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

A Publisher Correction to this article was published on 28 September 2020

This article has been updated


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.

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 scale near domain walls and could lead to exceptional properties and coupling phenomena.

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Fig. 1: Mechanisms leading to polar domain walls.
Fig. 2: Polar domain walls in non-polar CaTiO3.
Fig. 3: Typical mechanisms of domain-wall conduction.
Fig. 4: Conduction at 180° domain walls.
Fig. 5: Exceptional properties arising at transition regions.

Change history

  • 28 September 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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G.F.N. thanks the Royal Commission for the Exhibition of 1851 for the award of a Research Fellowship. J.K. and M.G. acknowledge financial support from the Fond National de Recherche Luxembourg through a PEARL grant (no. FNR/P12/4853155/Kreisel). J.H. acknowledges financial support from the Czech Science Foundation (project no. 19-28594X). D.M. was supported by the Research Council of Norway through its Centres of Excellence funding scheme, project number 262633, “QuSpin” and by NTNU via the Onsager Fellowship Program and the Outstanding Academic Fellows Program. E.K.H.S is grateful to EPSRC (EP/K009702/1) and the Leverhulme Foundation (RPG-2012-564).

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Layer group

A group of symmetry operations applicable to objects possessing a lattice translation invariance along two directions only in 3D space. Planar domain walls in crystals are such objects.


Qualifying a group that does not contain inversion as a symmetry operation.

Point group

A set of symmetry operations that keep at least one point of the crystal fixed. The point group symmetry is relevant when describing only physical properties of crystals or domain walls.

Ginzburg–Landau type modelling

Modelling approaches that exploit the dependence of the thermodynamical potential on the magnitudes and gradients of order parameter components. For example, it allows one to predict profiles of the course of order parameters across a ferroelectric domain wall.

Fowler–Nordheim behaviour

One of the possible tunnelling behaviours of electrons under a high electric field.

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Nataf, G.F., Guennou, M., Gregg, J.M. et al. Domain-wall engineering and topological defects in ferroelectric and ferroelastic materials. Nat Rev Phys 2, 634–648 (2020).

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