Mapping out the spin-wave modes of constriction-based spin Hall nano-oscillators in weak in-plane fields

TL;DR

This study investigates spin-wave modes in constriction-based spin Hall nano-oscillators under low in-plane magnetic fields, identifying two distinct modes and demonstrating frequency doubling for high-frequency operation at low fields.

Contribution

The paper provides the first experimental and micromagnetic analysis of spin-wave modes in constriction-based SHNOs in weak in-plane fields, revealing mode hopping and localization effects.

Findings

Two distinct spin-wave modes identified: linear-like and spin-wave bullet.

Micromagnetic modeling confirms mode characteristics and localization.

Frequency doubling enables operation above 9 GHz at low magnetic fields.

Abstract

We experimentally study the auto-oscillating spin-wave modes in NiFe/$\beta-$W constriction-based spin Hall nano-oscillators as a function of bias current, in-plane applied field strength, and azimuthal field angle, in the low-field range of 40-80 mT. We observe two different spin-wave modes: i) a linear-like mode confined to the minima of the internal field near the edges of the nanoconstriction, with weak frequency dependencies on the bias current and the applied field angle, and ii) a second, lower frequency mode that has significantly higher threshold current and stronger frequency dependencies on both bias current and the external field angle. Our micromagnetic modeling qualitatively reproduces the experimental data and reveals that the second mode is a spin-wave bullet and that the SHNO mode hops between the two modes, resulting in a substantial increase in linewidths. In contrast to the linear-like mode, the bullet is localized in the middle of the constriction and shrinks with increasing bias current. Utilizing intrinsic frequency doubling at zero field angle we can reach frequencies above 9 GHz in fields as low as 40 mT, which is important for the development of low-field spintronic oscillators with applications in microwave signal generation and neuromorphic computing.