Ferroic materials (ferromagnets, ferroelectrics, ferroelastics and ferrotoroidics) are functional materials par excellence, and have been the object of an intense research activity for decades. They spontaneously exhibit domain structures. Regions of uniform order are called domains, and the boundaries between adjacent domains, are called domain walls.

Ferroelectric and ferroelastic domain walls are extremely narrow, frequently with thicknesses approaching the unit cell level, and can therefore be considered as genuine 2D objects. When dimensional confinement is considered in combination with now widespread observations of emergent functional properties at domain walls, such as polarity in non-polar systems or greatly enhanced electrical conductivity in otherwise insulating materials, it becomes clear that domain walls represent new and exciting objects in matter. Moreover, as domain walls can be created, eliminated or moved by an external field (e.g. an electric field), the 2D functionality they offer is not fixed but rather can be actively and dynamically deployed. 

In this review article, we discuss the exotic polarization profiles that can arise at domain walls, such as the so-called Bloch wall shown below, and the different mechanisms that lead to domain-wall polarity in non-polar ferroelastic materials. We also provide an overview of the general notions that have been postulated as fundamental mechanisms responsible for domain-wall conduction in ferroelectrics. The possibility that mobile conducting ferroelectric domain walls could transform nanoscale electronics and the way we think about dynamic circuitry is exciting and we believe that domain walls could play a key role in the transition from nanoscale to atomic-scale electronics.

Figure caption: Schematic of a Bloch wall, where the ferroelectric polarization (indicated by the arrows) rotates in the plane of the wall between two 180° ferroelectric domains (corresponding to the areas with blue and green arrows).