Ordering of ferroelectric polarization and its trajectory in response to an electric field are essential for the operation of transducers, non-volatile memories and electro-optic devices. However, for voltage control of capacitance and frequency, domain walls have long been thought to be a hindrance because they lead to high dielectric loss and hysteresis in response to an applied electric field. To avoid these effects, tunable dielectrics are often operated under piezoelectric resonance conditions, relying on operation well above the ferroelectric Curie temperature, where tunability is compromised. Therefore, there is a seemingly unavoidable trade-off between the requirements of high tunability and low loss in tunable dielectric devices, which leads to severe limitations on their figure of merit.

At the same time, realization of tunable materials that are multifunctional and maintain high performance in dynamically changing environments is a fundamental goal of materials science and engineering. Tunable dielectrics form the basis of a wide variety of microwave, sub-mm and mm-wave communication and sensing devices, and require breakthrough performance improvement to enable next-generation technologies. Engineering the ferroelectric polarization-energy landscape offers intriguing new opportunities for tailoring properties.

I will discuss our re-examination of the ferroelectric polarization-energy landscapes associated with domain walls and their motion. We use intrinsically tunable materials with properties that are defined not only by their chemical composition, but also by the proximity and accessibility of thermodynamically predicted strain-induced, ferroelectric domain-wall variants. Starting from application of Ginzburg-Landau-Devonshire theory, under special conditions we predict and observe extraordinarily high dielectric tunability and the emergence of dynamic behavior that remarkable resonant responses. I will also present our recent collaborative work to design and model the domain structure-property relationships of film materials that exhibit exceptionally large tunable dielectric response over a wide temperature range and feature tunability that is itself controllable. These results suggest that domain engineering is a powerful approach for achieving unprecedented modulation of functional properties in ferroelectric films.

The role of the emerging electric depolarization fields during the field-driven polarization switching or the temporal domain structure formation remains enigmatic. In this communication a conceptual problem of the electric-field-mediated polarization correlations during the stochastic formation of polarization domain structure after quenching from the high temperature paraelectric state is addressed by using a recently advanced exactly solvable stochastic model of polarization development in a uniaxial ferroelectric. Considering the stochastic polarization and the electric field components as the Gauss random variables, integrodifferential equations for the polarization correlation function and the mean polarization are derived and solved. A full set of time-dependent two-point correlation coefficients between all random variables is obtained analytically, evaluated numerically, and presented graphically in three dimensions. It appears that some cross-correlations in a single crystal vanish at certain directions and planes that has fundamental physical reasons related to the potential and, respectively, solenoidal nature of the involved physical fields. These results allowed insight into the temporal development of anisotropic spatial characteristics of the emerging domain structure. Particularly, the analysis of the charge density correlations revealed a strong reduction of the charges at the nominally charged domain walls in uniaxial ferroelectrics which can be related to the recent observations of the saddle-point domain structures in triglycine sulfate and lead germanate.

Formation of polarization domain structure in ferroelectrics after quenching from high-temperature to a low-temperature phase is a stochastic process. It significantly depends both on external fields (electrical, mechanical, thermal) and initial conditions. This provides possibilities for controlling the domain structure development and improvement of the functional properties of materials. A self-consistent stochastic model of domain formation was created to predict the ordering process depending on external influences and quenching conditions like the cooling rate and temperature. The system of nonlinear differential equations for average polarization and its variance was solved showing the bifurcation behavior of domain ordering depending on the initial conditions and the applied electric field. The value of coercive field separating the regimes of single-domain and polydomain ordering increases with the increasing initial polarization fluctuation magnitude and spatial scale of fluctuations. The nonmonotonic evolution of domain structure is accompanied by the appearance of an incubation period, characterized by a low polarization value and its variance, and consequent interim phases with a rather asymmetric polarization. The analytical expressions for correlation length and polarization correlation coefficient were obtained by solving integrodifferential equations for different initial correlation functions, initial disorder magnitude and spatial scale. A satisfactory agreement with available experimental data in triglycine sulfate single-crystals is shown. Both correlation length and correlation coefficient exhibit the universal behavior being independent of the applied electric field. The obtained results show a significant impact of the initial disorder on the domain structure formation and open the opportunities for creation ferroelectric materials with functional properties in demand.