Micromagnetic study of spin Hall nano-oscillator arrays and their synchronization dynamics

Abstract: Spintronics is the study of electron spins and their utilization in electronic devices. Within this field, spin-based oscillators have shown promise for mi- crowave signal generation as they can operate at high frequencies, are small in scale and are compatible with modern fabrication techniques. Among these oscillators are the spin Hall nano-oscillators (SHNOs). They are nanoscale thin-film structures driven by pure spin-current injection from a primary con- ductor into a ferromagnetic material. This process can be used to generate microwave signals through oscillations in the material’s magnetization. By constraining the current flow in the device to individual constrictions, an ar- ray arrangement of multiple oscillators can be realized. These oscillators can then be coupled together via their internal interactions to achieve mutual syn- chronization and improve their characteristics.In this work, a versatile micromagnetic modelling procedure for simulating constriction-based SHNOs and their synchronization dynamics in different ar- ray arrangements is presented. A case study of various 2x2 array geometries is conducted along with an exploration of higher-order networks of 4x4, 6x6 and 8x8 oscillators. A perturbative optimization algorithm is developed to improve excitation conditions and drive geometries into a synchronized regime. Lastly, a comparison to nonlinear auto-oscillator theory is presented to illustrate the dependence of generated signals on constriction sizes and the spacing between oscillators. Mutual synchronization between multiple oscillators is achieved and favourable geometry and excitation conditions are defined. The conducted simulations show good agreement with experimental results and illustrate the potential for future studies of SHNO characteristics through micromagnetic modelling.