Probing phase coupling between two spin-torque nano-oscillators with external source

TL;DR

This paper experimentally investigates phase coupling in two dipolarly coupled spin-torque vortex nano-oscillators using an external microwave field, revealing how phase-locking influences their interaction and providing insights for oscillator network design.

Contribution

It introduces an experimental method to probe phase coupling in coupled nano-oscillators using external fields and analytically links frequency pulling to dipolar and microwave interactions.

Findings

Frequency pulling observed when one oscillator is phase-locked.

Analytical model shows dipolar and microwave couplings cause frequency pulling.

Determined dipolar coupling amplitude and phase lag between oscillators.

Abstract

Phase coupling between auto-oscillators is central for achieving coherent responses such as synchronization. Here we present an experimental approach to probe it in the case of two dipolarly coupled spin-torque vortex nano-oscillators using an external microwave field. By phase-locking one oscillator to the microwave field, we observe frequency pulling on the second oscillator. From coupled Thiele equations we show analytically that this frequency pulling results from concerted actions of dipolar and microwave couplings. The analysis allows us to determine the amplitude of dipolar coupling and the phase lag of each oscillator, yielding important information for the implementation of large oscillator networks.