Thermodynamics and kinetics of the initial stages of polarization switching in ferroelectrics

The thermodynamics and kinetics of polarization switching in ferroelectrics are studied in the specific case of switching in intrinsic ferroelectrics with 180° domains. The initial stage of the switching in the region of weak metastability is analyzed. An expression relating the critical domain size to the switching field is derived. An equation describing the evolution of the size distribution function of the switched domains is obtained. Expressions for calculating the number of polarization switching nuclei as a function of the switching field are derived.     

Polarization switching kinetics in ferroelectrics in the region of strong metastability

The thermodynamics and kinetics of polarization switching in ferroelectrics are studied in the framework of the field theory in the vicinity of the critical point of first-order phase transitions. The study is exemplified by the switching of intrinsic ferroelectrics with 180° domains. An expression describing the dependence of the domain critical size on the switching field is derived. The switching process is studied at high switching fields. Relationships for calculating the field dependence of the number of switched domains are obtained.     

Switching kinetics of ferroelastic ferroelectrics

Switching kinetics of uniaxial ferroelastic ferroelectrics (FFs) in external electric and stress fields is studied using classical theory of nucleation and growth. The stage in which the polarization and deformation reversal involves the main body of the FF and the final stage (Ostwald ripening) of the FF switching are studied with allowance for the change in the repolarization and redeformation during the phase transition. The time dependences of the repolarization and redeformation are found, and equations are derived from which the polarization current and the deformation flux, as well as their time dependence, can be calculated. The calculated main characteristics of the FF switching are compared with the experimental data for switching of Rochelle salt single crystals.     

Theory of switching of multiaxial ferroelectrics (the main stages)

The kinetics of switching of multiaxial ferroelectric crystals with 180° and 90° domains under conditions of normal and layer-by-layer domain growth is studied using the multidimensional theory of first-order phase transitions. The main stages of the process of switching of a multiaxial ferroelectric are considered under the assumption that repolarized cylinder-shaped domains grow three-dimensionally. A closed set of equations describing the kinetics of switching is derived with allowance for a change in repolarization in the course of the phase transition. Equations for the time-dependent switching current are derived. The main characteristics of switching are compared qualitatively with the experimental data on barium titanate.     

Thermodynamics and kinetics of switching of ferroelastic ferroelectrics at its initial stage

Thermodynamics and kinetics of switching of ferroelastic ferroelectrics (FFs) are studied at the initial (weak-metastability) stage. It is shown that in the switching of a uniaxial FF, the role of the electric field and mechanical stress simultaneously applied to the FF is analogous to that of supersaturation or supercooling of solutions and melts in the process of a conventional phase transition. The dependence of the critical size of a domain on the strength of the switching field is derived. In the space of domain sizes, the dependence of the steady flux of repolarized and redeformed nuclei on the applied field is determined and the time required for this steady flux to set in (latent time) and the time during which this flux is steady are estimated.     

Dynamics of the domain structure in a ferroelectric triglycinesulfate crystal

The dynamics of the domain structure in ferroelectrics of order-disorder type like triglycinesulfate is studied. The polarization properties of ferroelectrics with relaxation-type absorption are described in terms of the pseudospin formalism. A kinetic equation describing the polarization dynamics of ferroelectrics is derived using the Hamiltonian of the problem. The domain structure dynamics is obtained for different problem parameters and initial conditions. Analytical results are compared with experimental data.     

Investigation into the domain structure dynamics in ferroelectrics with an incommensurate phase

The domain structure dynamics in ferroelectrics with an incommensurate phase is studied. Sodium nitrite is considered to be a prominent representative of the above ferroelectrics. The polarization properties of these ferroelectrics are described using pseudospin formalism. A kinetic equation for describing polarization of ferroelectrics is derived using the Hamiltonian. This equation is numerically solved simultaneously with the sound-vibration equation. The results are analyzed for various crystal parameters and initial conditions. The crystal domain structure is shown to be localized for reasonably long times. This circumstance makes it possible to conclude that these domain-structure states are long-lived states of a soliton type. The importance of finding and describing these states is emphasized. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 66–70, August, 2006.     

Kinetic approach for describing the fatigue effect in ferroelectrics

A new kinetic approach is proposed for explaining the fatigue effect in ferroelectrics. A self-consistent variation in the area and geometry of the switching region of a sample upon a cyclic switching accompanied by the formation and growth of kinetically frozen domains is considered. It is assumed that fatigue is due to self-organized formation of a spatially inhomogeneous internal bias field due to retardation of bulk screening of the depolarization field. Variations in the switching charge and in the amplitude of switching current, which are calculated with the help of computer simulation of domain kinetics upon cyclic switching, are in good agreement with experimental data obtained for thin lead zirconate-titanate (PZT) thin films.     

Unusual domain evolution in semiconducting ferroelectrics: A phase field study

The effect of electrical conductivity on the domain evolution of semiconducting ferroelectrics is investigated using a phase field model which includes the drift of space charges. Phase field simulations show that the tail-to-tail 90° charged domain wall appears during the domain formation in the semiconducting ferroelectrics at zero field, which is prohibited in common insulating ferroelectrics. Due to the screening of polarization charges, the domain switching takes place through the motion of head-to-head 180° charged domain wall in the semiconducting single-domain ferroelectrics subjected to an electric field. Comparing to the insulating ferroelectrics, the semiconducting ferroelectrics have a lower speed of domain evolution due to the decrease of mobility of charged domain walls. The response of semiconducting ferroelectrics to a mechanical load is also found different from that of insulating ferroelectrics.     

Theory of switching of multiaxial ferroelectrics (Initial stage)

The classical theory of nucleation and growth is used to study the thermodynamics and kinetics of switching of multiaxial ferroelectrics. The initial stage of 180°-and 90°-domain switching is studied in the tetragonal, orthorhombic, and trigonal phases. The multidimensional kinetic theory of first-order phase transitions is applied to describe the initial stage of switching of ferroelectric crystals in the general case where three-dimensional growth (along the radius and height) of repolarized domains occurs. The energy of nucleus formation is calculated in the vicinity of the saddle point of an activation barrier in the space of sizes and shapes, and the dependence of the critical domain size on the switching field is found. The two-dimensional Fokker-Planck kinetic equation is reduced to a one-dimensional Zel’dovich equation, and a stationary solution to the Zel’dovich equation is obtained. The diffusion coefficients are derived in the size space for the normal and layer-by-layer mechanisms of domain growth. The main characteristic of the initial switching stage, namely, the steadystate flux of repolarized domains, is found as a function of the applied field.

     

Potts-Ising model for simulation of polarization switching in polycrystalline ferroelectrics

This paper proposes a scheme based on the Potts and Ising models for simulating polarization switching of polycrystalline ferroelectrics using the Monte Carlo method. The polycrystalline texture with different average grain size is produced from the Potts model. Then Ising model is implemented in the polycrystalline texture to produce the domain pattern and hysteresis loop. The domain patterns and hysteresis loops have been obtained for polycrystalline texture with different average grain size. From the results of domain pattern evolution process under an applied electric field using this scheme, an extended domain, which covers more than one grain with polarization aligned roughly in the same direction, has been observed during the polarization reversal. This scheme can well reproduce the basic properties of polycrystalline ferroelectrics and is a valuable tool for exploring the physical properties of polycrystalline ferroelectrics.     

Nonequilibrium states of the soft mode anharmonic phonons

A theory of the nonequilibrium state of the soft mode optical phonons in ferroelectrics exposed to the pumping electromagnetic field has been developed. The self-consistent field equation, which determines the phase transition temperature shift and the dielectric permeability change due to a deviation of the system from the equilibrium state is derived. A two-temperature model describing the energy transport in the presence of pumping is suggested. Analytic solutions of this model both for evolving in time and for stationary states are obtained. Spatial oscillations of the soft mode temperature are predicted for the observation time approximately equal to the energy relaxation time. It is shown that nonlinear effects can be a reason of forming of the bottleneck in the energy relaxation process. An exactly solvable model of a breather: the breather with the one-site non-linearity has been constructed and investigated.     

Ferroelectric Properties of Polycrystalline Ceramics with Dipolar Defect Simulated from the Potts--Ising Model

Physical properties of polycrystailine ferroelectrics including the contributions of the fixed dipolar defects and the average grain size in the Potts-Ising model are simulated by using the Monte Carlo method. Domain pattern, hysteresis loop and switching current of the polarization reversal process are obtained. Two processes are considered in our simulation. In the first one, the grain texture of ferroelectric ceramics are produced from the Ports model, and then the Ising model is implemented in the obtained polycrystailine texture to produce the domain pattern, hysteresis loop and switching current. It is concluded that the defect has the ability to decrease the remnant polarization P~ as well as the coercive field E~. The back switching is obviously observed after the electric field is off, and it shows some variation after introducing the fixed dipolar defect. Meanwhile, the spike of the switching current is found to lower with the increasing defect concentration and the decreasing average grain size.     

Time domain response and the data analysis of ferroelectric discharge current

The time domain method is more reliable for the study of nonlinear dielectric response compared with frequency domain analysis. A Tikhonov regularization method, which is widely adopted for ill-posed problem, is described for derivation of the relaxation time distribution function, g(τ), from the ferroelectric discharge current in time domain. The new method allows study of the structure variation and the relaxation behavior of ferroelectrics at different temperatures. For barium stannate titanate ceramics (BTS20), g(τ) has been successfully derived; the relaxation peaks move to shorter times with increasing temperature in the range 20–60°C, which may indicate a space charge thermal activation process. However, g(τ) could not be derived from the discharge current by the regularization method for BTS20 at temperatures above 60°C or for lanthanum-doped lead zirconium titanate transparent ceramic (PLZT), since the data do not satisfy the discrete Picard condition, which is a valid criterion for regularization method.     

Simulation of the dynamics of the spatial domain structure of a ferroelectric triglycine sulfate crystal

The dynamics of a domain structure of order-disorder ferroelectrics similar to triglycine sulfate is considered. Starting from the Hamiltonian of the problem, a kinetic equation describing the polarization dynamics of ferroelectrics is derived. The results are analyzed and compared with the experimental data.     

Switching current noise and relaxation of ferroelectric domains

We simulate field-induced nucleation and switching of domains in a three-dimensional model of ferroelectrics with quenched disorder and varying domain sizes. We study (1) bursts of the switching current at slow driving along the hysteresis loop (electrical Barkhausen noise) and (2) the polarization reversal when a strong electric field was applied and back-switching after the field was removed. We show how these processes are related to the underlying structure of domain walls, which in turn is controlled by the pinning at quenched local electric fields. When the depolarization fields of bound charges are properly screened we find that the fractal switching current noise may appear with two distinct universal behaviors. The critical depinning of plane domain walls determines the universality class in the case of weak random fields, whereas for large randomness the massive nucleation of domains in the bulk leads to different scaling properties. In both cases the scaling exponents decay logarithmically when the driving frequency is increased. The polarization reverses in the applied field as a power-law, while its relaxation in zero field is a stretch exponential function of time. The stretching exponent depends on the strength of pinning. The results may be applicable for uniaxial relaxor ferroelectrics, such as doped SBN:Ce. Received 7 February 2002 / Received in final form 10 April 2002 Published online 9 July 2002     

Modeling of Seignette salt by a ferroelectric: Polarization lattices as a result of interaction with the acoustic subsystem

The dynamics of the domain structure observed in ferroelectrics with two dipoles per ferroelectric cell—analogues of the Seignette salt crystal—is studied. Kinetic equations for the mean values of pseudospin operators are derived based on the Hamiltonian of the problem. These equations are used to numerically study the evolution of the ferroelectric polarization as a function of the problem parameters for both transparent and polarized interfaces.     

Magnetic field penetration into half-space for type-II superconductors of the second kind

Equations that simulate the magnetic induction and current density distributions in half-space in view of the power I-V characteristic are derived. The magnetization front velocity is determined for a given mean rate of external magnetic field variation at the boundary of the sample. An integral condition for the electrical resistance (nonlinearly depending on the magnetic field) under which the magnetic flux penetrates into the sample with a finite rate is found. An analytical solution that simulates the power variation of the magnetic field at the boundary is given. The Bean generalized model describing the current density distribution near the critical current is considered. It is shown that solutions like shock waves may arise beyond the applicability domain of the Bean model.     

Study of ferroelectric switching by domain-wall induced light scattering

Measurements of 90°-scattering of weak laser light are used to investigate pulsed domain switching in ferroelectrics. The studies were performed on strontium-barium niobate (SBN) single crystals. A good agreement of the switching parameters estimated from the optical measurements with those obtained by means of conventional electrical methods proves the validity of the optical method for switching studies. Due to the limited scattering volume in all three spatial dimensions, the method facilitates local probing of the switching within the crystal bulk. In particular, local specialities of the domain density can be detected. Furthermore, the excellent time resolution inherent in optical probing techniques allows for a comprehensive study of the dynamics.