A novel mesoscale state comprising of an ordered polar vortex lattice has been demonstrated in ferroelectric superlattices of PbTiO/SrTiO. Here, we employ phase-field simulations, analytical theory, and experimental observations to evaluate thermodynamic conditions and geometric length scales that are critical for the formation of such exotic vortex states. We show that the stability of these vortex lattices involves an intimate competition between long-range electrostatic, long-range elastic, and short-range polarization gradient-related interactions leading to both an upper and a lower bound to the length scale at which these states can be observed. We found that the critical length is related to the intrinsic domain wall width, which could serve as a simple intuitive design rule for the discovery of novel ultrafine topological structures in ferroic systems.

High-performance piezoelectrics are lead-based solid solutions that exhibit a so-called morphotropic phase boundary, which separates two competing phases as a function of chemical composition; as a consequence, an intermediate low-symmetry phase with a strong piezoelectric effect arises. In search for environmentally sustainable lead-free alternatives that exhibit analogous characteristics, we use a network of competing domains to create similar conditions across thermal inter-ferroelectric transitions in simple, lead-free ferroelectrics such as BaTiO 3 and KNbO 3 . Here we report the experimental observation of thermotropic phase boundaries in these classic ferroelectrics, through direct imaging of low-symmetry intermediate phases that exhibit large enhancements in the existing nonlinear optical and piezoelectric property coefficients. Furthermore, the symmetry lowering in these phases allows for new property coefficients that exceed all the existing coefficients in both parent phases. Discovering the thermotropic nature of thermal phase transitions in simple ferroelectrics thus presents unique opportunities for the design of 'green' high-performance materials.

The metal-insulator transition in correlated materials is usually coupled to a symmetrylowering structural phase transition. This coupling not only complicates the understanding of the basic mechanism of this phenomenon but also limits the speed and endurance of prospective electronic devices. We demonstrate an isostructural, purely electronically driven metal-insulator transition in epitaxial heterostructures of an archetypal correlated material, vanadium dioxide. A combination of thin-film synthesis, structural and electrical characterizations, and theoretical modeling reveals that an interface interaction suppresses the electronic correlations without changing the crystal structure in this otherwise correlated insulator. This interaction stabilizes a nonequilibrium metallic phase and leads to an isostructural metal-insulator transition. This discovery will provide insights into phase transitions of correlated materials and may aid the design of device functionalities.

A novel nonlinear phase-field model is proposed for modeling microstructure evolution during highly nonequilibrium processes. We consider electrochemical reactions at electrode/electrolyte interfaces leading to electroplating and electrode/electrolyte interface evolution. In contrast to all existing phase-field models, the rate of temporal phase-field evolution and thus the interface motion in the current model is considered nonlinear with respect to the thermodynamic driving force. It produces Butler-Volmer-type of electro-chemical kinetics for the dependence of interfacial velocity on the overpotential at the sharp-interface limit. At the low overpotential it recovers the conventional Allen-Cahn phase-field equation. This model is generally applicable to many other highly non-equilibrium processes where linear kinetics breaks down.

Tensile strain along the cR-axis in epitaxial VO2 films raises the temperature of the metal insulator transition and is expected to stabilize the intermediate monoclinic M2 phase. We employ surfacesensitive x-ray spectroscopy to distinguish from the TiO2 substrate and identify the phases of VO2 as a function of temperature in epitaxial VO2/TiO2 thin films with well defined biaxial strain. Although qualitatively similar to our Landau-Ginzburg theory predicted phase diagrams, the stabilization of the M2 phase in epitaxial films results from nearly an order of magnitude more strain than expected. Our results reveal that the elongation of the cR axis is insufficient for describing the transition pathway of VO2 epitaxial films and that a strain induced increase of electron correlation effects must be considered.