# Tunable, synchronized frequency down-conversion in magnetic lattices with defects

## TL;DR

This paper demonstrates tunable, synchronized frequency down-conversion in a nonlinear magnetic lattice with defects, enabling energy transfer between multiple frequencies and phase control through localized and extended vibrational modes.

## Contribution

It introduces a mechanical lattice system with defect-induced localized modes that nonlinearly couple to extended modes, enabling autonomous and tunable frequency conversion and synchronization.

## Key findings

- Localized vibrational modes can be nonlinearly coupled to extended modes.
- The system achieves tunable energy transfer between arbitrary frequencies.
- Defect synchronization enables phase control of energy transfer.

## Abstract

We study frequency conversion in nonlinear mechanical lattices, focusing on a chain of magnets as a model system. We show that by inserting mass defects at suitable locations, we can introduce localized vibrational modes that nonlinearly couple to extended lattice modes. The nonlinear interaction introduces an energy transfer from the high-frequency localized modes to a low-frequency extended mode. This system is capable of autonomously converting energy between highly tunable input and output frequencies, which need not be related by integer harmonic or subharmonic ratios. It is also capable of obtaining energy from multiple sources at different frequencies with a tunable output phase, due to the defect synchronization provided by the extended mode. Our lattice is a purely mechanical analog of an opto-mechanical system, where the localized modes play the role of the electromagnetic field, and the extended mode plays the role of the mechanical degree of freedom.

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Source: https://tomesphere.com/paper/1704.07226