Mutual Synchronization of Constriction-Based Spin Hall Nano-Oscillators in Weak In-Plane Magnetic Fields

Abstract

We study mutual synchronization in double nanoconstriction-based spin Hall nano-oscillators (SHNOs) under weak in-plane magnetic fields (${\ensuremath{\mu}}_{0}{H}_{\mathrm{IP}}=30--40$ mT) and also investigate its angular dependence. We compare SHNOs with different nanoconstriction spacings of 300 and 900 nm. In all devices, mutual synchronization occurs below a certain critical angle, which is higher for the 300 nm spacing than for the 900 nm spacing, reflecting the stronger coupling at shorter distances. Alongside the synchronization, we observe a strong second harmonic consistent with predictions that the synchronization may be mediated by the propagation of second-harmonic spin waves. However, although Brillouin light scattering microscopy confirms the synchronization, it fails to detect any related increase of the second harmonic. Micromagnetic simulations instead explain the angular-dependent synchronization as predominantly due to magnetodipolar coupling between neighboring SHNOs.