketch of the 2D MC flip chipped onto the MSL in contact with the dielectric substrate. (b) Bottom view of the YIG film with the MC consisting of $\mathrm{Cu}$ disks, and the MSL in contact with the YIG film. The MC is tilted at an angle θ. (c) Cross-section sketch of the 3D model cut along the red dashed line shown in (d). (d) Enlarged view of the area near the edge of the MC and MSL from (b). (e) Bird’s eye view of (b).

Figure 2

(a) Photos of the top view of the fabricated 2D MCs with a tilting angle θ relative to the SW incident direction, like calculation models. (b) Transmission S₂₁ spectra through the 2D MC. (c) Real part of the S₂₁ spectra. Red and blue plots correspond to experimental and calculated results, respectively, with triangles indicating the spectral positions of MBGs.

Figure 3

SW incident angle θ dependence for 2D MCs: (a),(b) transmission S₂₁ spectra and (c),(d) their real part. (a),(c) show calculated and (b),(d) show measured results.

Figure 4

Process for preparing the 2D MC samples. (a) Single-crystal YIG was grown on a GGG substrate. (b) $\mathrm{Cu}$ was deposited. (c) Photoresist was patterned using a maskless aligner. (d) $\mathrm{Cu}$ uncovered by photoresist was etched. (e) Photoresist was exposed again for SW absorber fabrication. (f) $\mathrm{Au}$ was deposited. (g) Photoresist was lifted off. (h) All metal on the YIG was removed. (i) Photo of the fabricated sample with an SW incident angle θ of 5° and (j) an enlarged image of the area near the MSL and SW absorber. (k) Overview of the measurement setup. Transmission spectra were measured by the VNA while a magnetic field was applied perpendicular to the sample using an EM.

Figure 5

Transmission S₂₁ spectra measured at an SW incident angle θ of 30° (a) Measured transmission S₂₁ spectrum (red) of MC at an applied field $H_{\text{0}}^{}$ of –2335 Oe and the corresponding calculated spectrum (blue). (b) SW spectroscopy results showing SW propagation curves. (c) Detailed view of (b) highlighting the MBG shift.

Figure 6

SW incident angle dependence of the first MBG in (a) calculations and (b) experiments. Triangles and circles indicate the low-frequency edge f_low and high-frequency edge f_high, of the MBG. Stars indicate the spectral position f_MBG of the MBG.