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 (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.

     

Surface waves in a crystal with switching Kerr nonlinearity

In this paper, we explore transverse electric surface waves propagating along the crystal with jump change of Kerr nonlinearity in dependence on field amplitude. The dielectric permittivity in the proposed model of nonlinearity is characterized by abruptly changing unperturbed dielectric constant and Kerr nonlinearity coefficient from one value to another when field amplitude exceeds the threshold value of the switching field. This allows to find exact solutions of model equations in different cases of nonlinearity signs, and to obtain the dependence of wave characteristics, including total power flux, on effective refractive index in explicit form. Such solutions describe two new types of nonlinear surface waves with specific structure depending on electric field amplitude. We derive the conditions of surface domain formation. It is found that the largest percentage of radiation is concentrated within the domain.     

Direct observation of ferroelectric domain switching in varying electric field regimes using in situ TEM

In situ Transmission Electron Microscopy (TEM) techniques can potentially fill in gaps in the current understanding interfacial phenomena in complex oxides. Select multiferroic oxide materials, such as BiFeO(3) (BFO), exhibit ferroelectric and magnetic order, and the two order parameters are coupled through a quantum-mechanical exchange interaction. The magneto-electric coupling in BFO allows control of the ferroelectric and magnetic domain structures via applied electric fields. Because of these unique properties, BFO and other magneto-electric multiferroics constitute a promising class of materials for incorporation into devices such as high-density ferroelectric and magnetoresistive memories, spin valves, and magnetic field sensors. The magneto-electric coupling in BFO is mediated by volatile ferroelastically switched domains that make it difficult to incorporate this material into devices. To facilitate device integration, an understanding of the microstructural factors that affect ferroelastic relaxation and ferroelectric domain switching must be developed. In this article, a method of viewing ferroelectric (and ferroelastic) domain dynamics using in situ biasing in TEM is presented. The evolution of ferroelastically switched ferroelectric domains in BFO thin films during many switching cycles is investigated. Evidence of partial domain nucleation, propagation, and switching even at applied electric fields below the estimated coercive field is revealed. Our observations indicate that the occurrence of ferroelastic relaxation in switched domains and the stability of these domains is influenced the applied field as well as the BFO microstructure. These biasing experiments provide a real time view of the complex dynamics of domain switching and complement scanning probe techniques. Quantitative information about domain switching under bias in ferroelectric and multiferroic materials can be extracted from in situ TEM to provide a predictive tool for future device development.     

Freezing of the Dynamics of Spontaneous Electric Field Domains in Microwave-Induced States with a Low Dissipation

The temperature dependence of the microwave photovoltage has been studied in microwave-induced states of a two-dimensional electron system, which are characterized by an almost dissipationless flow of a low-frequency current. At decreasing temperature, a smooth transition has been found from a bistable state, where the photovoltage demonstrates switching between two levels, which are due to reversals of the spontaneous electric field in a domain structure, to a steady state. The transition occurs as the shift of one of the levels of the bistable photovoltage to the other level accompanied by a decrease in the switching frequency. The results indicate the freezing of the dynamic domain structure in the state corresponding to the more stable configuration of the electric field.     

Magnetic fluid droplet deformation in electrostatic field

The stability of the ferrofluid (FF) subjected to the electric field is crucial for the application in high voltage (HV) technology. There are several cases where the fluid interacts with solid interfaces. We examined experimentally FF drop on a glass surface. The drop was exposed to the steady electric field. During tests the suspended particles started to aggregate. Changing drop's shape was recorded during a time period. It was observed that the further deformation development depends on aggregates shape and location. The results are compared with the behaviour of pure carrier fluid. Understanding the phenomenon associated with FF drop deformation can help more reliable HV component design.     

Finite temperature simulation studies of spin–flop magnetic random access memory devices

Spin–flop structures are currently being developed for magnetic random access memory devices. We report simulation studies of this system. We found the switching involves an intermediate edge-pinned domain state, similar to that observed in the single layer case. This switching scenario is quite different from that based on the coherent rotation picture. A significant temperature dependence of the switching field is observed. Our result suggests that the interplane coupling and thus the switching field has to be above a finite threshold for the spin–flop switching to be better than conventional switching methods.     

Magnetization reversal of single domain permalloy nanowires

Magnetization reversal process and magnetoresistance (MR) hysteresis of single domain permalloy nanowires are numerically investigated by using OOMMF. It is shown that the abrupt jumps in the magnetoresistance are due to the domain formation and domain wall propagation so that a magnetic domain suddenly switches from one state into another. A nonmonotonic angular dependence of the jump (switching) field is found. Coherent rotation mode is responsible for the smooth variation of MR curves. The nucleation pattern of newly born domains depends on the tilted angle of external field.     

Dependence of switching process on the perpendicular magnetic anisotropy constant in P-MTJ

We investigate the dependence of the switching process on the perpendicular magnetic anisotropy(PMA) constant in perpendicular spin transfer torque magnetic tunnel junctions(P-MTJs) using micromagnetic simulations. It is found that the final stable states of the magnetization distribution of the free layer after switching can be divided into three different states based on different PMA constants: vortex, uniform, and steady. Different magnetic states can be attributed to a trade-off among demagnetization, exchange, and PMA energies. The generation of the vortex state is also related to the non-uniform stray field from the polarizer, and the final stable magnetization is sensitive to the PMA constant. The vortex and uniform states have different switching processes, and the switching time of the vortex state is longer than that of the uniform state due to hindrance by the vortex.     

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 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     

Domain wall creep in epitaxial ferroelectric Pb(Zr(0.2)Ti(0.08)O(3) thin films

Ferroelectric switching and nanoscale domain dynamics were investigated using atomic force microscopy on monocrystalline Pb(Zr(0.2)Ti(0.8))O(3) thin films. Measurements of domain size versus writing time reveal a two-step domain growth mechanism, in which initial nucleation is followed by radial domain wall motion perpendicular to the polarization direction. The electric field dependence of the domain wall velocity demonstrates that domain wall motion in ferroelectric thin films is a creep process, with the critical exponent mu close to 1. The dimensionality of the films suggests that disorder is at the origin of the observed creep behavior.     

An investigation of time-dependent domain wall pinning effects in Tb/Fe multilayer thin films

Reverse domain nucleation time measurements have been performed on two Tb/Fe multilayer magneto-optic films exhibiting different degrees of domain wall pinning. A linear relationship between ln (reverse domain nucleation time) and the applied field has been predicted and observed for a sample exhibiting weak domain wall pinning. This is in agreement with theoretical work presented which addresses time dependence in systems possessing weak domain wall pinning. A non-linear relationship applicable over a restricted field range has been derived for a sample exhibiting strong domain wall pinning. Experimental results have indicated that this relationship is also valid.     

Analysis of ferroelectric switching in sodium nitrite:poly(vinyl alcohol) nanocomposite films

The Fourier transform infrared (FTIR) spectra and switching current response in sodium nitrite:poly(vinyl alcohol) nanocomposite films have been studied as a function of composition of NaNO₂. The switching current data fitted well to infinite-grain model (IGM) in the region t<t _s and to finite-grain model (FGM) in the region t≥t _s . The microscopic parameters like the dimensionality, the domain wall velocity, and the nucleation rate have been evaluated which provide more physical insight of the switching phenomena in the composite films. The polarization current and nucleation rate are optimum in 50 wt.% composite film and have been discussed in terms of grain size and strain variations with the composition. The effect of applied field and pulse width variation on the switching behavior of 50 wt.% composition has also been studied. The exponential field dependence of the domain wall velocity and the nucleation rate indicate that nucleation mechanism is responsible for switching phenomena in the composite films. The writing pulse width affects significantly on the switching behavior of the composite films.     

Polarization switching kinetics in ferroelectrics

The switching kinetics in ferroelectrics in the bulk polarization switching stage and in the final stage of the process are studied. Consideration is given to the specific case of switching of intrinsic ferroelectrics with 180° domains. A complete system of equations describing the switching processes and taking into account the change in repolarization in the course of a phase transformation is derived. The solution of this system is found. All the main characteristics of the switching process are calculated; namely, the evolution of the domain size distribution function is revealed and the time dependences of the domain density and flux are determined. An expression describing the variation in repolarization with time is obtained. The mechanisms of domain growth are studied. An equation for calculating the switching current and its variation with time is derived. A method is proposed for determining a number of constants for ferroelectric crystals by studying the switching current evolution.     

Ultrafast magnetization reversal dynamics investigated by time domain imaging

Spatiotemporal magnetization reversal dynamics in a Ni(80)Fe(20) microstructure is studied using ps time scale scanning Kerr microscopy. Time domain images reveal a striking change in the reversal associated with the reduction in switching time when a transverse bias field is applied. Magnetization oscillations subsequent to reversal are observed at two resonance frequencies, which sensitively depend on the bias field strength. The oscillation at f = 2 GHz is caused by the damped precession of M, while the lower frequency approximately 0.8 GHz mode is interpreted in terms of domain wall oscillation.     

Nonlinear constitutive behavior of ferroelectric materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results. Supported by the National Natural Science Foundation of China (Grant No. 10572138)     

Switching process in hard Co–Pt films

The switching process of electrodeposited Co-rich Co–Pt thin films with perpendicular magnetic anisotropy is investigated by out-of-plane angle-dependent hysteresis loop measurements. The switching field angular dependence is discussed in terms of basic reversal mechanisms. A model is proposed, based on a two-step switching process, to evaluate the variations of the intensity and orientation of the internal field as the modulus of external magnetic field is varied at each angle φ. Several experimentally observed salient features are well-understood, indicating that switching is due to inverse domain propagation.     

AC susceptibility of thin Pb films in intermediate and mixed state

Thin films of type I superconductors of a thickness comparable or less than a flux penetration length behave like type II superconductors in a mixed state. With decreasing film thickness normal domains carrying a magnetic flux get smaller with smaller number of flux quanta per domain and finally transform into single quantum flux lines, i.e. quantum vortices similar to those found in type II superconductors. We give an evidence of this behavior from the measurements of the nonlinear response of a total magnetic moment to an applied AC magnetic field, directly from the temperature dependence of an AC susceptibility.     

Dynamics of solenoidal magnetic structures in soft magnetic thin-film elements

We report on the dynamics of magnetic domain structure conversions exhibited by soft magnetic thin-film elements of elementary geometrical shape (square, disc, triangle) when exposed to a strong external magnetic field. Starting from flux closure vortex patterns, the magnetic structures evolve towards an in-plane saturated state under the influence of an external field. This irreversible and nucleation-free magnetization process occurs on the time scale of picoseconds. The details of this conversion are investigated by means of a time-resolved micromagnetic finite element modeling. We find a sensitive dependence of the temporal evolution of the magnetic structure on the value of the damping parameter in Gilbert's equation of motion. In the case of high damping, domain wall motion dominates the process, while lower damping leads to the formation of a 360° wall which collapses by emitting magnetization waves. It is shown that the mobility of vortices is generally much lower than that of domain walls. The calculations indicate that at a low damping, a magnetic vortex can act almost as a source for concentric waves in ferromagnetic thin-film elements.