M. D. Glinchuk

The internal electric field originating from the mismatch effect and its influence on ferroelectric thin film properties

The influence of the mismatch effect on thin ferroelectric film properties has been studied in the phenomenological theory framework. The polarization dependent part of the surface energy that defined the boundary conditions for the Euler–Lagrange differential equation was written as a surface tension energy. The latter was expressed via the surface polarization and the tension tensor related to the mismatch of the substrate and film lattice constants and thermal expansion coefficients. The interfacial strain caused by the mismatch effect induces the additional surface polarization Pm via a piezoelectric effect that arises near the surface in any film. The new parameter Pm/PS (PS is the known value of the spontaneous polarization in the bulk ferroelectric material at T = 0 K) appeared in the derived phenomenological equations. So we calculate the influence of the parameter Pm/PS on the depth distribution of the dimensionless film polarization P/PS, its dependence on temperature, film thickness and applied electric field, as well as that on the hysteresis loop shape, coercive field values, phase diagram and average dielectric susceptibility temperature dependence. Non-zero Pm/PS values cause a mismatch induced thickness dependent internal electric field Em. We have shown that this field drastically influences all the properties. In particular, the polarization profile becomes asymmetrical, the polarization temperature dependence resembles that in the external electric field and there is a possibility of external field screening by the internal field Em. The asymmetry obtained for the hysteresis loop suggests that it is possible that the self-polarization phenomenon recently observed in some films is related to the mismatch effect. The thickness induced ferroelectric–paraelectric phase transition has been shown to exist when |Pm|/PS 1 could be the physical reason for the ferroelectric phase conservation in ultrathin film. The possibility of observing the peculiarities of the film property temperature and thickness dependences related to the mismatch effect is discussed.The ferroelectric thin film properties were calculated in phenomenological theory framework. Surface energy that defined boundary conditions for Euler-Lagrange differential equation was written as surface tension energy. The latter was expressed via surface polarization and tension tensor related to mismatch of a substrate and a film lattice constants and thermal expansion coefficients. The calculations of the film polarization distribution, temperature, thickness and external electric field dependence and hysteresis loops as well as average dielectric susceptibility dependence on temperature and film thickness have been performed allowing for mismatch-induced polarization Pm, leading to appearance of internal thickness dependent field. It has been shown that this field influences drastically all the properties behaviour. In particular the polarization profile becomes asymmetrical, average polarization temperature dependence resembles the one in the external electric field, and there is possibility of external field screening by the internal one. The obtained asymmetry of hysteresis loop makes it possible to suppose that the self-polarization phenomenon recently observed in some films is related to mismatch effect. The thickness induced ferroelectric-paraelectric phase transition has been shown to exist when the Pm value is smaller than the polarization PS in the bulk. The large enough mismatch effect could be the physical reason of ferroelectric phase conservation in ultrathin film. The possibility to observe the peculiarities of the films properties temperature and thickness dependencies related to mismatch effect is discussed.

Phase transitions induced by confinement of ferroic nanoparticles

A general approach for considering primary ferroic (ferroelectric, ferromagnetic, ferroelastic) nanoparticle phase transitions was proposed in phenomenological theory framework. The surface stress, order parameter gradient, and striction, as well as depolarization, demagnetization, and de-elastification effects, were included into the free energy. The strong intrinsic surface stress under the curved nanoparticle surface was shown to play the important role in the shift of transition temperature (if any) up to the appearance of a new ordered phase absent in the bulk ferroic. Euler-Lagrange equations obtained after the Landau-Ginzburg-Devonshire free energy minimization were solved by direct variational method. This leads to the conventional form of the free energy with renormalized coefficients depending on nanoparticle sizes, surface stress, and electrostriction tensor values, and so opens the way for polar property calculations by algebraic transformations. Surface piezoeffect causes built-in electric field that induces an electretlike polar state and smears the phase transition point. The approximate analytical expression for the size-induced ferroelectric transition temperature dependence on cylindrical or spherical nanoparticle sizes, polarization gradient coefficient, correlation radius, intrinsic surface stress, and electrostriction coefficient was derived. Under the favorable conditions (radius of

The depolarization field effect on the thin ferroelectric films properties

5\char21{}50\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

Influence of impurities on the properties of rare-earth-doped barium- titanate ceramics

and compressive surface stress), spatial confinement induces a ferroelectric phase in incipient ferroelectric nanowires and nanospheres. The prediction of size-induced ferroelectricity in

Random fields and their influence on the phase transitions in disordered ferroelectrics

\mathrm{K}\mathrm{Ta}{\mathrm{O}}_{3}

Interfacial polarization and pyroelectricity in antiferrodistortive structures induced by a flexoelectric effect and rotostriction

nanorods with radius less than

Ferroelectric thin film properties—Depolarization field and renormalization of a “bulk” free energy coefficients

5\char21{}20\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

Central-Peak Components and Polar Soft Mode in Relaxor PbMg1/3Nb2/3O3 Crystals

at room temperature could be useful for the next generation of devices based on three-dimensional nanostructures.

Giant magnetoelectric effect induced by intrinsic surface stress in ferroic nanorods

Abstract The calculation of the spontaneous polarization (Ps), dielectric susceptibility (χ) and pyroelectric coefficient (Π) of the ferroelectric films has been performed in the phenomenological theory framework. Euler–Lagrange equation was solved analytically under the boundary conditions with different extrapolation lengths at two surfaces, respectively. The depolarization field contribution was taken into account in the model of short-circuited mono domain ferroelectric film, treated as perfect insulator. The detailed analysis of the aforementioned quantities’ space distribution and their average values in two cases with and without depolarization field was carried out. It was shown that the depolarization field shifts critical temperature to smaller value and critical thickness to bigger value in comparison to those obtained without accounting for the depolarization field, this shift being larger the smaller the extrapolation length values. This phenomenon is related to the different thickness dependence of the critical temperature, namely Tc−Tcl∼1/l or Tc−Tcl∼1/l2 with and without depolarization field contribution correspondingly. Meanwhile average values of Ps, χ and Π are similar in both cases. The depolarization field was shown to flatten Ps, χ and Π space distributions, which have the peculiarities otherwise (e.g. small maxima in χ and Π coordinate profiles near the film surfaces). It was shown that depolarization field influence in a short-circuited film could be neglected when the film thickness or the extrapolation lengths in the boundary conditions are larger than correlation length value.

Ferroelectric and glassy states in La-modified lead zirconate titanate ceramics: A general picture

Investigations of impurity centers, electrical resistivity and microstructure of BaTiO3 ceramics doped with rare-earth ions Y, La, Nd, Sm, Dy and Lu at concentrations x = 0.001–0.005 were carried out. Electron paramagnetic resonance, X-ray diffraction and electron microscopy were used for measurements. The most intense EPR lines were shown to belong to paramagnetic complexes Fe3+–VO and Ti3+–Ln3+ (Ln = rare-earth ion, VO = oxygen vacancy). A change in symmetry of the center Fe3+–VO at the transition temperature from the ferroelectric to paraelectric phase has been revealed for the first time. Measurements of the dependence of EPR line intensities and electrical resistivity with rare-earth ion concentrations were performed. The observed correlation in their behaviour showed an essential role of the identified paramagnetic complexes in the appearance of BaTiO3 ceramic semiconducting properties and the positive temperature coefficient of resistance (PTCR) effect. The latter effect was at a maximum for x ≈ xc where xc ≈ 0.002–0.003 is the critical rare-earth ion concentration which determines the excess charge compensation mechanism. Up to xc, the rare earths investigated, (except for the small ion Lu), substitute for barium, and the main compensation mechanism is an electronic mechanism. At high concentrations (x > xc) in the case of large ions (e.g. La), substitution is at barium sites, with the creation of titanium vacancies, whereas intermediate ions (e.g. Y) begin to substitute for titanium. The influence of impurities on the BaTiO3 microstructure, including the grain sizes, is discussed.