Stochastic model of dispersive multi-step polarization switching in ferroelectrics due to spatial electric field distribution

A stochastic model for polarization switching in tetragonal ferroelectric ceramics is introduced, which includes sequential 90{\deg}- and parallel 180{\deg}-switching processes and accounts for the dispersion of characteristic switching times due to a nonuniform spatial distribution of the applied field. It presents merging of the recent multistep stochastic mechanism (MSM) with the earlier nucleation limited switching (NLS) and inhomogeneous field mechanism (IFM) models. The new model provides a much better description of simultaneous polarization and strain responses over a wide time window and a deeper insight into the microscopic switching mechanisms, as is exemplarily shown by comparison with measurements on lead zirconate titanate.Comment: 11 pages, 3 figure

Stochastic theory of ferroelectric domain structure formation dominated by quenched disorder

A self-consistent stochastic model of domain structure formation in a uniaxial ferroelectric, quenched from a high-temperature paraelectric phase to a low-temperature ferroelectric phase, is developed with an account of the applied electric field and the feedback effect via local depolarization fields. Both polarization and field components are considered as Gauss random variables. A system of integro-differential equations for correlation functions of all involved variables is derived and solved analytically and numerically. Phase diagram in terms of the average value and dispersion of polarization reveals different possible equilibrium states and available final single-domain and multi-domain states. The time-dependent evolution of the average polarization and dispersion discloses a bifurcation behavior and the temperature-dependent value of the electric field, deciding between the single-domain and multi-domain final states, which can be interpreted as the coercive field. Analytical and numerical results for the time-dependent correlation length and correlation functions exhibit plausible agreement with available experimental data.Comment: 33 pages, 10 figure

Tuning the Polar States of Ferroelectric Films via Surface Charges and Flexoelectricity

Using the self-consistent Landau-Ginzburg-Devonshire approach we simulate and analyze the spontaneous formation of the domain structure in thin ferroelectric films covered with the surface screening charge of the specific nature (Bardeen-type surface states). Hence we consider the competition between the screening and the domain formation as alternative ways to reduce the electrostatic energy and reveal unusual peculiarities of distributions of polarization, electric and elastic fields conditioned by the surface screening length and the flexocoupling strength. We have established that the critical thickness of the film and its transition temperature to a paraelectric phase strongly depend on the Bardeen screening length, while the flexocoupling affects the polarization rotation and closure domain structure and induces ribbon-like nano-scale domains in the film depth far from the top open surface. Hence the joint action of the surface screening (originating from e.g. the adsorption of ambient ions or surface states) and flexocoupling may remarkably modify polar and electromechanical properties of thin ferroelectric films.Comment: 33 pages, 5 figure

Defect driven flexo-chemical coupling in thin ferroelectric films

Using Landau-Ginzburg-Devonshire theory, we considered the impact of the flexoelectro-chemical coupling on the size effects inpolar properties and phase transitions of thin ferroelectric films with a layer of elastic defects. We investigated a typical case, when defects fill a thin layer below the top film surface with a constant concentration creating an additional gradient of elastic fields. The defective surface of the film is not covered with an electrode, but instead with an ultra-thin layer of ambient screening charges, characterized by a surface screening length. This geometry is typical for the scanning probe piezoelectric force microscopy. Obtained results revealed an unexpectedly strong effect of the joint action of Vegard stresses and flexoelectric effect (shortly flexo-chemical coupling) on the ferroelectric transition temperature, distribution of the spontaneous polarization and elastic fields, domain wall structure and period in thin PbTiO3 films containing a layer of elastic defects. A nontrivial result is the ferroelectricity persisting at film thicknesses below 4 nm, temperatures lower than 350 K and relatively high surface screening length (~0.1 nm). The origin of this phenomenon is the re-building of the domain structure in the film (namely the cross-over from c-domain stripes to a-type closure domains) when its thickness decreases below 4 nm, conditioned by the flexoelectric coupling and facilitated by negative Vegard effect. For positive Vegard effect, thicker films exhibit the appearance of pronounced maxima on the thickness dependence of the transition temperature, whose position and height can be controlled by the defect type and concentration. The revealed features may have important implications for miniaturization of ferroelectric-based devices.Comment: 25 pages, 9 figure

Multi-step stochastic mechanism of polarization reversal in rhombohedral ferroelectrics

A stochastic model for the field-driven polarization reversal in rhombohedral ferroelectrics is developed, providing a description of their temporal electromechanical response. Application of the model to simultaneous measurements of polarization and strain kinetics in a rhombohedral Pb(Zr,Ti)O3 ceramic over a wide time window allows identification of preferable switching paths, fractions of individual switching processes, and their activation fields. Complementary, the phenomenological Landau-Ginzburg-Devenshire theory is used to analyze the impact of external field and stress on switching barriers showing that residual mechanical stress may promote the fast switching.Comment: 33 pages, 9 figure

Space-charge mechanism of aging in ferroelectrics: an exactly solvable two-dimensional model

A mechanism of point defect migration triggered by local depolarization fields is shown to explain some still inexplicable features of aging in acceptor doped ferroelectrics. A drift-diffusion model of the coupled charged defect transport and electrostatic field relaxation within a two-dimensional domain configuration is treated numerically and analytically. Numerical results are given for the emerging internal bias field of about 1 kV/mm which levels off at dopant concentrations well below 1 mol%; the fact, long ago known experimentally but still not explained. For higher defect concentrations a closed solution of the model equations in the drift approximation as well as an explicit formula for the internal bias field is derived revealing the plausible time, temperature and concentration dependencies of aging. The results are compared to those due to the mechanism of orientational reordering of defect dipoles.Comment: 8 pages, 4 figures. accepted to Physical Review

Dynamic scaling properties of multistep polarization response in ferroelectrics

Ferroelectrics are multifunctional smart materials finding applications in sensor technology, micromechanical actuation, digital information storage etc. Their most fundamental property is the ability of polarization switching under applied electric field. In particular, understanding of switching kinetics is essential for digital information storage. In this regard, scaling properties of the temporal polarization response are well-known for 180{\deg}-switching processes in ferroelectrics characterized by a unique field-dependent local switching time. Unexpectedly, these properties were now observed in multiaxial polycrystalline ferroelectrics, exhibiting a number of parallel and sequential non-180{\deg}-switching processes with distinct switching times. This behaviour can be explained by a combination of the multistep stochastic mechanism and the inhomogeneous field mechanism models of polarization reversal. Scaling properties are predicted for polycrystalline ferroelectrics of tetragonal, rhombohedral and orthorhombic symmetries and exemplarily demonstrated by measurements of polarization kinetics in (K,Na)NbO3-based ferroelectric ceramic over a timescale of 7 orders of magnitude. Dynamic scaling properties allow insight into the microscopic switching mechanisms, on the one hand, and into statistical material characteristics, on the other hand, providing thereby the description of temporal polarization with high accuracy. The gained deeper insight into the mechanisms of multistep polarization switching is crucial for future ultrafast and multilevel digital information storage.Comment: 22 pages, 3 figure

Mesoscopic theory of defect ordering-disordering transitions in thin oxide films

Ordering of mobile defects in functional materials can give rise to fundamentally new phases possessing ferroic and multiferroic functionalities. Here we develop the Landau theory for strain induced ordering of defects (e.g. oxygen vacancies) in thin oxide films, considering both the ordering and wavelength of possible instabilities. Using derived analytical expressions for the energies of various defect-ordered states, we calculated and analyzed phase diagrams dependence on the film-substrate mismatch strain, concentration of defects, and Vegard coefficients. Obtained results open possibilities to create and control superstructures of ordered defects in thin oxide films by selecting the appropriate substrate and defect concentration.Comment: 30 pages, 5 figures, 1 appendi

Polarization dynamics across the morphotropic phase boundary in Ba(Zr0.2Ti0.8)O-3-x(Ba0.7Ca0.3)TiO3 ferroelectrics

Analysis of polarization switching dynamics by means of the inhomogeneous field mechanism model allows insight into the microscopic mechanism of reversed polarization domain nucleation. For all chemical compositions studied, two distinct field regions of nucleation are established. In the high-field region, the activation energy barrier is found to be inversely proportional to the local field according to the Merz law. In contrast, the barriers in the low-field region exhibit a linear field dependence with a minimum in the compositional region of phase instability, which can explain the corresponding peak ferroelectric properties.open7