Spin Hall nano-oscillators (SHNOs) have shown applications in unconventional computing schemes and broadband frequency generation in the presence of applied external magnetic field. However, under external magnetic field free conditions, the oscillation characteristics of nanoconstriction-based SHNOs exhibits a notable reliance on the effective field, which can be adjusted by varying the constriction width. In this study, we explore how the width of the nanoconstriction affects the magnetization dynamics in field free SHNOs assisted by anisotropy. In uniaxial anisotropy-based field free SHNOs, either the anisotropy field $\left(B_{\mathrm{anis}}\right)$ or the demagnetization field $\left(B_{\mathrm{demag}}\right)$ dominates the magnetization dynamics depending on the constriction width. Our findings reveal distinct auto-oscillation characteristics in narrower constrictions with 20- and 30-nm constriction width compared to their wider counterpart with 100-nm width. The observed frequency shift variations with input current ($I_{\mathrm{dc}}$) and constriction widths stem from the inherent nonlinearity of the system. The interplay between the $B_{\mathrm{demag}}$ and $B_{\mathrm{anis}}$, controlled by constriction width, yields rich dynamics, and offers control over frequency and amplitude of auto-oscillations, and the threshold current needed for auto-oscillations. Notably, the spatial configuration of spin-wave wells within the constriction undergoes transformations in response to changes in both constriction width and anisotropy. The findings highlight the significant influence of competing internal fields at the constriction on the field free auto-oscillations of SHNOs, with the impact intensifying as the constriction width is varied.

• Received 19 August 2023
• Revised 6 March 2024
• Accepted 7 March 2024

DOI:https://doi.org/10.1103/PhysRevB.109.134421