Magnetic chimeras in voltage-driven nano-oscillators

Abstract

The emergence of spatiotemporal coherence is ubiquitous in nature. Intriguingly, in systems with uniform energy injection and dissipation mechanisms, coherent regions can be neighboring zones with non-coherent (e.g., chaotic or quasi-periodic) motions, giving rise to the so-called chimera states. This article studies the chimeric self-organization of magnetic nano-oscillators coupled with dipolar fields under energy losses and injection. The chimera states arises from an alternating voltage that, in the presence of insulating barriers, modulates the magnetic anisotropy fields, an effect known as voltage-controlled magnetic anisotropy. This field allows the efficient manipulation of the magnetization because it can produce magnetic switching and resonances, among other dynamic responses, while avoiding the Joule heating. In the classical limit, magnetization dynamics are governed by the Landau–Lifshitz equation. We consider three setups composed of N={4,6,10} interacting oscillators, each one of them regarded as a macrospin that moves rigidly. Our main results are Small magnetic chimeras, Weak magnetic chimeras, and a meta-chaos state. Chimera states are composed of a synchronized and a chaotic group of oscillators, both sets typically having hundreds of units; on the other hand, small chimeras are composed of a few – usually around five – oscillators dividing into coherent and non-coherent regions. A weak chimera has two or more sets of coherently oscillating units, but the groups possess different frequencies. Finally, the meta-chaos state is a chaotic transient. Beyond the previous zoology, fully synchronized states are also present, as the bifurcation diagram reveals.