# Global formation of topological defects in the multiferroic hexagonal manganites

## TL;DR

This study investigates the formation of topological defects during phase transitions in multiferroic hexagonal manganites, combining theoretical development of a global Kibble-Zurek framework with experimental verification of defect scaling behaviors.

## Contribution

It introduces a comprehensive Kibble-Zurek model accounting for fluctuation regime transitions and experimentally confirms its predictions in multiferroic manganites.

## Key findings

- Reversal of defect scaling in the intermediate fluctuation regime
- Experimental validation of the global Kibble-Zurek picture
- Identification of intrinsic defect formation features beyond original theory

## Abstract

The spontaneous transformations associated with symmetry-breaking phase transitions generate domain structures and defects that may be topological in nature. The formation of these defects can be described according to the Kibble-Zurek mechanism, which provides a generic relation that applies from cosmological to interatomic lengthscales. Its verification is challenging, however, in particular at the cosmological scale where experiments are impractical. While it has been demonstrated for selected condensed-matter systems, major questions remain regarding e.g. its degree of universality. Here we develop a global Kibble-Zurek picture from the condensed-matter level. We show theoretically that a transition between two fluctuation regimes (Ginzburg and mean-field) can lead to an intermediate region with reversed scaling, and we verify experimentally this behavior for the structural transition in the series of multiferroic hexagonal manganites. Trends across the series allow us to identify additional intrinsic features of the defect formation beyond the original Kibble-Zurek paradigm.