A statistical physics approach to predicting the static and dynamic behaviour of domain walls

Ferroelectric materials are characterized by having regions (domains) with different homogeneous properties, separated by nanoscale domain walls with distinct structures and properties. The high-speed manipulation of these nanostructures is the prime factor for the development of the next generation of new and low-power functional devices for computation and communication. However, controlling these nanostructures is challenging since their behaviour is governed by the competition between their elastic energy and the varying potential landscape which allows pinning, leading to characteristic roughening and a complex dynamic response. The framework of disordered elastic systems is a powerful tool that allows us to unravel the physics of domain walls and has served to understand many of their properties. However, this approach is severely limited by its formal applicability only to univalued and smooth functions describing the domain wall position, thus inducing uncontrolled approximations. Solving domain wall dynamics and statics in more realistic systems beyond the elastic approximation is still a largely open theoretical/analytical problem. We address this problem by analysing a Ginzburg-Landau model that allows us to extend the theory of disordered elastic systems, clearly demonstrating the connection between our approach and disordered elastic systems theory. We show how through this connection it is possible to numerically mimic typical experimental protocols used to probe ferroelectric domain walls. We show how with our approach we can explain the roughening process observed in driven domain walls in thin ferroelectric films.