Evolution of the statistical distribution in a topological defect network.

Fei Xue,Sang-Wook Cheong,Yijia Gu,Xueyun Wang,Ion Socolenco,Long-Qing Chen

doi:10.1038/srep17057

Abstract

The complex networks of numerous topological defects in hexagonal manganites are highly relevant to vastly different phenomena from the birth of our cosmos to superfluidity transition. The topological defects in hexagonal manganites form two types of domain networks: type-I without and type-II with electric self-poling. A combined phase-field simulations and experimental study shows that the frequencies of domains with N-sides, i.e. of N-gons, in a type-I network are fitted by a lognormal distribution, whereas those in type-II display a scale-free power-law distribution with exponent ∼2. A preferential attachment process that N-gons with a larger N have higher probability of coalescence is responsible for the emergence of the scale-free networks. Since the domain networks can be observed, analyzed, and manipulated at room temperature, hexagonal manganites provide a unique opportunity to explore how the statistical distribution of a topological defect network evolves with an external electric field.

Highlights

Polarization direction either along the positive (+ c) or negative (–c)[17]
The trimerization of the hexagonal REMnO3 is caused by the displacements of related oxygen atoms, which can be described by the magnitude Q and the azimuthal angle Φ 21
Where a, b, c, c′, g, g ′,and ap are the coefficients for the Landau free energy function, sQx, sQz, sPx, and sPz are coefficients for the gradient energy terms, and Ez is an external electric field along the z direction

Summary

Introduction

Polarization direction either along the positive (+ c) or negative (–c)[17]. Type-II networks result from poling by external electric fields or self-poling induced by chemical gradients, e.g. the concentration gradients of chemical defects[18]. Detailed analysis based on the simulation results demonstrates that a preferential attachment process, i.e. a process that the N-gons with a larger N have higher probability to coalesce with other N-gons during transition from type-I to type-II networks, is responsible for the appearance of the power-law behavior.

Results

Conclusion