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Sci Rep. 2015 Nov 20;5:17057. doi: 10.1038/srep17057.

Evolution of the statistical distribution in a topological defect network.

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Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA.


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.

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