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The review covers the theoretical and experimental results obtained in the recent years by the scientists with the help of comprehensive investigation of nanoferroics and multiferroics. The main attention will be paid to spontaneous flexoeffects and reentrant phase in nanoferroics as well as to a recently discovered giant magnetoelectric effect in multiferroics., Comment: 15 pages, 8 figures

In the framework of Landau--Ginzburg--Devonshire (LGD) phenomenological theory, the influence of misfit strains, surface energy, and finite-size effects on phase diagrams, polar properties, and hysteresis loops has been calculated for multilayered thin films of the type ferroelectric/virtual ferroelectric. The influence of elastic deformations that arise at the interface thin film--substrate owing to a mismatch between the lattice constants in the film and the substrate on the phase diagrams of multilayered thin films virtual ferroelectric SrTiO$_{3}$/ferroelectric BaTiO$_{3}$ has been studied for the first time. In contrast to bulk BaTiO$_{3}$, in which only four phases (cubic, tetragonal, orthorhombic, and rhombohedral) can exist, it turned out that six thermodynamically stable BaTiO$_{3}$ phases (paraelectric phase and tetragonal (FEc), two monoclinic (FEaac and FEac), and two orthorhombic (FEa and FEaa) ferroelectric phases) can exist in multilayered SrTiO$_{3}$/BaTiO$_{3}$ films. The main polar properties of hysteresis loops (shape, coercive field, and spontaneous polarization) in thin multilayered SrTiO$_{3}$/BaTiO$_{3}$ films are calculated. It is shown that the system demonstrates a strong dependence of its polar properties on the thickness of SrTiO$_{3}$ and BaTiO$_{3}$ layers, as well as on the elastic misfit strains, with SrTiO$_{3}$ playing the role of dielectric layer: the thicker the layer, the stronger is the depolarization field, which, in its turn, reduces the spontaneous polarization in the BaTiO$_{3}$ film., Comment: 9 pages, 5 figures

Using the symmetry theory we analyze of the flexomagnetic effect in all 90 magnetic classes and showed that 69 of them are flexomagnetic. Then we explore how the symmetry breaking, inevitably present in the vicinity of the surface, changes the local symmetry and thus the form of the flexomagnetic tensors. All possible surface magnetic classes (in the number of 19) were obtained from the 90 bulk magnetic classes for the surface cuts 001, 010 and 100 types. It appeared that all 90 bulk magnetic classes become flexomagnetic, piezomagnetic and piezoelectric in the vicinity of surface. Using the free energy approach, we show that the flexomagnetic effect leads to a new type of flexo-magnetoelectric (FME) coupling in nanosized and bulk materials, in all spatial regions, where the polarization and (anti)magnetization vectors are spatially inhomogeneous due to external or internal forces. The linear FME coupling, proportional to the product of the gradients of (anti)magnetization and polarization, flexoelectric and flexomagnetic tensors, is significant in nanosized ferroelectrics-(anti)ferromagnetics, where gradients of the polarization and magnetization obligatory exist. The spontaneous FME coupling induced by the spatial confinement give rise to the size-dependent linear magnetoelectric coupling in nanosized ferroelectrics-(anti)ferromagnetics. We show that the flexomagnetic effect may lead to improper ferroelectricity in bulk (anti)ferromagnetics via the linear and nonlinear FME coupling. Inhomogeneous spontaneous polarization is induced by the (anti)magnetization gradient, which exists in all spatial regions, where polarization varies and (anti)magnetization vector changes its direction. The gradient can be induced by the surface influence as well as by external strain via e.g. the sample bending., Comment: 29 pages, 6 figures, 5 tables

Based on our analytical results [http://arxiv.org/abs/1006.3670], we predict that undoped nanoparticles (size <10-100nm) of incipient ferroelectrics without any magnetic ions can become ferromagnetic even at room temperatures due to the inherent presence of a new type of magnetic defects with spin S=1, namely oxygen vacancies, where the magnetic triplet state is the ground state in the vicinity of the surface (magnetic shell), while the nonmagnetic singlet is the ground state in the bulk material (nonmagnetic core). Consideration of randomly distributed magnetic spins (S=1) had shown that magnetic properties of incipient ferroelectric nanoparticles are strongly size and temperature dependent due to the size and temperature dependence of their dielectric permittivity and the effective Bohr radius proportional to permittivity. The phase diagrams in coordinates temperature - particle radius are considered. In particular, for particle radii less that the critical radius ferromagnetic long-range order appears in a shell region of thickness 5 - 50 nm once the concentration of magnetic defects exceeds the magnetic percolation threshold. The critical radius is calculated in the mean field theory from the condition of the magnetic defects exchange energy equality to thermal energy. For particle radii higher than critical value only the paramagnetic phase is possible. The conditions of the super-paramagnetic state appearance in the assembly of nanoparticles with narrow distribution function of their sizes are discussed also., Comment: 33 pages, 7 figures, 2 appendices

Using the quantum-mechanical approach combined with the image charge method we calculated the lowest energy levels of the impurities and neutral vacancies with two electrons or holes located in the vicinity of flat surface of different solids. We obtained that the magnetic triplet state is the ground state of the impurities and neutral vacancies in the vicinity of surface, while the nonmagnetic singlet is the ground state in the bulk for e.g. He atom, Li+, Be++, etc. ions. The energy difference between the lowest triplet and singlet states strongly depends on the electron (hole) effective mass, dielectric permittivity of the solid and the distance from the surface. Pair interaction of the identical surface defects (two doubly charged impurities or vacancies with two electrons or holes) reveals the ferromagnetic spin state with the maximal exchange energy at the definite distance between the defects (~5-25 nm). We obtained that the nonmagnetic singlet state is the lowest one for a molecule with two electrons formed by a pair of identical surface impurities (like surface hydrogen), while its next state with deep enough negative energy minimum is the magnetic triplet. The metastable magnetic triplet state appeared for such molecule at the surface indicates the possibility of metastable orto-states of the hydrogen-like molecules, while they are absent in the bulk of material. We hope that obtained results could provide an alternative mechanism of the room temperature ferromagnetism observed in TiO2, HfO2, and In2O3 thin films with contribution of the oxygen vacancies., Comment: 59 pages, 11 figures, 5 appendices

The symmetry breaking inevitably present in the vicinity of any surface, namely an inversion center disappears in surface normal direction and only axes and planes normal to the surface conserve, gives rise to the spontaneous piezomagnetic, piezoelectric and magnetoelectric effects in nanosystems, while the effects can be absent in a bulk material. All these phenomena are inherent to nanos made of materials belonging to all ninety bulk magnetic classes. Therefore the new linear magnetoelectrics should appear among nanomaterials, nonpiezomagnetic and nonpiezoelectric in the bulk. To demonstrate this we consider the typical cases of ultra-thin films, nanowires and nanospheres. Coupled with a surface stress for nanoparticles and a mismatch strains for thin films on substrates the surface piezomagnetic and piezoelectric effects lead to the appearance of built-in magnetic and electric fields respectively. The built-in fields play an important role in the appearance of self-magnetization and self-polarization in the nanosystems paramagnetic and paraelectric in the bulk and can lead to the appearance of some other interesting properties absent in the bulk. We obtained analytical dependencies on sizes for the built-in fields and magnetoelectric coupling coefficients. The values of the built-in fields increase with the decrease of film thickness h or nanoparticles radii R as ~1/h or 1/R2 respectively, while the magnetoelectric coupling is inversely proportional to the sizes in both cases. This shows the strong influence of sizes on the considered properties of nanos and so opens the ways to govern the properties by the choice of the sizes and to create new multifunctional nanomaterials., Comment: 12 pages, 2 Tables, 1 Appendix

In the paper we present analytical calculations of the profiles and average values correlation radius of polarization fluctuations and generalized susceptibility in thin ferroelectric films of thickness L with in-plane (a-films) and out-of-plane (c-films) polarization orientation. The contribution of polarization gradient, surface energy and depolarization field (if any) were taken into account. For the second order ferroelectrics the correlation radius and generalized susceptibility diverge at the film critical thickness Lcr as anticipated. In the case of a-films where depolarization field is absent, the surface energy and polarization gradient govern the size effects such as thickness-induced phase transition, corresponding correlation radius and generalize susceptibility divergence in the phase transition point. In the case of c-films with strong depolarization field, the surface energy, polarization gradient, intrinsic depolarization effect related with polarization inhomogeneous distribution and incomplete screening in the electrodes determine the correlation radius and generalized susceptibility size effect. At that contribution of all the factors are comparable at reasonable material parameters, but could be easily tuned by varying of surface energy coefficients, polarization gradient contribution and screening conditions., Comment: 20 pages, 4 Figures, 2 Appendices

For the first time we predict the conditions of superparaelectric phase appearance in the ensemble of non-interacting spherical ferroelectric nanoparticles. The superparaelectricity in nanoparticle was defined by analogy with superparamagnetism, obtained earlier in small nanoparticles made of paramagnetic material. Calculations of correlation radius, energetic barriers of polarization reorientation and polarization response to external electric field, were performed within Landau-Ginzburg phenomenological approach for perovskites Pb(Zr,Ti)O3, BiFeO3 and uniaxial ferroelectrics rochelle salt and triglycine sulfate., Comment: 28 pages, 7 figures, 3 Appendices, to be submitted to Phys. Rev. B

We show that misfit strain originated from the film-substrate lattice mismatch strongly increases the value of the quadratic magnetoelectric coupling. The giant magnetoelectric coupling, size effects and misfit strain cause strong changes of ferroic films phase diagrams at zero external magnetic and electric fields, in particular, the transformation of antiferromagnetic phase into ferromagnetic or ferrimagnetic ones for compressive or tensile misfit strains correspondingly as well as thickness induced paramagnetic or/and paraelectric phases appearance. Ferromagnetism appearance and magnetoelectric coupling increase in thin ferroelectric-antiferromagnetic films is in agreement with available experimental data and opens the way for tailoring of ferroic films magnetic and electric properties., Comment: 25 pages, 3 Figures, 1 Table, 2 Appendices

We show that the presence of free carriers in a substance can generate the multiferroic behavior. Namely, if the substance has mixed-valence ions, which can supply free carriers and have electric dipole and spin moments, all three types of long-range order (ferromagnetic, ferroelectric and magnetoelectric (ME)) can occur at low temperature. The physical origin of the effect is that charge carriers can mediate the multiferroic behavior via spin - spin (RKKY), dipole-dipole and dipole - spin interactions. Our estimate of the interaction magnitude shows that there exist an optimal carrier concentration, at which the strength of ME interaction is maximal and comparable to that of spin-spin RKKY interaction. This permits to conclude that in substances, where RKKY interaction between local spins is not small, a substantial value of free carriers mediated ME interaction can occur. Our analysis shows that disorder in the above substances does not suppress multiferroic effects., Comment: 4 pages, 1 figure

The general approach for the consideration of the magnetoelectric effects in ferroic nanorods is proposed in the framework of the phenomenological theory. The intrinsic surface stress, magneto- and electrostriction as well as piezoelectric and piezomagnetic effects are included into the free energy. The intrinsic surface stress under the curved nanoparticle surface is shown to play an important role in the shift of ferroelectric and ferromagnetic transition temperatures and built-in magnetic and electric fields appearance, which are inversely proportional to the nanorod radius. We consider the case of quadratic and linear magnetoelectric coupling coefficients. The linear coupling coefficient is radius independent, whereas the quadratic ones include terms inversely proportional to the nanorod radius and thus strongly increase with decrease of the radius. The predicted giant relative dielectric tunability in the vicinity of ferromagnetic and ferroelectric phase transition points induced by quadratic magnetoelectric coupling increases by 2-50 times. The quadratic magnetoelectric coupling dramatically changes the phase diagrams of ferroic nanorods when the radius decreases. In particular the second order phase transition may become a first one, the triple point state characterized by continuous set of order parameters appears at zero external electric and magnetic fields and the tricritical points appear under external fields., Comment: 36 pages, 11 figures, 3 Appendices

Using electron spin resonance, lattice position and dynamic properties of Mn2+ ions were studied in 0.5 and 2 % manganese doped SrTiO3 ceramics prepared by conventional mixed oxide method. The measurements showed that Mn2+ ions substitute preferably up to 97 % for Sr if the ceramics is prepared with a deficit of Sr ions. Motional narrowing of the Mn2+ ESR spectrum was observed when temperature increases from 120 K to 240-250 K that was explained as a manifestation of off-center position of this ion at the Sr site. From the analysis of the ESR spectra the activation energy Ea = 86 mV and frequency factor 1/?0 ? (2-10)x10^(-14) 1/s for jumping of the impurity between symmetrical off-center positions were determined. Both values are in agreement with those derived previously from dielectric relaxation. This proves the origin of dielectric anomalies in SrTiO3:Mn as those produced by the reorientation dynamics of Mn2+ dipoles., Comment: 16 pages, 6 figures

Recently new incipient ferroelectrics with off-center ions SrTiO3 with Mn2+ substituted for Sr2+ was revealed (Tkach et. al PRB 73, 104113 (2006). Experimental investigation of Sr1-xMnxTiO3 properties, namely temperature, frequency and external electric field dependence of dielectric permittivity at different concentrations gave evidence about phase transitions induced by the impurities. However their nature was not found out up to now because of the absence of the theoretical analysis of the results. In this paper we performed such analysis by the theoretical description of the temperature of dielectric permittivity maxima dependence on Mn2+ concentration, the change of residual polarization with temperature, frequency and temperature dependence of the permittivity with Arrhenius and Vogel-Fulcher law at smaller and larger concentration respectively. The obtained results had shown that at x less than 0,03 and x between 0,15 and 0,03 the considered system Sr1-xMnxTiO3 is in dipole glass state and mixed ferroglass phase respectively., Comment: 8 pages, 3 figures

In the paper we consider size effects of phase transitions and polar properties of the thin antiferroelectric films. We modified phenomenological approach proposed by Kittel. The Euler-Lagrange equations were solved by direct variational method. The free energy with renormalized coefficients depending on the film thickness has been derived. The approximate analytical expression for the coefficients dependence on film thickness, temperature, polarization gradient coefficient and extrapolation lengths were obtained. We have shown how the anti-ferroelectric double hysteresis loop transforms into the ferroelectric single one under the film thickness decrease. Proposed theoretical consideration explains the experimental results obtained in antiferroelectric PbZrO_3 thin films., Comment: 15 pages, 5 figures, 2 appendices

In this paper we study the size effects of the ferroelectric nanotube phase diagrams and polar properties allowing for effective surface tension and depolarization field influence. The approximate analytical expression for the paraelectric-ferroelectric transition temperature dependence on the radii of nanotube, polarization gradient coefficient, extrapolation length, surface tension and electrostriction coefficient was derived. It was shown that the transition temperature could be higher than the one of the bulk material for negative electrostriction coefficient. Therefore we predict conservation and enhancement of polarization in long ferroelectric nanotubes. Obtained results explain the observed ferroelectricity conservation and enhancement in Pb(Zr,Ti)O_3 and BaTiO_3 nanotubes., Comment: 10 pages, 3 figures, to be presented at "VIII Ukrainian-Polish Meeting on Ferroelectrics"

For the first time we proposed the model for the calculations of the relaxor ferroelectrics films properties in the framework of the random field theory. We took into account the misfit strain between film and substrate as well as surface piezoelectric effect that causes built-in electric field in the strained films. In the statistical theory framework we calculated random field distribution function with the electric dipoles and monopoles as the field sources. It was shown that with thickness decrease the mean field decreases, while the width of the distribution function increases. This leads to the additional smearing of the phase transition in the films in comparison to the bulk relaxors. As an example the dependence of the order parameter and dielectric susceptibility on the film thickness, temperature and random fields distribution function parameters was obtained. For free standing film the existence of critical thickness of relaxor state transformation into glassy state was predicted. Contrary to this the appearance of misfit strain induced ferroelectric phase appeared to be possible for some pairs film-substrate. We have shown that susceptibility temperature maximum shift with frequency in relaxor ferroelectric thin films obeys Vogel-Fulcher law with parameters dependent on film thickness. For the first time the analytical dependences of freezing temperature decreases and activation energy on the thickness was obtained, namely freezing temperature decreases and activation energy increases with film thickness decrease. Obtained results quantitatively agree with the available experimental data for PbMg1/3Nb2/3O3 relaxor thin films., Comment: 18 pages, 6 figures

We calculated the influence of surface tension on the barriers of oxygen ionic conductivity in nanograin ceramics. Activation energy of oxygen ions diffusion via oxygen vacancies which were considered as the dilatational centers was calculated. This energy was shown to decrease with nanoparticle sizes decreasing. The distribution function of activation energy was derived on the basis of distribution of nanoparticle sizes. We obtained an analytical expressions of ionic conductivity dependence on the temperature and nanograin sizes. These formulas fitted pretty good the observed earlier behaviour of oxygen conductivity in nanograin ceramics of ZrO2:16% Y observed earlier. Therefore the consideration we carried out had shown that the surface tension in nanoparticles is physical mechanism responsible for the essential enhancement of the oxygen ionic conductivity observed in nanograin samples, the main contribution to the conductivity being related to the region in vicinity of the particle surface., Comment: 8 pages, 7 figures

The theoretical and experimental investigation of ferroelectric nanopowders is performed. The manifestation in radiospectroscopy spectra of size driven ferroelectric-paraelectric phase transition at some critical particle average size was the main goal of the consideration. In theoretical part the size effect for the materials with ferroelectric tetragonal phase and cubic paraelectric phase was considered allowing for the spontaneous polarization inhomogeneity inside a particle and distribution of particle sizes. In ESR the transformation of the spectra from tetragonal symmetry to cubic symmetry with decreasing of nanoparticle sizes was calculated. Measurements of Fe3+ ESR spectra in nanopowder of BaTiO3 were carried out at room temperature. The decrease of intensity of tetragonal symmetry ESR lines of Fe3+ and appearance of cubic symmetry line with asymmetry of the shoulders was observed with the average sizes decrease with complete disappearance of tetragonal spectrum at average size less or equal 40 nm. The comparison of the theory with experiment was carried out. The value of critical size Rc = 40 nm was extracted from ESR data. The asymmetry and broadening of right hand side shoulder of ESR cubic symmetry line was shown to be related to contribution of paramagnetic centers in the vicinity of the particles surface. The deconvolution of the cubic line allowed to show, that this region size is about 3 nm., Comment: 10 pages, 8 figures

In present work we calculated the three components of polarization in phenomenological theory framework by consideration of three Euler-Lagrange equations, which include mismatch effect and influence of misfit dislocations, surface piezoelectric effect caused by broken symmetry on the film surface, surface tension and depolarization field. These equations were solved with the help of variational method proposed by us earlier. This approach lead to the free energy in the form of algebraic equation of different powers of polarization components with the coefficients dependent on film thickness, mismatch effect, temperature and other parameters. Several new terms proportional to misfit strain appeared in the free energy expression: built-in electric field normal to the surface originated from piezoelectricity in vicinity of surface even for the cubic symmetry of bulk ferroelectrics, odd powers of normal to the surface component of polarization. The obtained free energy made it possible to calculate all properties of the film by conventional procedure of minimization. As an example we calculated phase diagrams of PZT 50/50 films on different substrates that lead to compressive or tensile strain. The calculations of pyroelectric coefficient and dielectric permittivity temperature dependencies had shown the electret-like polar state, e.g. existence of pyroelectricity, below the critical thickness of ferroelectric-paraelectric phase transitions. Our theory predicts, that mismatch-induced field could be compatible with thermodynamic coercive field and thus cause self-polarization in thin ferroelectric films., Comment: 23 pages, 7 figures, 1 table

The model for calculation of relaxor ferroelectrics thin films properties is proposed. The basis of the model is the theory of random field. This field is originated from the chemical disorder allowing for influence of the film surfaces, which destroys the polar long-range order and transform it into mixed state of ferroelectric glass (FG) or dipole glass (DG). The spatial profiles and averaged over coordinate inside the film values of properties of relaxor ferroelectric film were calculated with the random field distribution function. As an example the dependence of the order parameter on film thickness, temperature and distribution function characteristics was obtained. The critical thickness and temperature of the size-driven phase transition from FG to DG state as a function of the film and distribution function characteristics were calculated., Comment: 12 pages, 8 figures

In present work we calculated the three components of polarization in phenomenological theory framework by consideration of three Euler-Lagrange equations, which include mismatch effect and influence of misfit dislocations, surface tension and depolarization field. These equations were solved with the help of variational method proposed by us earlier. This approach lead to the free energy in the form of algebraic equation of different powers of polarization components with the coefficients dependent on film thickness, mismatch effect, temperature and other parameters. Several new terms proportional to misfit strain appeared in the free energy expression: built-in electric field normal to the surface originated from piezoelectricity in vicinity of surface even in the cubic symmetry of bulk ferroelectrics, renormalization of bulk transition temperature via electrostriction, odd powers of normal to the surface component of polarization. The obtained free energy made it possible to calculate all properties of the film by conventional procedure of minimization. It was shown that in both cases self-polarized phase does exist in definite regions of aforementioned coordinates, its nature being mismatch effect. The calculations of pyroelectric coefficient and dielectric permittivity dependencies on temperature, strain and thickness had shown the unusual behaviour of these quantities, e.g. existence of pyroelectricity at thicknesses less than critical one for ferroelectric-paraelectric phase transition., Comment: 19 pages, 10 figures, 1 table

Within the framework of the phenomenological Ginzburg-Landau theory influence of semiconductor electrodes on the properties of thin ferroelectric films is considered. The contribution of the semiconductor electrodes with different Debye screening length of carriers is included in functional of free energy. The influence of highly doped semiconductor electrodes on the depolarization field and the film properties was shown to be great., Comment: 3 pages, 1 figure

Within the framework of the phenomenological Ginzburg-Landau theory influence of metallic electrodes on the properties of thin ferroelectric films is considered. The contribution of the metallic electrodes with different screening length of carriers is included in functional of free energy. The influence of conventional metallic electrodes on the depolarization field and the film properties was shown to be practically the same as for superconductive ones., Comment: 3 pages, 1 figure

We explain the phenomena of ferroelectric phase transition temperature $T_c$ enhancement beyond the end members in perovskite solid solutions like BiMeO$_3$-PbTiO$_3$ (Me=Sc, In, etc.) is related to nonlinear and spatial correlation effects. The explanation is based on the calculation of $T_c$ in the framework of our random field theory with additional account for nonlinear effects in the above substances. We show that the maximum of $T_c$ for certain PbTiO$_3$ content takes place when coefficient of nonlinearity is positive, the value of this coefficient is found from best fit between theory and experiment. This nonlinearity coefficient is the only adjustable parameter of the theory. We show that enhancement of positive nonlinearity coefficients enhances greatly the $T_c$ maximum over its value for end members. The theory lays the foundation to calculate not only $T_c$ for above solid solutions but virtually any equilibrium and/or nonequilibrium thermodynamic characteristics such as static and dynamic dielectric susceptibility, specific heat etc as a functions of PbTiO$_3$ content, temperature, electric field and other external parameters., Comment: Accepted for publication in PRB. 5 Pages, 2 figures

The films of order-disorder type ferroelectrics were considered in the mean field approximation taking into account depolarization field. It was shown that size effects in this system could be described on the base of bulk system equation of state with Curie temperature dependent on the film thickness. The critical size hc and critical temperature Tc of phase transition from ferroelectric to paraelectric phase was calculated allowing for the depolarization field contribution. The comparison of the polarization dependence on the film thickness, temperature and electric field for the films of order-disorder and displacement type ferroelectrics is performed. In particular it was shown that all the dipoles become ordered at T=0 independently on the film thickness for h>hc contrary to the displacement type ferroelectrics. Critical thickness appeared larger and polarization distribution sharper for the displacement type ferroelectrics than for order-disorder type ferroelectrics., Comment: 7 pages, 4 figures, 1 table

We have performed the calculations of the size effect in the temperature dependence of BaTiO3 nanograin ceramics specific heat and dielectric permittivity. We took into account the distribution of the grain sizes, that exists in any real nanomaterial. This distribution lead to the distribution of the temperatures of the size driven transition from ferroelectric to paraelectric phase because of relation between the temperature and the sizes. We calculated the transition temperature distribution function on the basis of the sizes distribution function. This function allowed to calculate the temperature dependence of any physical quantity in a nanomaterial. As an examples we calculated specific heat and dielectric permittivity in nanograin ferroelectric ceramics. The results demonstrate the strong influence of the size distribution on the observed properties and especially on extracted from experiment values of critical size and temperature. We carried out the comparison of the theory with the measured specific heat and dielectric permittivity in BaTiO3 nanomaterial. The developed theory described the experimental data pretty good. The possibility of the extraction of size distribution function parameters as well as real values of critical parameters from experimental data is discussed., Comment: 9 pages, 6 figures, 2 tables

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., Comment: 11 pages, 7 figures

The theory of size effects of the properties of nanocrystalline ferroelectric ceramic or nanoparticle powder allowing for surface tension and depolarization field is proposed. Surface tension was included into free energy functional and surface energy was expressed via surface tension coefficient. The latter was shown to be dependent on temperature due to its relation to dielectric permittivity of the nanoparticles. The depolarization field effect was calculated in the model taking into account the space charge layer on the surface, this space-charge being able to compensate depolarization field in the bulk material. Euler-Lagrange Equation for inhomogeneous polarization of nanomaterial with boundary condition where extrapolation length was shown to be temperature dependent quantity was solved analytically both in paraelectric and ferroelectric phase of size driven phase transition. This phase transition critical temperature dependence on the particle size was calculated. Temperature and size dependence of nanomaterials polarization and dielectric susceptibility was obtained. The possibility to calculate these and other properties by minimization of conventional free energy in the form of different power polarization series, but with the coefficients which depend on particles size, temperature, contribution of depolarization field and surface tension coefficient was demonstrated. These latter effects were shown to influence essentially the nanomaterial properties. The comparison with available experimental data is performed., Comment: 30 pages, 11 figures

The calculation of the polarization in ferroelectric thin films is performed using an analytical solution of the Euler-Lagrange differential equation with boundary conditions with different extrapolation lengths of positive sign on the surfaces. The depolarization field effect is taken into account in the model for a short-circuited single domain film, that is a perfect insulator. It is shown that the calculation of the polarization and other properties profiles and average values can be reduced to the minimization of the free energy expressed as a power series of the average polarization with a renormalized coefficient which depends on temperature, film thickness, extrapolation lengths, and a coefficient for the polarization gradient term in the free energy functional, the depolarization field being also included into the renormalized coefficient. The function defining the space distribution properties is calculated as well and its amplitude is shown to coincide with the average polarization. The detailed calculations of the spontaneous polarization, dielectric susceptibility and pyrocoefficient is performed. The divergence of the dielectric susceptibility and pyrocoefficient for critical parameters of the thickness induced ferroelectric phase transition, namely at temperature T(cl) and critical length l(c), is shown to exist with and without the depolarization field contribution, although the values of T(cl) and l(c) are different in both cases. The detailed analysis of the depolarization field space distribution and of this field dependence on temperature and film thickness is performed., Comment: 25 pages, 8 figures

The 93Nb and 45Sc NMR spectra in PbSc_1/2Nb_1/2O_3 (PSN) and PbMg_1/3Nb_2/3O_3 (PMN) disordered relaxor ferroelectrics at the temperature T > T_0 (T_0 is the temperature of the dielectric susceptibility maximum) have been studied. Spectra analysis was performed on the base both of the analytical description of NMR lines shapes, allowing for homogeneous and inhomogeneous broadening related to a random distribution of the electric field gradients and numerical Monte Carlo method taking into account electric field gradients originated from random distribution of Mg, Sc and Nb ions (which may be shifted or not) over B-type cation sites. The observed 1/2 -1/2 transition spectrum both of the 93Nb and 45Sc nuclei in the PSN was shown to contain a narrow (3-4 kHz) almost isotropic part and a broad strongly anisotropic part. These two components of NMR spectra are related to 1:1 Sc/Nb ordered and compositionally disordered regions of the crystal, respectively. It was shown that in the disordered regions Sc^3+, Nb^5+ and O^2- ions are shifted from their cubic lattice sites at one of three possible directions: <100>, <110> or <111>. In PMN the NMR spectrum of 93Nb contains practically only the broad component. The portion of unbroadened spectrum that may correspond to ideal 1:2 regions accounts only for 1-2 percent of the total integral intensity. No evidance was obtained about existence of the 1:1 regions in PMN. The NMR data demonstrate that in PMN the cubic symmetry at T > T_0 is locally broken due to ions shifts similar to that in disordered PSN. The values of the ion shifts were estimated in the point charges point dipoles approximation of the electric field gradients calculation both in the PSN and PMN.

We calculate the pyrocoefficient, static dielectric susceptibility profiles and its thickness dependence of ferroelectric thin films. Also, the temperature dependences of above quantities have been calculated. For the calculations we use Landau phenomenological theory, leading to Lame equations. These equations subject to boundary conditions with different extrapolation length on the surfaces have been solved numerically. The divergency of pyroelectric coefficient and static dielectric susceptibility in the vicinity of thickness induced ferroelectric phase transition (i.e. at $l\approx l_c$ or $% T\approx T_{cl}$) has been shown to be the most prominent size effect in ferroelectric thin films., Comment: 14 pages, 11 figures

The equations for phase transitions temperatures, order parameters and critical concentrations of components have been derived for mixed ferroelectrics. The electric dipoles randomly distributed over the system were considered as a random field sources. We derive a random field distribution function for different orientations of the electric dipoles with nonlinear and spatial correlation effects included., Comment: 7 pages, 4 figures, ReVTeX

We suggest a random field based model for calculation of physical properties of mixed ferroelectric relaxors. Our model naturally incorporates the different orientations of electric dipoles (related to different solid solution components) as well as the contribution of nonlinear and correlation effects of random field. We calculate the transition temperature $T_c$ as well as concentrational and temperature dependence of order parameters., Comment: 7 pages, 10 embedded postscript figures

A thermodynamic theory of ferroelectric thin film multilayers is developed. The free energy function is written down using a multilayer model in which c-domain layers of one ferroelectric material alternate with a-domain layers of a second ferroelectric material. We assume that the interfaces are perfectly sharp and that the polarization at these boundaries is zero. The renormalization of the free energy coefficients due to the stresses in the films and to the depolarizing field was taken into account, as well as the renormalization of the coefficients of the polarization gradients. The equilibrium inhomogeneous polarization temperature and its thickness dependence were determined from the solutions of the Euler-Lagrange equations resulting from the minimization of the free energy functional. A thickness induced ferroelectric phase transition is shown to exist and its transition temperature and critical layer thickness depend on the domain orientation. The criteria for ''a/c'', ''c/c'' and ''a/a'' domain multilayering are calculated and expressed via coefficients of the free energy density and the layer thickness. The calculated multilayer susceptibility diverges at the transition temperature of the thickness induced ferroelectric phase. This divergence is shown to be the origin of the giant dielectric response observed in some multilayers. The theory gives an excellent fit to the temperature dependence of the giant susceptibility observed recently in multilayers of PbTiO$_{3}$-Pb$_{1-x}$La$_{x}$TiO$_{3}$ ($x=0.28$)., Comment: 19 pages, 16 embedded postscript figures

Theory of the first order Raman scattering (FOR) line shape allowing for nonlinear and correlation effects contribution to inhomogeneous broadening as well as dynamic mechanisms of homogeneous broadening is developed. It is shown that in general case FOR line contains two maxima, shape of low frequency one being defined by homogeneous broadening. Our theory explains the peculiarity of observed FOR scattering of TO_2 hard phonon in KTL and KTN at different temperatures and concentrations of Li and Nb ions., Comment: 9 pages, 6 figures

We present the theory of dielectric spectra allowing for homogeneous and inhomogeneous broadening mechanisms contributions. The dielectric absorption line shape for oscillators with memory and Debye type relaxors with distribution of, respectively, resonant frequencies and relaxation times (due to random electric fields distribution) has been calculated. The conditions of hole burning observation are discussed. It is shown that the investigations of the inhomogeneously broadened line shape and width as well as hole burning can give valuable information about the distribution of random fields and relaxation times. The latter seems to be extremely important for the disordered systems like supercooled liquids and relaxor ferroelectrics., Comment: LaTeX, 7 pages, 2 figures. To be published in "Ferroelectrics"

The distribution function of relaxation times in disordered dielectrics has been calculated in the random field theory framework. For this purpose, we first consider the dynamics of single two-orientable impurity electric dipole in a random electric field $E$ created by the rest of impurities in disordered ferroelectric. This dynamics is conveniently described by Langevin equation. Relaxation time $\tau $ is then a reciprocal probability (calculated on the base of Fokker-Planck equation) of the dipole transition through barrier in a double-well potential (corresponding to two possible dipole orientations), distorted by a random fields. The obtained dependence $\tau (E)$ made it possible to obtain the expression for relaxation times distribution function $F(\tau)$(via random fields distribution function $f(E)$. Latter function has been calculated self-consistently in the random field theory framework. Nonlinear random field contribution and effects of spatial correlations between impurities have also been taken into account. It was shown that nonlinear contribution of random field gives asymmetric shape of $F(\tau)$, while in linear case it is symmetric. Comparison of calculated $F(\tau)$ curves with those extracted from empirical Cole-Cole (CC), Davidson-Cole (DC), Kohlrausch-William-Watts (KWW) and Havriliak-Negami (HN) functions had shown, that they correspond to mixed ferro-glass phase with coexistence of short and long-range order. Different forms of $F(\tau)$ are determined by linear (CC) or nonlinear (DC, KWW, HN) contributions of random field., Comment: 10 Pages, RevTex, 8 figures

Phase diagram of solid solutions of antiferroelectric and ferroelectric materials like PbZr$_{1-x}$Ti$_x$O$_3$ (PZT), Rb$_x$(NH$_4$)$_{1-x}$H$_2$PO$% _4$ (RADP) is calculated at the region $x\leq 0.1$. Antiferroelectric and ferroelectric order parameters (which correspond respectively to the difference and sum of two sublattices ions shifts) were introduced for antiferroelectric host lattice. Small admixture of ferroelectric component was considered as a random electric field source. The influence of this field on both aforementioned order parameters was calculated. Self consistent averaging with calculated random field distribution function made it possible to obtain the system of equations for order parameters of mixed system. The antiferroelectric $T_a$ and ferroelectric $T_c$ phase transition temperature concentrational dependence was expressed through the transition temperatures of the composition and members. The obtained $T_a(x)$ dependence was shown to fit pretty good the observed values for PZT and RADP. The application of the proposed theoretical approach to other types of mixed systems is discussed., Comment: 5 pages, RevTeX, 2 figures