Corrado C. Capriata, Bengt G. Malm Division of Electronics and Embedded Systems, KTH Royal Institute of Technology, Stockholm, Sweden Abstract Body Two-dimensional synchronized arrays of Nanoconstriction Spin-Hall nano-oscillators (NC-SHNO) 1 have several promising features like higher power, better stability, and applications in neuromorphic computing 2-3. For all these applications, the synchronization of the oscillator array is crucial. Oscillators are synchronized with the neighboring ones via dipolar and exchange coupling. In a recent study 4, NC-SHNO arrays were simulated under an injection locked condition and a one-dimensional array was investigated in 5. Our previous study 6 demonstrated how local variations of the exchange coupling can induce multiple oscillation modes in single devices and cause variability in the oscillation frequency. In this study, the aim is to expand the modeling to free-running 2x2 and 4x4 synchronized arrays using the MuMax3 7 micromagnetic simulator. Here, we illustrate results from the 2x2 array with 100 nm pitch and 50 nm width (Fig.1 inset). The exchange coupling is reduced to 15 % at a line in between the columns or rows. The presence of grains is equivalent to the coexistence of multiple lines and it is an expansion towards a real thin film representation. In this case, the exchange is randomly reduced to 10-30 % and assigned to each grain. Modifying the exchange coupling inside the array results in a minor shift of the synchronized frequency at low and medium currents while the array is much more disturbed at high currents, Fig.1. The phase and power analysis, Fig.2, shows that the shape of the oscillating volume is disturbed by the presence of grains. At high current (3 mA), the excited mode becomes propagating while at lower currents it is localized and well phase synchronized. In general, disturbed oscillators can be synchronized column-wise or diagonally, the extreme case is only one device of the array delivering output power. Similar results have been found for the 2x2 array with 200 nm pitch and 120 nm width, highlighting that the phase synchronization is not always guaranteed or can be broken by local variations in the exchange coupling strength in some operating conditions.

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6: C. C. M. Capriata, et al. "Impact of Random Grain Structure on Spin-Hall Nano-Oscillator Modal Stability", IEEE Electron Device Letters, vol. 43, no. 2, pp. 312-315, Feb. 2022.
7: J. Leliaert, et al. "Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3", AIP Advances 7, 125010 (2017). Frequency stability of 2x2 NC-SHNO array under different conditions.