0000000000131602
AUTHOR
E. Klotins
Notes on the Electroelastic Interaction in Joint Hamiltonian and Stochastic Treatment of Polarization Response
Conventional Landau theory for ferroelectric phase instability is extended by entities accounting for the violation of thermodynamic equilibrium and the impact of thermal fluctuations. The physical content concerns Ginzburg-Landau type model Hamiltonians assigned to the mean field interaction of macroscopically small and microscopically large lattice cells affected by thermal fluctuations. A special topic derived in a systematic way is long range electroelastic interaction formally given by selfconsistent solution of the polarization and strain fields. Test solution for inhomogeneous strain in a slab is presented within the framework of lattice cell picture.
Polar nanoregions in Pb(Mg1/3Nb2/3)O3 (PMN): insights from a supercell approach
Abstract We report construction of a model of polar nanoregions in the PMN relaxor ferroelectric based on first-principles lattice dynamics for chemically ordered supercells [S.A. Prosandeev et al., Phys. Rev. B 70, 134110 (2004)], combined with invariance under permutations and dipole-dipole interaction as a source supporting randomly oriented residual polarization. Representative analytical estimates of polar nanore-gion — supercell mapping reproduce both nonzero local and zero macroscopic polarization of the structure, as well as the temperature change of the supercell anisotropy at cooling and field cooling.
Finding Electron-Hole Interaction in Quantum Kinetic Framework
The present research has been supported by the Institute of Solid State Physics, the University of Latvia within the framework of National Research Program IMIS2. [Grant numbers VPPI IMIS2, IMIS4].
Quantum chemical study of electron‐phonon interaction in crystals
Study of the interaction of the electromagnetic radiation with nonlocal potentials and the electron-phonon interaction is motivated by its key role in non-classical phenomena in dielectrics and semiconductors. Actual in second quantization is decoupling of the undesirable mixture of electronic and phonon birth/annihilation operators and obtaining the effect of radiation in presence of the nonlocal potentials. Here we transform an arbitrary effective electron- phonon Hamiltonian in two matrices – the matrix of a new interaction Hamiltonian and the matrix of the transformation. For a particular effective Hamiltonian formulated in second quantization these two matrices outline a starting point…
High Field Polarization Response in Ferroelectrics: Current Solutions and Challenges
Polarization response including ergodicity breaking and the divergence of relaxation time is reproduced for model Hamiltonians of growing complexity. Systematic derivation of the dynamical equations and its solutions is based on the Fokker-Planck and imaginary time Schrödinger equation techniques with subsequent symplectic integration. Test solutions are addressed to finite size and spatially extended problems with microscopically interpretation of the model parameters as a challenge.
Laser heterodyne displacement measuring using PLZT frequency shifter
Abstract The implementation of a frequency shifter based on lead lanthanum zirconate titanate ceramic (PLZT) and a voltage-controlled λ/4 plate is described. The capabilities of these elements are demonstrated with results from a Michelson-type laser heterodyne displacement measuring interferometer with 0.01 μm accuracy and 1 Hz display update rate.
Numerical Evidences of Polarization Switching in PMN Type Relaxor Ferroelectrics
We present a conceptual and computational framework for chemically ordered Pb(Mg 1/3 Nb 2/3 O 3) (PMN) type supercells violating disorder of the host lattice. The effective Hamiltonian is specified by invariance under permutations of supercells and by the dipole-dipole interaction supporting both local nonzero and zero mean polarization of the structure. Statistics treated in canonical ensemble within the mean field approach reveals emergence of polar nanoregions as supported by interplay between the (random) initial state polarization of supercells and their interactions increased at cooling.
Intrinsic localized excitations in nonlinear lattices: Heuristic explanation for the nature of polar nanoregions?
The study is addressed to a topical problem of self-localization in condensed state with special emphasis on a class of complex oxides categorized as ferroelectric relaxors. Basically, their anomalous temperature response is associated with the dynamics of microscopic scale polar regions supported by somewhat artificial metastable configurations. A unified approach to the spontaneous emergence and stability of the polar nanoregions is assigned to intrinsic localized excitations in Hamiltonian lattices with nonlinearity and non-Gibbsian statistics as necessary and sufficient ingredients of the theory.
Semiadiabatic High-Field Polarization Response in Ferroelectrics I: Hysteresis and Nonlinear Susceptibility
Ginzburg-Landau theory for ferroelectric phase instability is combined with Langevin, Fokker-Planck and imaginary time Schrodinger equation techniques to model impact of thermal noise in the kinetics of ferroelectric polarization. The proposed real space/real time numerical method allows to efficiently simulating relaxation, dynamic hysteresis and general dielectric response.
Electronic Processes in Solid State: Dirac Framework
The present paper proposes canonical Dirac framework adapted for application to the electronic processes in solid state. The concern is a spatially periodic structure of atoms distinguished by birth and annihilation of particle states excited due to interaction with the electromagnetic field. This implies replacing the conventional energy-momentum relation specific of the canonical Dirac framework and permissible for particle physics by a case specific relation available for the solid state. The advancement is a unified and consistent mathematical framework incorporating the Hilbert space, the quantum field, and the special relativity. Essential details of the birth and annihilation of the …
Mesoscopic Scale Structural Instability in Ferroelectrics
First-principles statistics addressed to structural phase transitions and temperature development of ferroelectric response is derived within the framework of the Fokker-Planck (Smoluchowsky) equation as complementary to the Monte Carlo [R.D King-Smith., D Vanderbilt, Phys. Rev. B 49, 5828–5844 (1994)] and molecular dynamics [T. Nishimatsu, U. V Waghmare, Y. Kawazoe., D. Vanderbilt, arXiv:0804.1853v2] simulations. Illustrative example of is given for 5 × 5 × 5 BaTiO 3 supercell.
Stochastic Dynamics of Ferroelectric Polarization
This study is addressed to the conceptual and technical problems emerging for ferroelectric systems out of thermodynamic equilibrium. The theoretical setup includes a lattice of interacting cells, each cell obeying regular dynamics determined by Ginzburg-Landau model Hamiltonians whereas relaxation toward minimum energy state is reproduced by thermal environment. Representative examples include polarization response of a single lattice cell, birth of a domain as triggered by the ergodicity breaking, and the effect of nonlocal electroelastic interaction all evidenced combining the Fokker-Planck, imaginary time Schrodinger and symplectic integration techniques.
The strain response of piezoelectric multilayer actuators under combined action of electric field and in-plane uniform load
Abstract The driving field governed strain of lead zirconate titanate piezoelectric multilayer actuators have been made within the 107 N/m2 stress and the 3 · 106 V/m triangle-like upward-down-ward driving voltage. A slow strain component as well as a specific relaxation pattern are detected being additional to the periodic part and attributed to the trapped space charge effects favored by nonuniform electric field of the multilayer.
Modeling of trapped charge effects in ferroelectrics: application to piezoactuators
The strain response of lead zirconate titanate piezoelectric multilayer actuators have been measured up to 10 7 N/m 2 stress and the 3.10 6 V/m periodic unipolar driving voltage. An additional nonstationary strain component is detected. This effect is explained in terms of a simple solution of polarization kinetics specific for unipolar driving voltage. Preliminary experimentally assertions are given for space charge effects which manifest itself in the strain as well as charge plot after removing the mechanical load. It demonstrates that the static load free equilibrium of the actuator is not complete and the charge recently supported by the piezo voltage and then trapped forms a nonunifor…
Phase transitions and properties of perovskite ferroelectric ceramics and films for certain applications
Abstract The structure-properties relationships and phase transitions in perovskite ceramics, and films of PLZT, PLZST, PST, PSN, PMNT compounds are discussed with regard to ordering, relaxor behaviour, pronounced ferroelectric, electromechanical and electrocaloric properties. The theoretical approach is extended to the time dependent Ginsburg-Landau model. The evolution of dielectric properties in relaxors after the change of temperature and electric field creating an increase of dielectric permittivity is found to follow a logarithmic law of decay. A strong electromechanical response is observed in a number of thin films of different compositions.
Theory and modeling of polarization switching in ferroelectrics
Abstract Kinetics of polarization response in ferroelectrics is reproduced within Langevin, Fokker–Planck and imaginary time Schrodinger equation techniques for energy functionals of growing complexity modeling an assembly of coarse grained particles with attractive first neighbor interaction. Symplectic integration based numerical approach captures dynamic hysteresis, polarization switching, and spatially extended stationary polarization. Solution of relevant nonstationary problem is adapted to large scale parallel computing.
STRUCTURAL INSTABILITY IN FERROELECTRICS: SUPERIMPOSING HAMILTONIAN AND STOCHASTIC DYNAMICS
ABSTRACT Structural instability of ferroelectrics distinguished by appearance of coexisting phases and spatial inhomogeneity is at variance with the predictions of statistics in the canonical ensemble. A more refined description includes ergodicity breaking which become apparent at critical temperature when the system resides in metastable state and its development lead to one of possible minimum energy states. In this study the domain growth and switching is reproduced within the framework of Fokker-Planck approach. The mathematical technique is developed for empiric Landau Hamiltonians and improved for application to first principles effective Hamiltonians with supercells and elementary l…
Application of elastostatic Green function tensor technique to electrostriction in cubic, hexagonal and orthorhombic crystals
The elastostatic Green function tensor approach, which was recently used to treat electrostriction in numerical simulation of domain structure formation in cubic ferroelectrics, is reviewed and extended to the crystals of hexagonal and orthorhombic symmetry. The tensorial kernels appearing in the expressions for effective nonlocal interaction of electrostrictive origin are derived explicitly and their physical meaning is illustrated on simple examples. It is argued that the bilinear coupling between the polarization gradients and elastic strain should be systematically included in the Ginzburg-Landau free energy expansion of electrostrictive materials.