Field induced evolution of regular and random 2D domain structures and shape of isolated domains in LiNbO₃ and LiTaO₃

The shapes of isolated domains produced by application of the uniform external electric field in different experimental conditions were investigated experimentally in single crystalline lithium niobate LiNbO3 and lithium tantalate LiTaO3. The study of the domain kinetics by computer simulation and experimentally by polarization reversal of the model structure using two-dimensional regular electrode pattern confirms applicability of the kinetic approach to explanation of the experimentally observed evolution of the domain shape and geometry of the domain structure. It has been shown that the fast domain walls strictly oriented along X directions appear after domain merging

Polarization reversal and jump-like domain wall motion in stoichiometric LiTaO 3 produced by vapor transport equilibration

The polarization reversal and domain structure evolution has been studied in stoichiometric lithium tantalate prepared by vapor transport equilibration process. The first in situ visualization of domain kinetics has demonstrated the jump-like motion of few strictly oriented plane domain walls, which leads to short isolated current pulses in the switching current data. The proposed model of jump-like domain wall motion caused by interaction with pinning centers representing the areas with increased value of the threshold field is based on the effect of retardation of bulk screening. The derived formulas were applied successfully for analysis of the field dependence of the total switching time. The durations of wall jumps and wall stays (rest times) extracted from the switching current data are analyzed separately. The deceleration of the wall motion velocity during jump is controlled by the trail of residual depolarization field produced by bound charges and screening charges in the area behind the wall. The duration of the rest time is governed by the bulk screening of residual depolarization field. The value of Hurst exponent 0.75 obtained by fractal analysis of the switching current data has confirmed the essential influence of prehistory on the domain wall motion. The measurements of the coercive field by switching in bipolar triangular pulses in wide range of the field ramp rate have allowed us to extract the record low value of coercive field 60 V/mm for quasi-static polarization reversal. © 2012 American Institute of Physics

Abelian Repetition Threshold Revisited

In combinatorics on words, repetition thresholds are the numbers separating avoidable and unavoidable repetitions of a given type in a given class of words. For example, the meaning of the “classical” repetition threshold RT(k) is “every infinite k-ary word contains an α -power of a nonempty word for some α≥ RT(k) but some infinite k-ary words contain no such α -powers with α> RT(k) ”. It is well known that RT(k)=kk-1 with the exceptions for k= 3, 4. For Abelian repetition threshold ART(k), avoidance of fractional Abelian powers of words is considered. The exact values of ART(k) are unknown; the lower bound ART(2)≥113, ART(3 ) ≥ 2, ART(4)≥95, ART(k)≥k-2k-3 for all k≥ 5 was proved by Samsonov and Shur in 2012 and conjectured to be tight. We present a method of study of Abelian power-free languages using random walks in prefix trees and some experimental results obtained by this method. On the base of these results, we suggest that the lower bounds for ART(k) by Samsonov and Shur are not tight for all k except k= 5. We prove ART(k)>k-2k-3 for k= 6, 7, 8, 9, 10 and state a new conjecture on the Abelian repetition threshold. © 2022, Springer Nature Switzerland AG.Ministry of Education and Science of the Russian Federation, Minobrnauka: FEUZ-2020-0016E. A. Petrova—Supported by the Ministry of Science and Higher Education of the Russian Federation, project FEUZ-2020-0016. A. M. Shur—Supported by Ural Mathematical Center, project 075-02-2022-877.Kulikov A.S.Raskhodnikova S

Branching Frequency and Markov Entropy of Repetition-Free Languages

We define a new quantitative measure for an arbitrary factorial language: the entropy of a random walk in the prefix tree associated with the language; we call it Markov entropy. We relate Markov entropy to the growth rate of the language and the parameters of branching of its prefix tree. We show how to compute Markov entropy for a regular language. Finally, we develop a framework for experimental study of Markov entropy by modelling random walks and present the results of experiments with power-free and Abelian-power-free languages. © 2021, Springer Nature Switzerland AG.Supported by the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center project No. 075-02-2021-1387)

Transition Property for Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair (u, v) of d-ary cube-free words, if u can be infinitely extended to the right and v can be infinitely extended to the left respecting the cube-freeness property, then there exists a “transition” word w over the same alphabet such that uwv is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained “transition property”, together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.E.A. Petrova — Supported by the Russian Science Foundation, grant 18-71-00043

Branching densities of cube-free and square-free words

Binary cube-free language and ternary square-free language are two “canonical” represen-tatives of a wide class of languages defined by avoidance properties. Each of these two languages can be viewed as an infinite binary tree reflecting the prefix order of its elements. We study how “homogenious” these trees are, analysing the following parameter: the density of branching nodes along infinite paths. We present combinatorial results and an efficient search algorithm, which together allowed us to get the following numerical results for the cube-free language: the minimal density of branching points is between 3509/9120 ≈ 0.38476 and 13/29 ≈ 0.44828, and the maximal density is between 0.72 and 67/93 ≈ 0.72043. We also prove the lower bound 223/868 ≈ 0.25691 on the density of branching points in the tree of the ternary square-free language. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.This research was funded by Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center project No. 075-02-2020-1537/1)

Static conductivity of charged domain wall in uniaxial ferroelectric-semiconductors

Using Landau-Ginzburg-Devonshire theory we calculated numerically the static conductivity of both inclined and counter domain walls in the uniaxial ferroelectrics-semiconductors of n-type. We used the effective mass approximation for the electron and holes density of states, which is valid at arbitrary distance from the domain wall. Due to the electrons accumulation, the static conductivity drastically increases at the inclined head-to-head wall by 1 order of magnitude for small incline angles theta pi/40 by up 3 orders of magnitude for the counter domain wall (theta=pi/2). Two separate regions of the space charge accumulation exist across an inclined tail-to-tail wall: the thin region in the immediate vicinity of the wall with accumulated mobile holes and the much wider region with ionized donors. The conductivity across the tail-to-tail wall is at least an order of magnitude smaller than the one of the head-to-head wall due to the low mobility of holes, which are improper carries. The results are in qualitative agreement with recent experimental data for LiNbO3 doped with MgO.Comment: 20 pages, 6 figures, 1 appendi

Finite size and intrinsic field effect on the polar-active properties of the ferroelectric-semiconductor heterostructures

Using Landau-Ginzburg-Devonshire approach we calculated the equilibrium distributions of electric field, polarization and space charge in the ferroelectric-semiconductor heterostructures containing proper or incipient ferroelectric thin films. The role of the polarization gradient and intrinsic surface energy, interface dipoles and free charges on polarization dynamics are specifically explored. The intrinsic field effects, which originated at the ferroelectric-semiconductor interface, lead to the surface band bending and result into the formation of depletion space-charge layer near the semiconductor surface. During the local polarization reversal (caused by the inhomogeneous electric field induced by the nanosized tip of the Scanning Probe Microscope (SPM) probe) the thickness and charge of the interface layer drastically changes, it particular the sign of the screening carriers is determined by the polarization direction. Obtained analytical solutions could be extended to analyze polarization-mediated electronic transport.Comment: 35 pages, 12 figures, 1 table, 2 appendices, to be submitted to Phys. Rev.

In situ imaging of domain structure evolution in labgeo5 single crystals

LaBGeO5 (LBGO) crystals are unique ferroelectric materials for manufacturing highly efficient UV laser sources based on frequency conversion. This is due to their low cut-off wavelength, high nonlinear-optical coefficients, and non-hygroscopicity. Periodical poling requires a deep study of domain kinetics in these crystals. Domain imaging by Cherenkov second harmonic generation microscopy was used to reveal the main processes of domain structure evolution: (1) growth and merging of isolated domains, (2) growth of stripe domains formed on the artificial linear surface defects, and (3) domain shrinkage. In a low field, growth of triangular domains and fast shape recovery after merging were observed, while in a high field, the circular domains grew independently after merging. The revealed essential wall motion anisotropy decreased with the field. The anisotropy led to significant shape transformations during domain shrinkage in low field. The formation of short-lived triangular domains rotated by 180 degrees with respect to the growing isolated domains was observed. The obtained results were explained within the kinetic approach to domain structure evolution based on the analogy between the growth of crystals and ferroelectric domains, taking into account the gradual transition from determined nucleation in low field to the stochastic one in high field. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.Russian Science Foundation, RSF: 19-12-00210Funding: This research was funded by the Russian Science Foundation, grant number 19-12-00210

Polarization reversal induced by heating-cooling cycles in MgO doped lithium niobate crystals

Polarization reversal during heating-cooling cycles was investigated in MgO doped lithium niobate (MgO:LN) crystal using piezoresponse force microscopy. The essential dependence of the domain structure evolution scenario on the maximal temperature in the cycle has been revealed experimentally. It has been shown that the heating of the engineered domain matrix from room temperature to 85 °C leads to light size reduction of the isolated domains at the matrix edges, whereas the heating to 170 °C leads to essential reduction of the domain size. The opposite strong effect of the domain formation and growth during cooling after pulse heating have been revealed in single domain MgO:LN. The simulation of the time dependence of the pyroelectric field during heating-cooling cycle allowed to reveal the temperature hysteresis and to explain all observed effects taking into account the temperature dependence of the bulk conductivity. © 2013 AIP Publishing LLC