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 maxi- mum 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 mono- tonically, 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.