Stochastic domain formation dominated by quenched disorder in ferroelectrics

The role of electric depolarization fields and field-mediated correlations in the formation of domain systems and their field-driven switching remains enigmatic. To consider this problem we develop a stochastic model of uniaxial ferroelectrics based on the time-dependent Landau-Ginzburg-Devonshire approach [1,2] where polarization and electric field are self-consistently treated as Gaussian random variables. A closed system of evolution equations for auto- and cross-correlation functions for all stochastic variables is formulated and analyzed analytically and numerically.

Evolution of the system starting from different initial quenched disordered states at different temperatures and applied electric fields is studied. A phase pattern of possible single-domain and multi-domain states in terms of average polarization and polarization dispersion is established, which depends on temperature and an applied field. The final states of the system evolution appear to be hardly dependent on the depolarization field-induced polarization correlations, however, the time evolution of the system is strongly affected by correlations. Explicit formulas for time-dependent longitudinal and transverse spatial correlations are derived.

Constrains on temperature and system properties are identified, for which the quenched disorder dominates over thermodynamic fluctuations in the system evolution. Development with time exhibits field-dependent tendencies to multi-domain and single-domain states at higher and lower temperatures, respectively. The correlation radius of polarization fluctuations, which can be interpreted as a characteristic domain size, is found analytically and demonstrates a diffusion-like time behavior.

[1] O.Y. Mazur, L.I. Stefanovich, and V.M. Yurchenko, Phys. Sol. State 57, 576 (2015).

[2] I.S. Vorotiahin, A.N. Morozovska, E.A. Eliseev, and Y.A. Genenko, Phys. Rev. B 95, 014104 (2017).