Injection dynamics in spin-wave active ring oscillator (SWARO)

Abstract

We investigated injection locking in spin-wave active ring oscillators (SWAROs) operating in the multi-mode regime. By applying external RF signals with varying frequency and power, we identified the locking behavior of individual modes and extracted the total locking ranges from spectral measurements. The results show asymmetric evolution of the lower and upper locking boundaries with drive power for the lower-frequency SWARO modes, while the highest-frequency mode exhibits nearly symmetric behavior. A maximum locking range of over 11 MHz is observed at a drive power of -10 dBm. To interpret these results, we develop an Adler-like model that captures the dependence of the locking range on drive power, showing good agreement for the higher-frequency modes. For the lowest-frequency mode, however, the model underestimates the locking range at low drive and saturates at high drive power levels, while the experimental range increases monotonically, indicating the influence of multi-mode interactions. These findings establish SWARO as a useful platform for exploring injection phenomena in spin-wave ring systems with delayed feedback and motivate the development of extended injection models that account for multi-mode dynamics.

Figures (5)

• Figure 1: (a) Transmission spectroscopy setup for detecting MSSWs propagating through the YIG film. (b) Transmission characteristics of MSSWs through the YIG delay line. The input power, $P_\text{in}$ = -40 dBm. The lower cut-off frequency of the MSSW manifold, $f_{k\text{0}}$ = 2.05291 GHz, which corresponds to an effective field $H_\text{eff}$ = 21.27 kA/m (estimated via Eq. (\ref{['eq:lower_limit_mssw_manifold']})).
• Figure 2: (a) Circuit diagram of spin-wave active ring oscillator (SWARO) with RF generator. (b) Phasor diagram for signals circulating in the driven SWARO circuit.
• Figure 3: Spectral output of free-running SWARO at $G_\text{2}$ = -8 dB. The SWARO modes are $f_\text{1}$ = 2.07998 GHz, $f_\text{2}$ = 2.08874 GHz, $f_\text{3}$ = 2.09755 GHz. The sidebands in the neighborhood of the SWARO mode are separated by a distance of 330 kHz.
• Figure 4: (a) Spectral output of SWARO at $P_\text{d} = \text{-15~dBm}$, plotted as a function of observation frequency $f$ and drive frequency $f_\text{d}$. Vertical dotted lines mark the $\pm$ 3 MHz windows around each free-running mode. Dashed horizontal lines indicate the extracted injection-locking ranges for modes 1–3. (b–d) Relative peak power difference $\Delta P$ as a function of $f_\text{d}$ for each mode, showing sharp dips that define the upper and lower locking boundaries. The corresponding bounds are highlighted by horizontal dashed lines in (a). Suppression of sidebands in neighboring modes is evident when a given mode is pulled toward the drive frequency.
• Figure 5: The experimentally estimated upper and lower limits of injection lock-in are shown for three SWARO modes $f_\text{1}$, $f_\text{2}$, and $f_\text{3}$. $f_\text{U} - \Delta f_\text{fit}$ as a function of drive power $P_\text{d}$ is plotted. $\Delta f_\text{fit}$ is prediction from the theoretical model given in Eq. \ref{['eq:adler_model']}. The orange regions denote the 95% confidence intervals of the fit.