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A strategy for a scalable synchronization of an array of spin-Halloscillators (SHOs) is illustrated. In detail, we present micromagneticsimulations of two and five SHOs realized by means of couples of triangulargolden contacts on the top of a Pt/CoFeB/Ta trilayer. Results highlight thatthe synchronization occurs for the whole current region that gives rise to theexcitation of self-oscillations. This is linked to the role of themagnetodipolar coupling, which is the phenomenon driving the synchronizationwhen the distance between oscillators is not too large. Synchronization turnsout to be also robust against geometrical differences of the contacts,simulated by considering variable distances between the tips ranging from 100nmto 200nm. Besides, it entails an enlargement of the radiation pattern that canbe useful for the generation of spin-waves in magnonics applications.Simulations performed to study the effect of the interfacialDzyaloshinskii-Moriya interaction show nonreciprocity in spatial propagation ofthe synchronized spin-wave. The simplicity of the geometry and the robustnessof the achieved synchronization make this design of array of SHOs scalable fora larger number of synchronized oscillators.

Scalable synchronization of spin-Hall oscillators in out-of-plane field