Spin wave propagation in a ring-shaped magnonic waveguide

TL;DR

This study addresses frequency filtering in a ring-shaped magnonic resonator integrated with a YIG waveguide. Using spatially resolved SNS-MOKE and μ-BLS, the authors reveal that multiple transverse width modes in the ring, together with anisotropic dispersion and demagnetising-field inhomogeneities, produce sharp, tunable transmission peaks via interference rather than simple damping. The observed peak at 3.92 GHz under 74 mT and its shift to 3.70 GHz at 70 mT are consistent with KS-model iso-frequency contours and width-mode quantisation. The results demonstrate field-controlled, high-selectivity magnonic filtering in a compact ring geometry, with implications for on-chip spin-wave processing and reconfigurable phonon/magnon circuits.

Abstract

We experimentally investigate frequency-selective spin wave (SW) transmission in a micrometre-scale, ring-shaped magnonic resonator integrated with a linear Yttrium Iron Garnet (YIG) stripe. Using super-Nyquist-sampling magneto-optical Kerr effect microscopy (SNS-MOKE) and micro-focused Brillouin light scattering (μ-BLS), we probe SW dynamics in the dipolar regime under in-plane magnetisation. Spatially resolved measurements reveal a sharp transmission peak at 3.92 GHz for an external field of 74 mT, demonstrating strong frequency selectivity. Our results show that this selectivity arises from scattering and interference between multiple SW modes within the ring. These modes are governed by the anisotropic dispersion relation, transverse mode quantisation due to geometric confinement, and inhomogeneities of the effective magnetic field. In addition, the anisotropy enforces fixed group velocity directions, leading to caustic-like propagation that limits efficient out-coupling. Fourier analysis reveals discrete wavevector components consistent with quantised transverse eigenmodes. Additional μ-BLS measurements at 70 mT show a shift of the transmission peak, confirming that the filtering characteristics are tunable by external parameters.

Figures (4)

• Figure 1: (a) Topographic image of the ring-shaped magnonic waveguide. Both stripe and ring have a width of $w = 7.5\,\upmu$m; the ring has an inner radius of $r_1 = 5\,\upmu$m and an outer radius of $r_2 = 12.5\,\upmu$m. A 2 $\upmu$m-wide gold microstrip antenna (gold cuboid) excites SWs in the BV geometry ($\vb*H\perp \vb*e_x$). Rectangles A, J, and B mark regions used to assess the SW amplitude before, at, and after the ring junction. (b) Micromagnetic simulation of the $x$-component of the effective field, $\mu_0 H_{x,\mathrm{eff}}$, at $\mu_0 H = 74$ mT for longitudinal magnetisation. The green arrow indicates the external field direction. (c) Width-mode-dependent dispersion relation in the BV geometry at $\mu_0 H = 74$ mT. The mode order is labelled by $m$. Blue circles show experimental values extracted from the stripe region.
• Figure 2: (a)–(d) Kerr maps recorded by SNS-MOKE at different excitation frequencies under an external magnetic field of $\mu_0 H = 74\,$mT. Left column: absolute spin wave amplitude $R = \sqrt{X^2 + Y^2}$ from lock-in detection. Right column: spin wave phase fronts represented as $\sin(\theta_\mathrm{LI})$, where $\theta_\mathrm{LI} = \arctan(Y/X)$. A clear transmission signal beyond the ring is visible in (c). The golden area marks the excitation antenna; the green arrow indicates the external field direction. Line profiles along the red and blue dashed lines in (a) are shown in Fig. \ref{['fig:Figure3']}(a). Fourier transform data were extracted from the grey and green contours (stripe and ring) and are shown in Fig. \ref{['fig:Figure1']}(c) and Fig. \ref{['fig:Figure3']}(b), respectively.
• Figure 3: (a) Line profiles of the amplitude $R$ for different excitation frequencies, extracted along the dashed red and blue lines in Figs. \ref{['fig:Figure2']}(a)–(d). The solid red curve shows an exponential fit to the red profile before the ring section. (b) Fourier transformed (FT) data extracted from the ring region. Red dashed circles indicate the quantised eigenmodes across the ring width. The observed spin wave modes are discretised due to geometric confinement. Cyan dashed lines correspond to the analytical Kalinikos and Slavin (KS) model for $\mu_0H=74\,$mT.
• Figure 4: (a) SNS amplitudes at $\mu_0 H = 74$ mT, averaged over regions A, J, and B (cf. Fig. \ref{['fig:Figure1']}(a)) as a function of the excitation frequency. Error bars represent the standard deviation of the mean. Small red dots and dashed red lines indicate the expected values at the centre of each region, assuming exponential decay in the stripe before the ring (cf. red fits in Fig. \ref{['fig:Figure3']}(a)). (b) $\upmu$-BLS results showing the normalised amplitude of the anti-Stokes peak of the coherent SW excitations. A frequency shift of the transmission peak is observed compared to the 74 mT case.