PHYSICAL REVIEW B 96, 054113 (2017) Correlated polarization-switching kinetics in bulk polycrystalline ferroelectrics: A self-consistent mesoscopic switching model Ruben Khachaturyan, 1 , * Jens Wehner, 2 and Yuri A. Genenko 1 , † 1 Institut of Materials Science, Technische Universität Darmstadt, Jovanka-Bontschits-Str. 2, D-64287 Darmstadt, Germany 2 Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany (Received 28 April 2017; revised manuscript received 28 July 2017; published 17 August 2017) Analysis of statistical distributions and auto- and cross correlations of polarization and electric field during the field-driven polarization reversal in a bulk polycrystalline ferroelectric is performed. A mesoscopic switching model is used which accounts self-consistently for the development of depolarization fields. Correlations mediated by electrostatic fields are shown to be mostly isotropic and short range at the typical scale of the grain size which is explained by an effective screening via adapting bound charges. The short-range screening clarifies the paradoxical ability of common statistical concepts neglecting the feedback effect of depolarization fields to adequately describe the polarization switching kinetics. The statistical distribution of the local electric field magnitudes is continuously spreading in the course of the global polarization reversal due to mismatching of both dielectric tensor and spontaneous polarization at grain boundaries. The increasing field dispersion substantially contributes to the well-known deceleration of the polarization reversal at long times. DOI: 10.1103/PhysRevB.96.054113 I. INTRODUCTION Electric field-driven switching of spontaneous polarization is a fundamental process in ferroelectric materials relevant to many applications, for example digital data storage. Despite the great significance of polarization dynamics for applica- tions, switching mechanisms remain poorly understood even for well-studied ferroelectrics in single crystal or polycrys- talline forms. Indeed, the classical picture of polarization switching developed in works by Landauer [1], Miller et al. [2], and Ishibashi et al. [3] suggests spontaneous nucleation and growth of domains of the opposite polarization within a previously homogeneously polarized medium. Polariza- tion reversal inevitably creates local bound charges due to polarization mismatch at the domain boundaries which, in turn, generate electric depolarization fields. In nonconducting media these large and long-range fields are not expected to be screened. Thus, depolarization fields have to play an essential role in the switching process by providing mutual influence of different switching regions. However, widely used statistical concepts of the polarization switching [3–8] assume independent and uncorrelated nucleation and growth of reversed domains and thus virtually neglect the feedback effect of the depolarization fields during the polarization reversal. Furthermore, the inhomogeneous field mechanism (IFM) model, recently advanced by the authors [9,10] and also assuming independent polarization switching in individual regions, describes the time-dependent response of various ferroelectric ceramics of different chemical compositions and phase symmetries [10–16] as well as of semicrystalline polymers [17] with high accuracy. Whereas in single-crystalline media the polarization switching may, in principle, occur by moving charge-free 90 ◦ -domain walls without generating local bound charges [18,19], avoiding local charges in polycrystalline media, * rubenftf@gmail.com † genenko@mm.tu-darmstadt.de such as bulk ferroelectric ceramics, is impossible because of inevitable mismatches of different crystalline orientation in adjacent grains. A paradoxical ability of statistical concepts, which neglect the feedback of depolarization fields, to ac- curately describe polarization switching kinetics in a variety of inorganic ferroelectric ceramics [6,7,9–16,20,21], organic ferroelectrics [17,22–27], and organic-inorganic ferroelectric composites [28,29] needs to be comprehended. Attempts made so far to account for the feedback of depolarization fields remained mostly within the mean-field approximation which assumes emergence of a time-dependent spatially uniform electric field due to averaging of multiple switching events [30–32]. Being an important step towards the understanding of the polarization switching in disordered media such an approach still misses the intrinsically stochastic nature of emerging depolarization fields which are possibly correlated at a finite scale. Particularly, in the case of long-range correlations a spatially and temporally coherent switching could, in principle, keep the depolarization fields small. This would explain, on the one hand, a weak effect of the depolarization field, but mean, on the other hand, that switching in different regions cannot be considered as being independent. The importance of collective domain dynamics was rec- ognized and studied in thin ferroelectric films for more than a decade by various methods. Strong correlations of domain structures extending across the grain boundaries have been observed by piezoelectric scanning probe microscopy (SPM) in polycrystalline thin films [33] and by transmis- sion electron microscopy (TEM) and piezoresponse force microscopy (PFM) in model single-grain structures [34–36]. Polarization response exhibited clustering ranging from few grains [33] to agglomerations of 10 2 –10 3 grains [37,38]. Macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline films revealed the dominant role of collective long-range strain interactions mediated by the local and global mechanical boundary conditions, possibly by elastic coupling through the substrate [39,40]. 2469-9950/2017/96(5)/054113(10) 054113-1 ©2017 American Physical Society