Flexoelectricity, incommensurate phases and the Lifshitz point

Macroscopic Polarization from Nonlinear Gradient Couplings

We show that a lattice mode of arbitrary symmetry induces a well-defined macroscopic polarization at first order in the momentum and second order in the amplitude. We identify a symmetric flexoelectric-like contribution, which is sensitive to both the electrical and mechanical boundary conditions, and an antisymmetric Dzialoshinskii-Moriya-like term, which is unaffected by either. We develop the first-principles methodology to compute the relevant coupling tensors in an arbitrary crystal, which we illustrate with the example of the antiferrodistortive order parameter in SrTiO_{3}.

Nanoscale Bubble Domains and Topological Transitions in Ultrathin Ferroelectric Films

Observation of a new type of nanoscale ferroelectric domains, termed as "bubble domains"-laterally confined spheroids of sub-10 nm size with local dipoles self-aligned in a direction opposite to the macroscopic polarization of a surrounding ferroelectric matrix-is reported. The bubble domains appear in ultrathin epitaxial PbZr_0.2 Ti_0.8 O₃ /SrTiO₃ /PbZr_0.2 Ti_0.8 O₃ ferroelectric sandwich structures due to the interplay between charge and lattice degrees of freedom. The existence of the bubble domains is revealed by high-resolution piezoresponse force microscopy (PFM), and is corroborated by aberration-corrected atomic-resolution scanning transmission electron microscopy mapping of the polarization displacements. An incommensurate phase and symmetry breaking is found within these domains resulting in local polarization rotation and hence impart a mixed Néel-Bloch-like character to the bubble domain walls. PFM hysteresis loops for the bubble domains reveal that they undergo an irreversible phase transition to cylindrical domains under the electric field, accompanied by a transient rise in the electromechanical response. The observations are in agreement with ab-initio-based calculations, which reveal a very narrow window of electrical and elastic parameters that allow the existence of bubble domains. The findings highlight the richness of polar topologies possible in ultrathin ferroelectric structures and bring forward the prospect of emergent functionalities due to topological transitions.

Polarization curling and flux closures in multiferroic tunnel junctions

Formation of domain walls in ferroelectrics is not energetically favourable in low-dimensional systems. Instead, vortex-type structures are formed that are driven by depolarization fields occurring in such systems. Consequently, polarization vortices have only been experimentally found in systems in which these fields are deliberately maximized, that is, in films between insulating layers. As such configurations are devoid of screening charges provided by metal electrodes, commonly used in electronic devices, it is wise to investigate if curling polarization structures are innate to ferroelectricity or induced by the absence of electrodes. Here we show that in unpoled Co/PbTiO₃/(La,Sr)MnO₃ ferroelectric tunnel junctions, the polarization in active PbTiO₃ layers 9 unit cells thick forms Kittel-like domains, while at 6 unit cells there is a complex flux-closure curling behaviour resembling an incommensurate phase. Reducing the thickness to 3 unit cells, there is an almost complete loss of switchable polarization associated with an internal gradient.

Ferroelectric vortex-type structures have only been seen in isolated films, leaving electrode effects unexplored. Here, Peters et al. show that the polarisation curling and formation of vortex and flux-closure structures is a generic effect appearing in ultrathin ferroelectric films.