  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.
