L.A. Tsyrulnikova1, A.R. Safin2

1,2 National Research University “Moscow Power Engineering Institute” (Moscow, Russia)

1,2 Kotelnikov Institute of Radioengineering and Electronics of RAS (Moscow, Russia

1 mila.tsyrulnikova@gmail.com; 2 arsafin@gmail.com

The hardware implementation of neuromorphic computing systems is a relevant task in recent years [1]. Currently, there are many ways to construct neuromorphic networks: optical networks [2], semiconductor-based networks [3], networks of nanomechanical oscillators [4], superconducting networks [5], and others. However, the proposed solutions for building large neuromorphic networks only partially meet the requirements of modern electronic technologies, such as integration with existing technologies, low power consumption, operation at room temperature, nanoscale, high speed, and scalability.

Spintronic oscillators (SO) are attractive for the hardware implementation of neuromorphic computing systems, as networks of synchronized SOs meet the above requirements [6-8]. The task of achieving stable synchronization of oscillators is crucial when implementing large neuromorphic networks, and synchronization of SOs arises due to several coupling mechanisms or their combinations: magnetodipole coupling [9], spin-wave coupling [10], coupling by alternating electric current [11], and coupling by pure spin current [12]. The aim of this work is to investigate two mechanisms of SO synchronization: coupling by alternating electric current and coupling by pure spin current. Coupling coefficients were obtained and synchronization bands for these coupling mechanisms of SO were calculated.

The coupling mechanisms of pure spin current and alternating electric current are non-local, which is advantageous for constructing large spintronic oscillator networks, as the coupling strength between SO pairs will be constant and uniform at different distances. The coupling by alternating electric current increases with the increase in the strength of the direct current passing through the normal metal (NM), which can provide a relatively high coupling coefficient and, consequently, a wide synchronization band (hundreds of MHz). The coupling by pure spin current does not depend on the current passing through the SO but is determined by the properties of the ferromagnetic material and the NM, making it independent of external factors while maintaining a sufficiently high coupling coefficient. However, coupling by alternating current is preferable, as a high coupling coefficient for all oscillators in the network, on the order of hundreds of MHz, can be achieved with relatively low current values (50-200 μA), comparable to the magnetodipole coupling coefficient, which is high only at small distances between SOs (a < 200 nm).

Tsyrulnikova L.A., Safin A.R. Mutual synchronization of spintronic oscillators by spin-polarized current and pure spin current. Radiotekh-nika. 2025. V. 89. № 1. P. 141−148. DOI: https://doi.org/10.18127/j00338486-202501-13 (In Russian)

1. Soman S., Jayadeva, Suri M. Big Data Analytics. Big Data Analytics. 2016. Т. 1. Р. 15. DOI: 10.1186/s41044-016-0013-1.
2. McMahon P. L., Marandi A., Haribara Y., Hamerly R., Langrock C., Tamate S., Inagaki T., Takesue H., Utsunomiya S., Aihara K., Byer R. L., Fejer M. M., Mabuchi H., Yamamoto Y. A fully programmable 100-spin coherent Ising machine with all-to-all connections. Science. 2016. Nov 4. V. 354, № 6312. P. 614–617. DOI: 10.1126/science.aah5178. Epub 2016 Oct 20. PMID: 27811274.
3. Kumar S., Strachan J.P., Williams R.S. Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing. Nature. 2017.
   V. 548. № 7667. DOI: 10.1038/nature23307.
4. Shim S.B., Imboden M., Mohanty P. Synchronized Oscillation in Coupled Nanomechanical Oscillators. Science. 2007. V. 316. P. 95–99. DOI: 10.1126/science.1137307.
5. Galin M.A., Borodianskyi E.A., Kurin V.V., Shereshevskiy I.A., Vdovicheva N.K., Krasnov V.M., Klushin A.M. Synchronization of Large Josephson-Junction Arrays by Traveling Electromagnetic Waves. Physical Review Applied. 2018. V. 9. № 5.
   DOI: 10.1103/physrevapplied.9.054032.
6. Yogendra K., Fan D., Jung B., Roy K. Magnetic Pattern Recognition Using Injection-Locked Spin-Torque Nano-Oscillators. IEEE Transactions on Electron Devices. 2016. V. 63. P. 1674–1680.
7. Ranjbar M., Dürrenfeld P., Haidar M., Iacocca E., Balinskiy M., Le T.Q., Fazlali M., Houshang A., Awad A.A., Dumas R.K., Åkerman J. CoFeB-Based Spin Hall Nano-Oscillators. IEEE Magnetics Letters. 2014. V. 5.
8. Zahedinejad M., Awad A. A., Muralidhar S., Khymyn R., Fulara H., Mazraati H., Dvornik M., Åkerman J. Two-Dimensional Mutually Synchronized Spin Hall Nano-Oscillator Arrays for Neuromorphic Computing. Nature Nanotechnology. 2020. V. 15. № 1. Р. 47–52. DOI: 10.1038/s41565-019-0593-9.
9. Belanovsky A.D., Locatelli N., Skirdkov P.N., Abreu Araujo F., Grollier J., Zvezdin K.A., Cros V., Zvezdin A.K. Phase Locking Dynamics of Dipolarly Coupled Vortex-Based Spin Transfer Oscillators. Physical Review B. 2012. V. 85. № 10. Р. 100409. /
   DOI: 10.1103/PhysRevB.85.100409.
10. Kaka S., Pufall M.R., Rippard W.H., Silva T.J., Russek S.E., Katine J.A. Mutual Phase-Locking of Microwave Spin Torque Nano-Oscillators. Nature. 2005. V. 437. № 7057. Р. 389–392. DOI: 10.1038/nature04035.
11. Taniguchi T. Synchronization of Spin Torque Oscillators through Spin Hall Magnetoresistance. IEEE Transactions on Magnetics. 2017. V. 53. № 11. Р. 1–7. Art. num. 3400907. DOI: 10.1109/TMAG.2017.2704588.
12. Taniguchi T. Phase dynamics of oscillating magnetizations coupled via spin pumping. Physical Review B. 2018. V. 97. P. 184408. DOI: 10.1103/PhysRevB.97.184408.
13. Slavin A., Tiberkevich V. Excitation of Spin Waves by Spin-Polarized Current in Magnetic Nano-Structures. IEEE Transactions on Magnetics. 2008. V. 44. P. 1916–1927. DOI: 10.1109/TMAG.2008.924537.
14. Slavin A., Tiberkevich V. Nonlinear Auto-Oscillator Theory of Microwave Generation by Spin-Polarized Current. IEEE Tran-sactions on Magnetics. 2009. V. 45. № 4. P. 1875–1918. DOI:10.1109/TMAG.2008.2009935