Mutual Synchronization Of Nanoconstriction-Based Spin Hall Nano-Oscillators Through Evanescent And Propagating Spin Waves

We perform a micromagnetic study of the synchronization dynamics in nanoconstriction-based spin Hall nanooscillator (SHNO) arrays. The simulation reveals that efficient synchronization in this kind of system is possible, and indicates that the synchronization is mediated by a combination of linear coupling through the overlap of localized modes and parametric coupling through propagating spin waves which are excited by the second harmonic oscillation in the SHNOs. Due to the anisotropic spinwave dispersion in the studied system, the synchronization properties decisively depend on the geometrical alignment of the SHNO array with respect to the external field. We find that, by utilizing the directional spin wave emission and correspondingly optimizing the alignment of the SHNO array, the synchronization is enhanced with a significant increase of the phase-locking bandwidth.