Observation of quantized spin wave modes in nano-constriction spin Hall nano-oscillators

Standing spin waves are crucial for advancing high-frequency spintronic devices and have been investigated using excitation methods such as cavity-based approaches, antenna-based techniques, and optical excitation methods. Unlike these conventional methods, we study quantized spin wave modes that satisfy the standing wave conditions across the nano-constriction in spin Hall nano-oscillators (SHNOs). We perform power spectral density measurements under various magnetic field conditions using Pt (6 nm)/Co89.4Gd10.6 (7 nm) SHNOs with constriction widths of 100 and 150 nm. In the SHNO with a constriction width of 150 nm, which is half of the wavelength of the spin wave, we observe two distinct spin wave modes: a propagating mode and a first-order quantized spin wave mode, the latter satisfying the standing wave confinement within the nano-constriction. Both modes are consistent with the Damon–Eshbach theory. Our findings demonstrate that geometric optimization enables the excitation of higher-order quantized modes at frequencies above the propagating mode, facilitating microwave signal generation at higher frequencies in SHNOs.