The expanding world of topological ferroelectrics

Topology is the branch of mathematics concerned with the continuous deformation of geometries, one of the main conclusions of which is that geometries cannot be distorted arbitrarily into any shape; that is, certain structures are topologically invariant. This may seem like a far cry from materials science, but science has a way of connecting fields as seemingly widely separated as nuclear physics and magnetism. Consider the magnetic skyrmion, so-called because its particle-like and chiral spin structures are topologically protected and cannot be deformed into bulk ferromagnetic phases. This is analogous to solutions to a nonlinear field theory by Tony Skyrme of interacting pions that resulted in stable particles¹. These magnetic skyrmions were first observed in 2009, and have potential for high-density information storage. It was almost a decade later before skyrmions (pictured) and similar topological structures were observed in another ferroic; ferroelectrics that possess permanent polarization and history-dependent switching behaviour under electric field^2,3. Complex heterostructures or nanostructures are required to balance competing energetics to stabilize topological structures, potentially limiting experimental accessibility and applications of these systems.

Figure adapted from ref. ⁴, Springer Nature Limited.

In an Article by Zheng Wen and colleagues an alternative approach for the formation of skyrmion domains is presented. The authors compose solid-solution alloys of ferroelectric PbTiO₃ and an antiferroelectric PbSnO₃, PbHfO₃ or PbZrO₃, where an antiferroelectric can be considered as a material with no overall polarization due to antiparallel polarizations within its unit cell. As there are differences in the polar axis orientation between ferroelectrics and antiferroelectrics, non-collinear orientations form that enable polarization rotation and so give rise to topological textures. These are observed using vector piezoresponse force microscopy and scanning transmission electron microscopy (STEM), while effective Hamiltonian simulations corroborate experimental results and show topological charge is equal to that of skyrmions. A full phase map for all alloys is presented, and electrical writing–erasure of skyrmions demonstrated. As Petro Maksymovych discusses in the accompanying News & Views article, this alloying approach may lead to rapid and scalable optimization, and notes this could enable platforms for the study of non-collinear textures.

It is the interaction between ferroelectrics and antiferroelectrics that drives skyrmion formation in the solid-solution alloys, but can antiferroelectrics themselves display topological textures such as skyrmions, or their two-dimensional equivalent vortices? A driving force for polarization rotation in ferroelectrics is the depolarization field at an interface; however, in antiferroelectrics this field does not occur. In a Letter by Gustau Catalan and colleagues, vortices and antivortices are observed using STEM in the prototypical antiferroelectric PbZrO₃. Analysis of the STEM data, in combination with second-principles simulations, show these topological objects form at ferroelastic domain walls. Ferroelastics are another class of ferroic, classified as materials that possess spontaneous strain. In PbZrO₃, there are six ferroelastic domain orientations and the interaction between local polarization and the ferroelastic domain wall between ferroelastic domains drives topological texture formation. Vortices manifest when the domain wall is head-to-tail (in terms of Pb displacement that generates polarity), and antivortices when the domain wall is head-to-head or tail-to-tail.

Polarization in perovskite ferroelectrics and antiferroelectrics is structural, relating to the displacement of the cation in the unit cell. In an Article by David Muller and colleagues, a polarization driven by anion displacements is reported. Thin films of NaNbO₃ are grown on a DyScO₃ substrate and under epitaxial tensile strain generate ferroelectricity. Using multislice electron ptychography that enables the imaging of atoms throughout the film, they image the metal cations and the oxygen anions in their sample. The oxygen octahedra present large rotations while the cation displacements are minimal. Moreover, density functional theory calculations indicate that several competing phases with similar energies can coexist, indicating a complex energy landscape. In the accompanying News & Views article by Xiaoyue Gao and Peng Gao, the authors suggest that manipulating the oxygen configuration under an external field could tune material properties, and that quantifying polarization solely through cation displacements could be inadequate for full characterization. This could also be the case for identifying topological objects.

Commercial applications of ferroelectrics have existed for decades. The study of topological texture in ferroelectrics is still in its infancy, and commercialization is likely a long time away. It is interesting to see if and how topological objects enable materials properties beyond the state of the art, for example with improved dielectric properties⁴, as well as how these objects can advance fundamental studies. Further studies on the dynamics of these objects are welcome. The development and study of these systems certainly relies on the dovetailing of advances in growth, characterization and modelling that epitomizes the multidisciplinarity of materials science.