# Coupled dynamics of magnetizations in spin-Hall oscillators via spin current injection

## TL;DR

This paper investigates the coupled behavior of spin-Hall oscillators connected via spin current injection, demonstrating that synchronization modes can be controlled by current density and spatial arrangement.

## Contribution

It introduces a model for coupled STOs via spin current injection and shows how their synchronization can be tuned, expanding understanding of spintronic oscillator networks.

## Key findings

- In-phase synchronization achieved by adjusting current density.
- Antiphase synchronization observed with specific distances.
- Coupling via spin current injection enables controllable oscillator networks.

## Abstract

An array of spin torque oscillators (STOs) for practical applications such as pattern recognition was recently proposed, where several STOs are connected by a common nonmagnet. In this structure, in addition to the electric and/or magnetic interactions proposed in previous works, the STOs are spontaneously coupled to each other through the nonmagnetic connector, due to the injection of spin current. Solving the Landau-Lifshitz-Gilbert equation numerically for such system consisting of three STOs driven by the spin Hall effect, it is found that both in-phase and antiphase synchronization of the STOs can be achieved by adjusting the current density and appropriate distance between the oscillators.