Domain-wall engineering and topological defects in ferroelectric and ferroelastic materials

Ferroelectric and ferroelastic domain walls are 2D topological defects with thicknesses approaching the unit cell level. When this spatial confinement is combined with observations of emergent functional properties, such as polarity in non-polar systems or electrical conductivity in otherwise insulating materials, it becomes clear that domain walls represent new and exciting objects in matter. In this Review, we discuss the exotic polarization profiles that can arise at domain walls with multiple order parameters and the different mechanisms that lead to domain-wall polarity in non-polar ferroelastic materials. The emergence of energetically degenerate variants of the domain walls themselves suggests the existence of interesting quasi-1D topological defects within such walls. We also provide an overview of the general notions that have been postulated as fundamental mechanisms responsible for domain-wall conduction in ferroelectrics. We then discuss the prospect of combining domain walls with transition regions observed at phase boundaries, homo- and heterointerfaces, and other quasi-2D objects, enabling emergent properties beyond those available in today’s topological systems. Ferroelectric and ferroelastic domain walls are 2D topological defects with thicknesses approaching the unit cell level and emergent functional properties. This Review discusses the exotic polarization profiles that arise at domain walls and the fundamental mechanisms responsible for domain-wall conduction. Key points In ferroelectrics, the emergence of an additional polarization component at the wall, distinct from the bulk domain polarization, leads to analogues of magnetic Bloch and Néel walls. The stabilization of these walls opens the possibility of quasi-1D topological defects separating wall regions of opposite polarities. Polar domain walls in ferroelastics rely on two mechanisms: a polarity imposed by the natural symmetry of strain-compatible domain walls, which can be described by flexoelectric coupling, and the emergence of a potentially switchable polarity when their natural symmetry is broken. Several mechanisms are responsible for domain-wall conduction in ferroelectrics: extrinsic intra-bandgap defect states, intrinsic depression of the conduction band and intrinsic shift of the band structure induced by local electric fields. Transition regions occurring at phase boundaries, homo- and heterointerfaces, and other quasi-2D objects probably exist at a smaller length sca