# Mutual synchronization of constriction-based spin Hall nano-oscillators in weak in-plane fields

## TL;DR

This study investigates the mutual synchronization of constriction-based spin Hall nano-oscillators under weak in-plane magnetic fields, revealing the role of nano-constriction spacing, angular dependence, and magneto-dipolar coupling in synchronization mechanisms.

## Contribution

It provides new insights into the synchronization behavior of SHNOs at weak fields, highlighting the influence of nano-constriction spacing and magneto-dipolar interactions.

## Key findings

- Synchronization occurs below a critical angle, higher for shorter spacing.
- Second harmonic spin waves are involved in synchronization.
- Magneto-dipolar coupling explains angular dependence of synchronization.

## Abstract

We study mutual synchronization in double nanoconstriction-based spin Hall nano-oscillators (SHNOs) under weak in-plane fields ($\mu_0H_\mathrm{IP}$ = 30-40 mT) and also investigate its angular dependence. We compare SHNOs with different nano-constriction 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 magneto-dipolar coupling between neighboring SHNOs.