# Controlling the synchronization properties of two dipolarly coupled vortex based spin-torque nano-oscillators by the intermediate of a third one

## TL;DR

This paper demonstrates how inserting an intermediate vortex-based spin-torque nano-oscillator can effectively control the phase-locking strength between two coupled oscillators, with potential applications in large oscillator arrays.

## Contribution

It introduces a method to tune phase-locking in coupled nano-oscillators using an intermediate oscillator, supported by micromagnetic and analytical simulations.

## Key findings

- Phase-locking strength can be controlled by adjusting the intermediate oscillator's current.
- Micromagnetic simulations confirm the tunability of phase-locking.
- Analytical models facilitate investigation of large oscillator arrays.

## Abstract

In this paper, we propose to control the strength of phase-locking between two dipolarly coupled vortex based spin-torque nano-oscillators by placing an intermediate oscillator between them. We show through micromagnetic simulations that the strength of phase-locking can be largely tuned by a slight variation of current in the intermediate oscillator. We develop simplified numerical simulations based on analytical expressions of the vortex core trajectories that will be useful for investigating large arrays of densely packed spin-torque oscillators interacting through their stray fields.