[Paper Review] Two-dimensional mutual synchronization in spin Hall nano-oscillator arrays

Mohammad Zahedinejad, Ahmad A. Awad+6 more|arXiv (Cornell University)|Dec 23, 2018

Neural dynamics and brain function1 references4 citations

TL;DR

This paper demonstrates robust two-dimensional mutual synchronization in spin Hall nano-oscillator (SHNO) arrays of up to 64 nano-constrictions, achieving a signal quality factor (Q) of 170,000—tenfold higher than previous records—through combined exchange and dipolar coupling. The synchronization enhances microwave signal coherence and power, enabling scalable neuromorphic computing and high-frequency signal generation at room temperature with nanoscale footprint.

ABSTRACT

Spin Hall nano-oscillators (SHNOs) utilize pure spin currents to drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and sometimes mutually synchronize, in pairs or in short linear chains. Here we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 x 2 to 8 x 8 nano-constrictions, observed both electrically and using micro-Brillouin Light Scattering microscopy. The signal quality factor, $Q=f/Δf$, increases linearly with number of mutually synchronized nano-constrictions ($N$), reaching 170,000 in the largest arrays. While the microwave peak power first increases as $N^2$, it eventually levels off, indicating a non-zero relative phase shift between nano-constrictions. Our demonstration will enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and neuromorphic computing.

Motivation & Objective

• To demonstrate robust mutual synchronization in two-dimensional arrays of spin Hall nano-oscillators (SHNOs) beyond linear chains.
• To achieve high signal quality factor (Q) and increased microwave output power through collective synchronization.
• To enable scalable, room-temperature, CMOS-compatible nano-oscillator networks for neuromorphic computing and high-frequency signal generation.
• To investigate the scaling behavior of linewidth, power, and phase coherence in large SHNO arrays.

Proposed method

• Fabrication of 2x2 to 10x10 SHNO arrays using Pt/NiFe bilayers with defined widths (w) and pitches (p) ranging from 50–300 nm.
• Use of electrical measurements and micro-Brillouin Light Scattering (mBLS) microscopy to confirm mutual synchronization and map spatial mode patterns.
• Tuning of coupling strength via applied magnetic field (in-plane and out-of-plane angles) and drive current to stabilize synchronized states.
• Analysis of power spectral density (PSD) to extract linewidth, center frequency, and signal quality factor (Q = f/Δf).
• Modeling of output power scaling with array size (N), accounting for phase shifts between oscillators using a 16° relative phase shift model.
• Investigation of current density dependence (J_Sync) on array dimensions and coupling parameters to assess synchronization stability.

Experimental results

Research questions

• RQ1 Can two-dimensional arrays of SHNOs achieve robust mutual synchronization beyond one-dimensional chains?
• RQ2 How does the signal quality factor (Q) scale with the number of synchronized SHNOs in 2D arrays?
• RQ3 What limits the microwave output power increase in large arrays, and how does phase incoherence affect scaling?
• RQ4 Can the synchronization be tuned and stabilized via magnetic field and current control in 2D geometries?
• RQ5 What is the maximum achievable Q-factor and power output in a scalable, room-temperature SHNO network?

Key findings

• The signal quality factor (Q) increases linearly with the number of synchronized SHNOs (N), reaching Q = 170,000 in 8x8 arrays, an order of magnitude higher than previous records.
• The microwave peak power initially scales as N² for small arrays (N = 4–25), but eventually levels off due to non-zero relative phase shifts between distant oscillators.
• The linewidth of the synchronized signal remains below 60 kHz at ~10 GHz, enabling high-coherence microwave emission.
• Synchronization current density (J_Sync) is nearly independent of array size for fixed w and p, indicating robust scalability.
• The observed power roll-off in larger arrays (N > 36) is well explained by a 16° relative phase shift model between chains, limiting further power growth.
• The 64-element array achieves stable mutual synchronization with minimal phase incoherence, demonstrating a viable path for large-scale neuromorphic and RF applications.