Magnetoinductive breathers in magnetic metamaterials

TL;DR

This paper investigates the existence, stability, and magnetic response effects of discrete breathers in one- and two-dimensional magnetic metamaterials with split-ring resonators, revealing stable localized excitations and their influence on magnetic properties.

Contribution

It demonstrates the existence of stable discrete breathers in both Hamiltonian and dissipative magnetic metamaterials across different dimensions and anisotropies, extending prior knowledge of localized excitations.

Findings

Stable breathers exist in 1D and 2D MMs.

Breathers can locally alter magnetic response from paramagnetic to diamagnetic.

Magnetic response can become negative near SRR resonance frequency.

Abstract

The existence and stability of discrete breathers (DBs) in one-dimensional and two-dimensional magnetic metamaterials (MMs), which consist of periodic arrangem ents (arrays) of split-ring resonators (SRRs), is investigated numerically. We consider different configurations of the SRR arrays, which are related to the relative orientation of the SRRs in the MM, both in one and two spatial dimensions. In the latter case we also consider anisotropic MMs. Using standard numerical methods we construct several types of linearly stable breather excitations both in Hamiltonian and dissipative MMs (dissipative breathers). The study of stability in both cases is performed using standard Floquet analysi s. In both cases we found that the increase of dimensionality from one to two spatial dimensions does not destroy the DBs, which may also exist in the case of moderate anisotropy (in two dimensions). In dissipative MMs, the dynamics is governed by a power balance between the mainly Ohmic dissipation and driving by an alternating magnetic field. In that case it is demonstrated that DB excitation locally alters the magnetic response of MMs from paramagnetic to diamagnetic. Moreover, when the frequency of the applied field approaches the SRR resonance frequency, the magnetic response of the MM in the region of the DB excitation may even become negative (extreme diamagnetic).