Multistep stochastic mechanism of polarization reversal in rhombohedral ferroelectrics

Abstract

A stochastic model of electric field-driven polarization reversal in orthorhombic ferroelectrics is advanced, providing a description of their temporal electromechanical response. The theory accounts for all possible parallel and sequential switching events. Application of the model to the simultaneous measurements of polarization and strain kinetics in a lead-free orthorhombic (K,Na)NbO3-based ferroelectric ceramic over a wide timescale of 7 orders of magnitude allowed identification of preferable polarization switching paths, fractions of individual switching processes, and their activation fields. Particularly, the analysis revealed substantial contributions of coherent non-180° switching events, which do not cause macroscopic strain and thus mimic 180° switching processes.

Competition between Ferroelectric and Ferroelastic Domain Wall Dynamics during Local Switching in Rhombohedral PMN-PT Single Crystals

“…The revealed kinetics of the polarization reversal are similar to those obtained earlier for switching by the uniform electric field in the same crystals, where switching from the c ↑- to c ↓-domain state was realized through two successive stages: a ↑- and a ↓- domain states [ 25 ], resulting from the lower potential barrier of the a- domain formation [ 28 ]. Nonetheless, the observed complex domain patterns revealed by PFM cannot be simply interpreted as a transitional state between c ↑- and c ↓-domain states because the increase in the voltage pulse duration and amplitude does not result in the “complete” reversal to the c ↓-domain state (see Supplementary Materials, Figure S1 ).…”

“…Note, however, that the last value represents only a rough estimation as the distribution changes significantly after the formation of a ↑-domains. As the threshold voltage for polarization reversal is assumed to be significantly determined by the energy barriers for the rearrangement of the crystalline lattice, the energy barriers to “compress” and “rotate” the polarization are thought to be different [ 28 ]. It should be noted that obtained threshold electric field values for the formation of a- domains are almost an order lower than the threshold field for the c- domain formation determined from the macroscopic experiment [ 25 ].…”

“…In situ optical and electron microscopy visualizations conclusively approved that 180-degree polarization reversal in the single crystals and thin films of ferroelectrics from c + -domain with upward-directed polarization to the c – -domain with downward-directed polarization predominantly occurs through the intermediate state of ferroelastic domain wall formation (growth of the a- domain), i.e., two 90-degree switching events in [001] cut tetragonal ferroelectrics [ 21 , 22 , 23 , 24 ], or subsequent 71°, 109°, and 180° switching events in [111] cut rhombohedral ferroelectrics [ 25 , 26 , 27 ]. Landau–Ginzburg–Devonshire calculations explain such behavior as an existence of the local energetical minimum between upward and downward-directed polarization states, associated with the formation of a- domains [ 28 , 29 , 30 ]. The transition between two global energetical minima usually occurs through the local minima due to lower energetical barriers [ 28 ].…”

“…Landau–Ginzburg–Devonshire calculations explain such behavior as an existence of the local energetical minimum between upward and downward-directed polarization states, associated with the formation of a- domains [ 28 , 29 , 30 ]. The transition between two global energetical minima usually occurs through the local minima due to lower energetical barriers [ 28 ]. The direct 180-degree polarization reversal is, by all appearances, possible in the case where the formation of the ferroelastic domains is hindered because of some reason, such as for strong film clamping to the substrate mediated by the compressive stress or in the local switching by the biased tip of the scanning probe microscope (SPM), where the switching volume is clamped by the unswitched matrix [ 31 , 32 , 33 , 34 ].…”

“…For example, the inhomogeneous electric field created by the biased tip can significantly change the ferroelectric and ferroelastic switching dynamics and create energetically non-favorable patterns of vortex-like domains [ 30 , 37 ]. Despite the different time constants, which is caused by the different threshold voltage for the a- and c -domain switching due to the significantly different energy barrier height [ 28 , 38 ], both processes can generally occur simultaneously, because of the local inhomogeneity of the electric field and mechanical stress [ 39 ]. Thereby, an interaction between a- domains [ 18 ], and between a- and c- domains [ 40 ], can occur, as well as some collective regimes of the domain dynamics [ 1 , 41 , 42 , 43 ].…”