Magnetoelectric fractals, Magnetoelectric parametric resonance and Hopf bifurcation

TL;DR

This paper investigates the complex nonlinear dynamics of magnetoelectric nanoparticles, revealing fractal structures, bifurcations, and chaos induced by electric fields and coupling strength, with implications for controlling magnetic and ferroelectric systems.

Contribution

It introduces a detailed analysis of magnetoelectric fractals, parametric resonance, and Hopf bifurcations in a coupled nanoparticle-ferroelectric system under various nonlinear regimes.

Findings

Chaotic dynamics arise at strong nonlinearity with small magnetoelectric coupling.

Bifurcations are identified as Hopf bifurcations leading to complex oscillations.

Magnetoelectric fractals are observed in the system's response.

Abstract

In the present work, we study the dynamics of a magnetic nanoparticle coupled through the magnetoelectric coupling to the ferroelectric crystal. The model of our interest is nonlinear, and we explore the problem under different limits of weak and strong linearity. By applying two electric fields with different frequencies, we control the form of the confinement potential of the ferroelectric subsystem and realize different types of dynamics. We proved that the system is more sensitive to magnetoelectric coupling in the case of double-well potential. In particular, in the case of strong nonlinearity, arbitrary small values of magnetoelectric coupling lead to chaotic dynamics. In essence, magnetoelectric coupling plays a role akin to the small perturbations destroying invariant tors according to the KAM theorem. We showed that bifurcations in the system are of Hopf's type. We observed the formation of magnetoelectric fractals in the system. In the limit of weak nonlinearity, we studied a problem of parametric nonlinear resonance and enhancement of magnetic oscillations through magnetoelectric coupling.