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Generation and manipulation of propagating spin waves (PSWs) in magnetic multilayer systems have opened new frontiers for magnonics and spin-wave-based computing [1]. The precise control of frequency and phase of PSWs in nanoscopic CMOS compatible systems is of high importance for emerging applications such as reservoir computing and Ising machines [1,2,3]. Recently, spin-orbit torques have been shown to drive PSW auto-scillations in perpendicular magnetic anisotropy (PMA)-based nano-constriction spin Hall nano-oscillators (SHNOs) [2]. Due to their long-range propagation, the mutual synchronization of SHNO, previously demonstrated in 1D chains [4] and 2D arrays [5], can also benefit from these PSWs.
In this work [6], we report spin-wave mediated variable-phase mutual synchronization in nano-constriction SHNOs, enabling both in-phase and anti-phase synchronization of their individual auto-oscillatory modes. Using W/CoFeB/MgO trilayers with PMA, SW auto-oscillations were observed and characterized via electrical measurements and phase-resolved micro-focused Brillouin light scattering ($\mu$-BLS) microscopy. Electrical power spectral density measurements on W/CoFeB/MgO samples with 500 nm spacing reveal distinct synchronization regimes, including constructive (in-phase) and destructive (anti-phase) interference patterns. These patterns (denoted as regions II and III) can be further controlled through the applied magnetic field and direct current. In contrast, in-plane magnetized W/NiFe systems showed no phase control due to the absence of PSWs. Phase-resolved $\mu$-BLS confirms both in-phase and out-of-phase states, providing conclusive evidence of long-range SW coupling. Micromagnetic simulations corroborate the experimental results and highlight the role of SW dispersion in phase tuning. Additionally, voltage-controlled magnetic anisotropy (VCMA) is proposed for localized phase control, offering a scalable mechanism for phase-tunable SHNO arrays. These findings hold significant promise for SW-based Ising machines, neuromorphic computing, and reconfigurable logic devices [1,3,6].
References
[1] A. V. Chumak et al.; IEEE Transactions on Magnetics, 2022, 58, 1. https://doi.org/10.1109/TMAG.2022.3149664
[2] H. Fulara et al.; Science Advances, 2020, 5, eaax846. https://doi.org/10.1126/sciadv.aax8467
[3] A. Litvinenko et al.; Communications Physics, 2023, 6, 227. https://doi.org/10.1038/s42005-023-01348-0
[4] A. Kumar et al.; Nano Letters, 2023, 23, 6720. https://doi.org/10.1021/acs.nanolett.3c02036
[5] M. Zahedinejad et al.; Nature Nanotechnology, 2020, 15, 47. https://doi.org/10.1038/s41565-019-0593-9
[6] A. Kumar et al.; Nature Physics, 2025, 21, 245-252. https://doi.org/10.1038/s41567-024-02728-1
