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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Topological defects in hexagonal manganites are crucial for understanding diverse phenomena, from cosmology to superfluidity.
  • These defects form two distinct domain network types: type-I (no electric self-poling) and type-II (with electric self-poling).

Purpose of the Study:

  • To investigate the statistical distributions of domain networks in hexagonal manganites.
  • To elucidate the mechanisms governing the formation of these network structures.
  • To explore the potential for manipulating these networks with external electric fields.

Main Methods:

  • Combined phase-field simulations and experimental studies were employed.
  • Analysis focused on the frequency distribution of N-sided domains (N-gons) within the networks.

Main Results:

  • Type-I domain networks exhibit a lognormal distribution of N-gon frequencies.
  • Type-II domain networks display a scale-free power-law distribution with an exponent of approximately 2.
  • A preferential attachment process, where larger N-gons have a higher coalescence probability, drives the scale-free nature of type-II networks.

Conclusions:

  • Hexagonal manganites offer a unique platform for studying topological defect network evolution at room temperature.
  • The distinct statistical properties of type-I and type-II networks are linked to their formation mechanisms.
  • External electric fields can potentially be used to control and modify the statistical distribution of these domain networks.