# Modulation and phase-locking in nanocontact vortex oscillators

## TL;DR

This paper investigates how nanocontact vortex oscillators can be modulated and phase-locked using external signals, revealing different behaviors in commensurate and chaotic regimes and explaining the spectral features through modulation theory.

## Contribution

It provides new insights into the phase-locking mechanisms and modulation effects in vortex oscillators, especially distinguishing between commensurate and chaotic dynamics.

## Key findings

- Phase-locking occurs in commensurate regimes but is impeded by chaos.
- Rich spectral features arise from modulation between external, gyration, and reversal frequencies.
- External signals can synchronize vortex modes, demonstrating controllable dynamics.

## Abstract

We have conducted experiments to probe how the dynamics of nanocontact vortex oscillators can be modulated by an external signal. We explore the phase-locking properties in both the commensurate and chaotic regimes, where chaos appears to impede phase-locking while a more standard behavior is seen in the commensurate phase. These different regimes correspond to how the periodicity of the vortex core reversal relates to the frequency of core gyration around the nanocontact; a commensurate phase appears when the reversal rate is an integer fraction of the gyration frequency, while a chaotic state appears when this ratio is irrational. External modulation where the power spectral density exhibits rich features, appears due to the modulation between the external source frequency, gyration frequency, and core reversal frequency. We explain these features with first- or second-order modulation between the three frequencies. Phase-locking is also visible between the external source frequency and internal vortex modes (gyration and core reversal modes).