Universal Scaling Laws

Around the year 2000 it was realized that the most common mechanisms driving magnetic and ferroelectric order tend to be mutually exclusive. One of the consequences of this "exclusion principle" is that multiferroics are an inherent source for unusual types of ferroelectric order. In many cases, the electric polarization is not the primary order parameter promoting the emergence of a spontaneous polarization. Instead, magnetic or distortive transitions induce the ferroelectric state so that it is improper. In the hexagonal manganites h-RMnO₃ (R = Sc, Y, Dy-Lu) ferroelectricity is driven by a lattice trimerization. The emergence of the trimerization-polarization domains is accompanied by a change of topological properties: Throughout the sample all six domain states meet in a "vortex line". This line represents a one-dimensional defects that is topologically protected -- It cannot be removed from the sample by domain wall movement or electric-field poling.

Enlarged view: Areal vortex-core density as a function of cooling rate with corresponding domain wall images [1] — Areal vortex-core density as a function of cooling rate with corresponding domain wall images [1]

We showed that the formation of the vortex defects follows the same laws applied earlier by Kibble and Zurek for describing the formation of topological defects ("strings") in the early universe during cooling. After this exciting discovery we are now expanding the investigation on universal scaling laws in condensed-matter systems in various directions. Some of these are:

Topological defect formation at parameters beyond the range of Kibble-Zurek scaling. This may allow us to make predictions about defect formation in an ultra-rapidly cooling universe.
Identifying new types of (multi)ferroics with topological phase transitions. The domains and defects related to their formation will be analyzed.
Investigation of the physical properties at the vortex defects.
Monte-Carlo simulations of the domain formation in improper and topological phase transitions.

Reference

S. M. Griffin, M. Lilienblum, K. Delaney, Y. Kumagai, M. Fiebig, N. A. Spaldin: Scaling Behaviour and Beyond Equilibrium in the Hexagonal Manganites, Physical Review X 2, 041022 (2012)