High-density arrays of mutually coupled nanoscale spintronic oscillators hold potential for mimicking nonlinear oscillatory neural networks, enabling efficient neuromorphic computing. Spin-torque nano-oscillators (STNOs) have been used in proof-of-concept vowel recognition, but current-based tunability is energy-inefficient and unsuitable for scaling. Spin Hall nano-oscillators (SHNOs) offer an energy-efficient alternative due to their ease of fabrication, flexible geometry, reduced power dissipation, and CMOS compatibility. Nano-constriction-based SHNOs exhibit robust mutual synchronization in arrays, but individual frequency control within the network remains a major challenge. Voltage-controlled magnetic anisotropy (VCMA) presents a highly energy-efficient approach for magnetization switching, offering significantly lower energy dissipation than current control. This research investigates the use of VCMA to achieve strong individual control of the threshold current and auto-oscillation frequency of nano-constriction-based SHNOs.

Prior work has demonstrated the potential of spintronic oscillators for neuromorphic computing, with STNOs showing promise but limitations in scalability and energy efficiency. SHNOs, particularly nano-constriction based designs, have emerged as a more efficient alternative, demonstrating mutual synchronization in both linear chains and 2D arrays. However, the ability to individually control the frequency of each SHNO in a large network is crucial for advanced neuromorphic tasks, and VCMA offers a potential solution due to its energy efficiency in magnetization switching applications. Previous studies have explored VCMA in various magnetic materials and its effects on magnetic anisotropy and damping, but its application to achieve giant damping modulation in SHNOs has not been fully explored.

The study utilized electrically gated W(5 nm)/(Co₀.₇₅Fe₀.₂₅)₇₅B₂₅(1.7 nm)/MgO(2 nm)/AlOx(2 nm) nano-constriction SHNOs. These devices were fabricated using a combination of sputtering, electron beam lithography, Argon ion beam etching, and lift-off techniques to create a structure with a gate electrode positioned above the nano-constriction. Microwave measurements were performed using a custom-built probe station to assess auto-oscillation power spectral density (PSD) under various gate voltages and drive currents. Spin-torque ferromagnetic resonance (ST-FMR) measurements were used to determine effective magnetization and damping constant at different gate voltages and microwave frequencies. Micromagnetic simulations employing the mumax3 software package were conducted to study the spatial distribution of the excited spin-wave mode within the nano-constriction under different gate voltages. The Kittel equation was used to extract effective magnetization from ST-FMR data. The damping parameter was calculated from the decay rate of the excited spin wave mode.

The study observed a significant voltage-controlled modulation of SHNO characteristics. A 22% modulation in threshold current (5.5%/V) and a 50 MHz frequency tunability (12 MHz/V) were achieved by varying the gate voltage. The most striking finding was a giant 42% modulation of the effective damping constant over a four-volt range (10.5%/V). ST-FMR measurements revealed a moderate voltage-controlled magnetic anisotropy (VCMA) effect, resulting in a less than 1% change in perpendicular magnetic anisotropy (PMA). Micromagnetic simulations demonstrated that the giant damping modulation arises from the VCMA's influence on the spin-wave mode volume within the nano-constriction. Negative gate voltages increased PMA, leading to delocalization of the mode and increased damping due to increased emission losses. Positive gate voltages resulted in stronger mode localization and reduced damping, mainly due to intrinsic losses. The simulations accurately predicted the experimentally observed effective damping modulation, confirming the proposed mechanism.

The findings demonstrate a significant advancement in the control of SHNOs. The giant voltage-controlled modulation of the effective damping constant allows for precise and energy-efficient control of the oscillator's threshold current. This is highly relevant for the development of large-scale SHNO arrays for neuromorphic computing. The observed frequency tunability is also sufficient for various neuromorphic applications. The small VCMA effect, coupled with the giant damping change, highlights the importance of the nano-constriction geometry and its effect on the excited spin-wave mode. The agreement between experimental results and micromagnetic simulations validates the understanding of the underlying mechanism.

This research demonstrated a giant voltage-controlled modulation of the effective damping and frequency of nano-constriction SHNOs, enabled by VCMA. This allows for energy-efficient control of individual oscillators in large arrays. Future work could explore further optimization of device geometry to enhance the damping modulation and investigate the use of ionic mechanisms for potentially even stronger and non-volatile control of the damping.

The study focused on a specific SHNO design and material stack. While the results demonstrate a significant advance, the generalizability to other SHNO designs and materials requires further investigation. The ST-FMR measurements were limited to positive gate voltages below 1V due to gate breakdown. Additionally, the precise contribution of intrinsic damping changes under gate voltage requires further exploration.