Understanding domain walls as a model disordered elastic system

Domain walls provide a useful model system for the static and dynamic behavior of an elastic interface in a disordered medium. In such systems, the equilibrium static configuration is governed by the competition between elasticity, which tends to flatten the interface to minimize the energy costs, and disorder, which promotes wandering among pinning sites in the randomly varying potential energy landscape, leading to a characteristic roughness configuration. When driven by an external force, such an interface presents a complex dynamic response, with a thermally-activated, non-linear creep motion for subcritical forces, followed by a transition towards depinning, and finally linear flow at high driving forces. This statistical physics approach provides a general framework in which the behavior of systems as diverse as propagating fractures, wetting lines, burning fronts or surface growth can be described.

Ferroelectric domain walls as pinned elastic interfaces: (a) Progressive domain growth at the edge of a metallic electrode patterned on a thin ferroelectric film film. Schematic representation of (b) the complex dynamic response (c) self-affine roughness scaling in such systems.

Although the equilibrium behavior of such interfaces is well understood, relatively little is known about out-of-equilibrium phenomena, such as ageing and thermal effects, or the role of a potentially complex internal structure. Studying the thermal evolution of the domain walls, we have shown a long term system memory of the initial configuration, governed by the disorder landscape. We have also demonstrated the individual strong pinning sites lead to a breakdown of the simple mono-affine roughness scaling of the domain wall configuration. At present, we are exploring environmental effects on the switching and growth of ferroelectric domains under a scanned probe microscopy tip.

In the presence of strong local variations of disorder, monoaffine roughness scaling breaks down, leading to locally higher displacements and roughness. Left: PFM image showing two ferroelectric domain walls. Right: local slopes along the walls.