1/<Emphasis Type="Italic">E</Emphasis><Superscript>2</Superscript> Law: Solution of the Unsolved Problem in the Physics of Ferroelectrics

An unusual frequency dependence of a coercive field observed in polycrystalline ferroelectric films of Pb(Zr_{1 ? x}Ti_x)O₃ solid solutions in a wide frequency range has been explained within the model of surface sources emitting thin ferroelectric domains with reversed polarization. This model makes it possible to interpret experimental data as the manifestation of the coercivity paradox in polycrystalline films and predicts the existence of the limiting frequency for switching of domains in agreement with the experiment. The proposed mechanism of polarization switching explains the observed temperature dependence of the activation field E_a ∝ T^?1/2. Furthermore, it predicts an increase in the activation energy for the nucleation of domains with an increase in the size of the source, indicating that the coercive field increases with the degradation of small     

Electro-optical features of antiferroelectric liquid crystal material (S)-(+)-4-(1-methylheptyloxycarbonyl) phenyl 4′-(6-octanoyloxyhex-1-oxy) biphenyl-4-carboxylate in its ferro and antiferroelectric phases

A detailed investigation of the electro-optical switching parameters of an antiferroelectric liquid crystal (S)-(+)-4-(1-methylheptyloxycarbonyl) phenyl 4′-(6-octanoyloxyhex-1-oxy) biphenyl-4-carboxylate (abbreviated as S-7H6Bi) has been carried out. S-7H6Bi has paraelectric (SmA^?) and ferroelectric (SmC^?) phases in addition to antiferroelectric (SmC^?_A) phase. Switching parameters viz. spontaneous polarization and switching time were determined by polarization reversal method. The spontaneous polarization (P_s) is found to be highly temperature dependent and decreases with temperature. The maximum value of P_s is found to be ∼90 nC/cm² whereas the switching time (t_s) is found to be of the order 1-2 ms. The temperature dependent torsional viscosity (γ_t) is of the order 10 Pa sec. It increases with decrease in temperature.     

Field-induced phase transitions and reversible field-induced inversion of chirality in tilted smectic phases of bent-core mesogens

Three homologous achiral five-ring bent-core mesogens are presented where 4-chlororesorcinol is the central core and the aromatic rings are linked by ester groups. These compounds form smectic phases with a tilted arrangement of the molecules (tilt angle ≈ 45^°). On cooling the isotropic liquid this phase adopts a fan-like texture which shows for two homologues at relatively high electric fields ( 25-35V μm^-1) an antiferroelectric electro-optical response based on the collective rotation of the molecules around their long axes. At lower temperature the application of a sufficiently high electric field leads to a continuous transition into a non-birefringent texture which exhibits randomly distributed domains of opposite handedness. These domains can be reversibly switched into a state of opposite chirality by reversal of the field polarity. This switching is bistable and shows a current response typical for a ferroelectric ground state. The possible mechanism of the field-induced phase transition, of the ferroelectric switching and of the field-induced inversion of the chirality is discussed on the base of XRD, ¹³C- and ¹H-NMR investigations, dielectric and electro-optical measurements.     

Weak dependence of spontaneous polarization on epitaxial strain in ferroelectric BiAlO3: A first-principles study

We investigate the effects of epitaxial strain on the ferroelectric properties of BiAlO₃ (BAO) using first-principles calculations. We find a large polarization (P) of 72.3 μC/cm² as well as a small energy barrier of ∼0.1 eV/formula unit for coherent ferroelectric switching of unstrained BAO. Thus, this material is suitable for applications in high-speed nonvolatile memory. We study the modification of P due to epitaxial strains of −5 to +5%, where the minus and plus signs represent the compressive and tensile strains, respectively. The polarization of BAO is insensitive to epitaxial strain; the polarization change is limited to below ∼6%. The weak sensitivity of the polarization is attributed to the stereochemical activity of Bi 6s² lone pairs as well as the inertness of the B-site Al to the polarization. The strain application modifies the switching energy barrier by up to 30%, which provides guidelines for design of devices based on BAO.     

Effects of oxygen partial pressure on the ferroelectric properties of pulsed laser deposited Ba0.8Sr0.2TiO3 thin films

The Ba_0.8Sr_0.2TiO₃ thin films were grown on the Pt–Si substrate at 700 °C by using a pulsed laser deposition technique at different oxygen partial pressure (PO₂) in the range of 1–20 Pa and their properties were investigated. It is observed that the PO₂ during the deposition plays an important role on the tetragonal distortion ratio, surface morphology, dielectric permittivity, ferroelectric polarization, switching response, and leakage currents of the films. With an increase in PO₂, the in-plane strain for the BST films changes from tensile to compressive. The films grown at 7.5 Pa show the optimum dielectric and ferroelectric properties and also exhibit the good polarization stability. It is assumed that a reasonable compressive strain, increasing the ionic displacement, and thus promotes the in-plane polarization in the field direction, could improve the dielectric permittivity. The butterfly features of the capacitance–voltage (C–V) characteristics and the bell shape curve in polarization current were attributed to the domain reversal process. The effect of pulse amplitude on the polarization reversal behavior of the BST films grown at PO₂ of 7.5 Pa was studied. The peak value of the polarization current shows exponential dependence on the electric field.     

Ferroelectric switching behavior of pulsed laser deposited Ba0.8Sr0.2TiO3 thin films

The effect of pulse amplitude on the ferroelectric and switching properties of pulsed laser deposited Ba_0.8Sr_0.2TiO₃ thin films has been studied. The structural and morphological analysis revealed that the films had a well crystallized perovskite phase and grain size of about 30–40 nm. A well saturated P–E hysteresis loop was observed with a remnant polarization (P_r) ≈ 4.8 μC/cm² and a coercive field ≈ 100 kV/cm at a frequency of 1 kHz. The P_r has been found to be decreased only 4.3% after passing 8.0 × 10⁸ cycles. The analysis of switching response with nucleation limited switching model reveals that characteristic switching time (t₀) variance is due to the random distribution of the local electric fields. The peak value of polarization current and t₀ exhibits exponential dependence on reciprocal of pulse amplitude.     

Nonlinear repolarization processes in ferroelectric liquid-crystal thin films

The dynamics of spontaneous polarization switching of the ferroelectric smectic C* in a variable electric field are examined theoretically and experimentally with the help of polarized light scattering. The observed effect of quasiresonant scattering both in freely suspended smectic films and in ordinary electro-optical cells is interpreted within the framework of the nonlinear model of isolated movable kinks in the director orientation distribution. It is shown that the maximum of the scattering intensity at the characteristic frequency of the applied electric field disappears at low temperatures and for small thicknesses of the smectic film. The dependence of the “resonant” frequency on the electric field amplitude, the proximity to the phase transition temperature, the film thickness and thickness of the ferroelectric domains, and also various material parameters is found. Estimates are made of such important characteristics as the dielectric anisotropy, viscosity, and elasticity of the smectic films. The effect of film thickness on the density distribution of the polar anisotropy energy in the film and on the corresponding shape of the moving orientation front within the film are discussed. Zh. éksp. Teor. Fiz. 111, 919–937 (March 1997)     

Fatigue of lead titanate and lead zirconate titanate thin films

The fatigue of lead titanate and lead zirconate titanate ferroelectric thin films, i.e., a change in the polarization as a function of the number of switching cycles in an external electric field, is investigated experimentally. The threshold numbers of switching cycles are determined to be 10¹⁰–10¹¹ for the lead titanate films and 10⁹–10¹⁰ for the lead zirconate titanate films. It is shown that a change in the temperature does not substantially affect the threshold number of switching cycles at which the switched polarization decreases drastically. However, an increase in the external field strength leads to a noticeable decrease in the threshold number of switching cycles. The process of fatigue is accompanied by an increase in the coercive field and the internal bias field. It is established that, as the number of switching cycles increases, the internal bias field changes more significantly as compared to the coercive field. The absence of a change in the phase composition in repeatedly switched samples indicates that the fatigue processes have a nonchemical nature. The anomaly observed in the frequency dependence of the permittivity in the frequency range 10⁶–10⁷ Hz due to the domain structure disappears after multiple switching cycles. This suggests that the observed fatigue phenomenon has a domain nature.     

Crystallization annealing effects on ferroelectric properties of Al-Doped HfO2 thin film capacitors using indium–tin–oxide electrodes

To investigate the effect of indium-tin-oxide (ITO) electrode on the Al-doped HfO₂ (Al:HfO₂) ferroelectric thin films, we fabricated and characterized the ITO/Al:HfO₂/ITO and ITO/Al:HfO₂/TiN capacitors by changing the annealing conditions. The ferroelectric remnant polarization (2P_r) was obtained to be 13.25 μC/cm² for the ITO/Al:HfO₂/TiN capacitors with the post-deposition annealing, which was termed T1. The 2P_r decreased after the post-metallization annealing due to the interface degradation between the Al:HfO₂ and ITO electrode. Alternatively, the switching time and activation field of the T1 for the ferroelectric polarization switching were 1.25 μs and 1.15 MV/cm. These parameters were sensitively influenced by the interfacial dead layer formation and the amounts of ferroelectric orthorhombic phase. Furthermore, the fatigue endurance of the T1 were improved by preventing the crowding of oxygen vacancies at interfaces between the Al:HfO₂ and top electrodes, in which the polarization values did not experience marked variations even after the fatigue cycles of 10⁸.     

Effect of the la concentration on the dielectric and optical properties of the transparent ferroelectric ceramics 75PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>-25PbTiO<Subscript>3</Subscript>

The dielectric, optical, and electro-optical properties of transparent ferroelectric ceramics 75PbMg_1/3Nb_2/3O₃-25PbTiO₃ (75PMN-25PT) with different La concentrations (2, 3, and 4 at %) have been studied. It has been shown that all the samples under study undergo a diffuse phase transition, and the degree of diffuseness increases with an increase in the La concentration. The temperature dependences of the optical transmission in different regimes of applying an electric field and the quadratic electro-optical effect have been investigated. It has been found that, at room temperature, the maximum electro-optical effect is observed in the ceramics with a La concentration of 3 at %. This is explained by the fact that the measurement temperature is close to the Vogel-Fulcher temperature at which the minimum electric field is required to induce ferroelectric states from the relaxor phase.     

Study of the paraelectric behavior of OH− ions in alkali halides with optical and caloric methods-I. Statics of dipole alignment

The electric field induced alignment of substitutional OH^? ions in a variety of alkali halide crystals was studied, using electro-optical and electro-caloric techniques. As basis for the electro-optical studies, the u.v. absorption of OH^? in various crystals was thoroughly investigated at different temperatures, and in several cases oscillator strength values were determined. The energy position of the u.v. absorption of OH^? in 13 alkali halides follows closely an Ivery-relation, which is discussed in terms of a charge-transfer model. The observed electric field induced zero-moment changes of the u.v. absorption, which depend strongly on light polarization, field direction and temperature, can be quantitatively accounted for by a paraelectric alignment model of permanent dipoles with moment p. The anisotropy of the OH^? electro-dichroism reveals <100> dipole orientation in NaCl, KCl, KBr, RBCl, RbBr and RbI, <110> orientation in KI, and <111> orientation in CsBr. The determined dipole moment values p show little variation with the host material, which excludes sizeable contributions to p from off-center shifts of the OH^? ion. The observed saturation of the electro-dichroism indicates a peculiar ‘mixed’ polarization behavior of the optical transition, which will be discussed. Reversible electro-caloric measurements, performed on several OH^? systems, reveal a field dependence and anisotropy in the high field range, which yield dipole orientation and dipole moment values in agreement with the electrooptical results.     

Anchoring energy and orientational elasticity of a ferroelectric liquid crystal

The dielectric susceptibility of a helix-free ferroelectric liquid crystal layer has been experimentally and theoretically studied as a function of the layer thickness. The investigation has been performed on the inner branch of the polarization hysteresis loop, in the region of a linear dependence of the polarization on the electric field. The experimental results are explained using the notion of effective layer thickness, which involves the characteristic distance ?? over which the orienting effect of interfaces is operative. Comparison of the experimental data and theoretical results made it possible to estimate this distance as ?? = 41 ??m and evaluate the anchoring energy (W = 2.8 × 10^?3?1.1 × 10^?2 J/m²) and the intralayer elastic constant (K?? ?? 1 × 10^?8?3 × 10^?7 N).     

Evidence of sustained ferroelectricity in glycine sodium nitrate single crystal

The nonlinear optical single crystals of glycine sodium nitrate were grown by the slow evaporation method. XRD confirmed monoclinic structure. Thermal stability and melting point (225 °C) were investigated. The dielectric behaviour of the crystals in the frequency range 20 Hz–2 MHz at different temperatures is reported in which a ferroelectric to paraelectric phase transition at T_c = 56 °C is observed. The activation energies of GSN were found to be 3.615 eV, 0.593 eV and 0.0733 eV in three temperature regions of conductivity plot due to a hopping conduction mechanism. The crystal has shown high piezoelectric charge coefficient (d₃₃) of 16 pC/N which is nearly double of observed value for γ-glycine single crystal. The spontaneous polarization P_s at room temperature was found to be 1.489 μC/cm² at applied maximum field of 26 kV/cm (1.194 μC/cm² at 12 kV/cm) and the pyroelectric coefficient was determined to be 400 μC/m²/°C. High value of squareness parameter (1.93) makes the GSN crystal suitable for switching applications. Detailed investigations of Ferro-/Piezoelectricity were observed for the first time in glycine sodium nitrate crystals which was found to preserve the ferroelectricity even after applying an electric field much higher than the saturation electric field (12–26 kV/cm). Application of GSN crystals as sensor, high power switch gears and storage memories has been established.     

Pyroelectric coefficient manipulation in doped TGS crystals

Pure and l-alanine doped Triglycine sulphate (TGS) crystals were grown in paraelectric phase (∼52 °C). Doped crystals show unequal growth rates along the ferroelectric axis. Pure TGS crystals show peculiar dielectric behavior in the ferroelectric phase, after crossing up and down the Curie point in two successive runs between room temperature and 80 °C. Much higher and unstable permittivity was found returning in the ferroelectric phase. At constant temperature (35 °C), permittivity follows a relaxation process, characterized by two relaxation times. l-Alanine doped TGS crystal shows more than one order of magnitude smaller permittivity and dielectric losses. Internal bias field of ∼1 kV/cm, induced by the dopant, made the crystal almost monodomain and pined polarization in one direction. Pyroelectric coefficient measurements were performed at constant heating rate of the samples, using a computer controlled He cryostat and Keithley 6517 electrometer. The temperature dependence of P⁺ polarization component, obtained by computer integration of the pyroelectric coefficient, was measured on a large temperature interval (−20/+80 °C). Pyroelectric coefficient of the doped samples was also measured by the same procedure, using a dc bias electric field, pointing in the opposite direction to the pined polarization. The polarization could be reversed, on the whole temperature range, by dc fields higher than bias or coercive field. Surprisingly, for the first time, the pyroelectric coefficient (p) was found constant on quite large temperature intervals. Doped TGS crystals show much smaller values of permittivity ?_r versus the pure one and consequently, get higher figure of merit M = p/?_r. The pyroelectric coefficient of this material can be tailored to become constant on a defined temperature range, under a dc field control. This characteristic makes this material valuable to be used as pyroelectric material for IR devices.     

Polarization switching properties of spray deposited CsNO3: PVA composite films

The ferroelectric and switching properties of spray deposited cesium nitrate: poly (vinyl alcohol) composite films at different substrate temperatures (T _s ) have been studied. The optimum value of remanent polarization was obtained in the film deposited at T _s =200°C, which may be due to larger structural distortion (c/a ratio) and less porosity as revealed by x-ray diffraction and field emission scanning electron microscope (FESEM) analysis. The switching current transients have been analyzed by nucleation limited switching model (NLS) with the Lorentzian distribution function. This model gives excellent agreement with the experimental polarization current throughout the whole time range. The switching parameters were determined in the composite films deposited at different T _s and found to be optimum at T _s =200°C. The effect of pulse amplitude on the domain switching properties has also been studied and analyzed. The peak value of polarization current exhibits an exponential dependence on the external applied field.     

Polarization switching kinetics of ferroelectric nanostructures of vinylidene fluoride-trifluoroethylene copolymer

The polarization switching kinetics of ferroelectric polymer Langmuir-Blodgett films and copolymer nanocrystals (nanomesas) was investigated using piezoresponse force microscopy. The nanocrystals were prepared by self-organization from Langmuir-Blodgett films of a 70% vinylidene fluoride and 30% trifluoroethylene copolymer. The polarization switching time exhibits an exponential dependence on reciprocal voltage and decreases with temperature being consistent with the nucleation switching dynamics.     

Effect of pore size on ferroelectric properties of multiferroic BiFeO3 films prepared on porous silicon

The ferroelectric properties of BiFeO₃ (BFO) films spray deposited on porous silicon have been studied. The analysis of XRD and FESEM investigations show that the crystalline strain in the BFO films increases with pore size. The BFO films on porous silicon substrate showed improvement in ferroelectric fatigue behavior, remanent polarization and ferroelectric switching time. A maximum memory window of 5.54 V at 1 MHz and a large remanent polarization (P_r) of 13.1 μC/cm² have been obtained at room temperature. The improvement in the ferroelectric properties of these films has been correlated to the crystalline strain.     

Effective coupling constants for beta and gamma transitions in medium and heavy nuclei

Effective coupling constants (g^eff) for favored (but hindered) beta and gamma transitions in medium and heavy nuclei are studied systematically. Experimental g^eff values for the β and γ transitions with parity change are presented, and are analyzed in terms of the susceptibility κ (polarization factor) defined as g^eff=g/(1 + κ). Most of the first forbidden β transitions and E1, M2, M4 gamma transitions are shown to have uniformly g^eff/g=0.2～0.4 and thus κ=3～2. Emphasis is placed upon the problem as to how large the value of susceptibility (or polarizability) due to nuclear spin-isospin core polarization is for the nuclear matter. Theories of the core polarization effects are reviewed, and are shown to predict well the observed susceptibilities κ for the various modes. Discussions are given on higher order effects, couplings with different modes, and mass and multipole dependence in the nuclear core polarization phenomena.     

Ferroelectric polarization and resistive switching characteristics of ion beam assisted sputter deposited BaTiO3 thin films

In this work, 150 nm thick polycrystalline BaTiO₃ (BTO) films were deposited on Pt/TiO₂/SiO₂/Si substrate by ion beam assisted sputter deposition technique. The bias voltage dependent resistive switching (RS) and ferroelectric polarization characteristics of Au/BTO/Pt devices are investigated. The devices display the stable bipolar RS characteristics without an initial electroforming process. Fittings to current–voltage (I–V) curves suggest that low and high resistance states are governed, respectively, by filamentary model and trap controlled space charge limited conduction mechanism, where the oxygen vacancies act as traps. Presence of oxygen vacancies is evidenced from the photoluminescence spectrum. The devices also display P–V loops with remnant polarization (P_r) of 5.7 μC/cm² and a coercive electric field (E_c) of 173.0 kV/cm. The coupling between the ferroelectric polarization and RS effect in BTO films is demonstrated.     

Hysteresis phenomena in the course of polarization evolution in a sinusoidal electric field in lead magnesium niobate crystals

The processes of polarization evolution in single crystals of the PbMg_1/3Nb_2/3O₃ model ferroelectric relaxor in a sinusoidal electric field are investigated at temperatures near and above the temperature T _d 0 of destruction of the induced ferroelectric state upon heating in zero electric field. The polarization switching current loops are measured in the ac electric field applied along the 〈111〉 and 〈110〉 pseudocubic directions. The electroluminescence intensity loops are obtained under the combined action of ac and dc electric fields applied along the 〈100〉 direction. In a certain temperature range above T _d 0 and the freezing temperature T _f in lead magnesium niobate, there are electric current anomalies, that correspond to the dynamic formation and subsequent destruction of the ferroelectric macroregions throughout each half-cycle of the ac electric field. The measurements of electroluminescence hysteresis loops demonstrate that the observed depolarization delay (related to the ac electric field amplitude) increases with an increase in the dc electric field and decreases as the ac field amplitude increases. The nature of the observed phenomena is discussed.