Magnetoelectric fractals, Magnetoelectric parametric resonance and Hopf bifurcation

Abstract

In the present work, we study the dynamics of the magnetic nanodisc coupled through a magnetoelectric coupling to a ferroelectric crystal. The model of our interest is nonlinear, and we explore the problem under different limits of weak and strong non-linearity. By applying two electric fields with different frequencies, we control the form of the confinement potential of a 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 non-linearity, arbitrary small values of magnetoelectric coupling lead to chaotic dynamics. In essence, magnetoelectric coupling plays a role akin to the small perturbations destroying invariant tori 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 non-linearity, we studied a problem of parametric nonlinear resonance and enhancement of magnetic oscillations through magnetoelectric coupling.