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Polarized Raman spectra of piezoelectric bismuth germanate single crystal were recorded using vortex light in order to verify the predicted symmetry selection rules for Raman scattering of photons with nonzero orbital angular momentum. At first, the phonon spectrum is fully characterized by the infrared reflectivity and Raman scattering with ordinary light. Then, vortex light Raman spectra were compared with the ordinary ones, but no influence of the orbital momentum on the Raman spectra of Bi$_4$Ge$_3$O$_{12}$ was observed. In particular, we experimentally negate the theoretical prediction that Raman scattering using vortex light can yield frequencies of the silent optic modes of Bi$_4$Ge$_3$O$_{12}$. We also have not seen evidence for the predicted symmetry-lowering of the Raman scattering tensors of $E$ modes. We propose that the orbital momentum effects are inaccessible to the ordinary Raman spectroscopy experiments because of the tiny magnitudes of typical phonon coherence lengths., Comment: 6 pages, 6 figures

Atomistic model calculations recently revealed that the polarization pattern at the cross-section through nanoscale ferroelectric nanodomains in rhombohedral barium titanate shows a clear antiskyrmion attributes such as the net invariant topological charge of minus two. The present work confirms that these topological defects also exist as local minima in the discretized Ginzburg-Landau-Devonshire model, which is widely used in the phase-field modeling studies. We explore by phase-field simulations how an electric field can be used to create or move antiskyrmions within a monodomain ferroelectric matrix. The process of the field-induced antiskyrmion annihilation reveals the existence of a discrete ladder of intermediate antiskyrmion states with distinct radii but common symmetry, topology and geometrical properties., Comment: 5 pages, 4 figures

Previous experiments with BaTiO$_3$ single crystals have shown that application of the electric field in the vicinity of the ferroelectric phase transition can be used to introduce peculiar persisting ferroelectric domain walls, accompanied by the compensating charge in the form of two-dimensional electron gas. The present in-situ optical observations of such electric poling process reveal formation of a transient coexistence of the cubic and ferroelectric phases, the latter one being broken into multiple martensitic superdomains, separated by superdomain walls. It is revealed that as the transient superdomains convert into the regular ferroelectric domains, the superdomain boundaries transform into the desired charged domain walls. In order to assign the observed transient domain patterns, to understand the shapes of the observed ferrolectric precipitates and their agglomerates as well as to provide the overall interpretation of the observed domain formation process, the implications of the mechanical compatibility of the coexisting superdomain states is derived in the framework of the Wechsler-Lieberman-Read theory. The results also suggest that the transport of the compensating charge carriers towards the final charged domain wall location is directly associated with the electric conductivity and interlinked motion and growth of the superdomain walls and phase fronts.

First principles density functional theory (DFT) simulations of antiferroelectric (AFE) PbZrO$_3$ and PbHfO$_3$ reveal a dynamical instability in the phonon spectra of their purported low temperature $Pbam$ ground states. This instability doubles the $c$-axis of $Pbam$ and condenses five new small amplitude phonon modes giving rise to an 80-atom $Pnam$ structure. Compared with $Pbam$, the stability of this structure is slightly enhanced and highly reproducible as demonstrated through using different DFT codes and different treatments of electronic exchange & correlation interactions. This suggests that $Pnam$ is a new candidate for the low temperature ground state of both materials. With this finding, we bring parity between the AFE archetypes and recent observations of a very similar AFE phase in doped or electrostatically engineered BiFeO$_3$., Comment: 14 pages, 3 figures and 4 tables

We study patterns of partial synchronization in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in human subjects. We report the spontaneous occurrence of synchronization phenomena that closely resemble the ones seen during epileptic seizures in humans. In order to obtain deeper insights into the interplay between dynamics and network topology, we perform long-term simulations of oscillatory dynamics on different paradigmatic network structures: random networks, regular nonlocally coupled ring networks, ring networks with fractal connectivities, and small-world networks with various rewiring probability. Among these networks, a small-world network with intermediate rewiring probability best mimics the findings achieved with the simulations using the empirical structural connectivity. For the other network topologies, either no spontaneously occurring epileptic-seizure-related synchronization phenomena can be observed in the simulated dynamics, or the overall degree of synchronization remains high throughout the simulation. This indicates that a topology with some balance between regularity and randomness favors the self-initiation and self-termination of episodes of seizure-like strong synchronization.

Domain boundaries and other twin boundaries in crystalline materials are receiving increasing interest. They can carry unique functional properties, which in many cases are absent in the surrounding bulk material. One such property of domain boundaries can be their electric polarity. Phenomenological insight in the polarity of domain boundaries was so far based either on the knowledge of the order parameter and the form of Landau-Ginzburg free energy functional, or on the knowledge of the symmetry of the domain boundaries. In the present work we show on the concrete examples of potassium thiocyanate (KSCN) and lacunar spinel crystals, that the concept of the primary order-parameter can help to find the layer group describing the maximal possible symmetry of a given domain boundary. Combination of layer group and order parameter symmetries is then employed to clarify the nature of the polarity of domain boundaries., Comment: 15 pages, 8 figures

The 212 species of structural phase transitions which break macroscopic symmetry are analyzed with respect to the occurrence of time-reversal invariant vector and bidirector order parameters. The possibility of discerning the orientational domain states of the low-symmetry phase by these `vectorlike' physical properties has been derived using a computer algorithm exploiting the concept of polar, axial, chiral and neutral dipoles. It is argued that for species 32 > 3, 422 > 4 and 622 > 6, Bogdanov-Yablonskii phenomenological theory for a ferromagnetic Bloch Skyrmions applies also to the ferroelectric Bloch Skyrmions. In these fully-ferroelectric and nonferroelastic species, the Ginzburg Landau functional allows a pseudo-Lifshitz invariant of chiral bidirector symmetry, analogous to the chiral Dzyaloshinskii-Moria term assumed in magnetic Bloch Skyrmion theory., Comment: 5 pages, 3 figures

Proximity to phase transitions (PTs) is frequently responsible for the largest dielectric susceptibilities in ferroelectrics. The impracticality of using temperature as a control parameter to reach those large responses has motivated the design of solid solutions with phase boundaries between different polar phases at temperatures (typically room temperature) significantly lower than the paraelectric-ferroelectric critical temperature. The flat energy landscapes close to these PTs give rise to polarization rotation under external stimuli, being responsible for the best piezoelectrics so far and a their huge market. But this approach requires complex chemistry to achieve temperature-independent PT boundaries and often involves lead-containing compounds. Here we report that such a bridging state is possible in thin films of chemically simple materials such as BaTiO3. A coexistence of tetragonal, orthorhombic and their bridging low-symmetry phases are shown to be responsible for the continuous vertical polarization rotation, recreating a smear in-transition state and leading to giant temperature-independent dielectric response. These features are distinct from those of single crystals, multi-domain crystals, ceramics or relaxor ferroelectrics, requiring a different description. We believe that other materials can be engineered in a similar way to form a class of ferroelectrics, in which MPB solid solutions are also included, that we propose to coin as transitional ferroelectrics., Comment: Limited figure quality. No Supplemental info included due to memory restrictions (available from corresponding author)

Neutron pair distribution function analysis and first principles calculations have been employed to study short-range correlations in heavily disordered dielectric material Sr$_x$Ba$_{1-x}$Nb$_2$O$_6$ ($x=0.35, 0.5$ and 0.61). The combination of methods has been fruitful in pinpointing main local-structure features, their temperature behaviour and interrelation. A rather complex system of tilts is found to be both temperature and Sr-content sensitive with the biggest tilt magnitudes reached at low temperatures and high $x$. Relative Nb-O$_6$ displacements, directly responsible for material's ferroelectric properties, are shown to be distinct in two octahedra sub-systems with different freezing temperatures and disparate levels of deviation from macroscopic polarization direction. Intrinsic disorder caused by Sr, Ba and vacancy distribution is found to introduce local strain to the structure and directly influence octahedra tilting. These findings establish a new atomistic picture of the local structure -- property relationship in Sr$_x$Ba$_{1-x}$Nb$_2$O$_6$.

From the new infrared (IR) reflectivity and time-domain terahertz (THz) spectra combined with available high-frequency dielectric data above the MHz range in a broad temperature range of 10-900 K, a full picture of the soft and central mode behavior in the classical relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 (PMN) is suggested. A detailed comparison is given with the recent hyper-Raman spectroscopy data (Phys. Rev. Lett. 117, 155501 (2016)), and also with other available experiments based on inelastic light and neutron scattering. The closest agreement is with the hyper-Raman data, both techniques yield the same number of soft-mode components and the same high-temperature softening towards the temperature T* ~ 400 K. In addition to evaluation of the IR-THz data using fitting with standard factorized form of the dielectric function, we performed a successful fitting of the same data using the effective medium approach (EMA), originally based on the assumption that the mesoscopic structure of PMN consists of randomly oriented uniaxially anisotropic polar nanodomains (PNDs) with somewhat harder TO polar modes in the direction along the local PND dipole (Phys. Rev. Lett. 96, 027601 (2006)). Evaluation using the Bruggeman EMA modelling has been successfully applied in the entire investigated temperature range. These results suggest that the response perpendicular to the local dipole moment, at high temperatures induced by random fields rather than PNDs, undergoes a classical softening from high temperatures with permittivity obeying the Curie-Weiss law, eps_per = C/(T-Tc), C = 1.7 x 10^5 K and Tc = 380 K. Below the Burns temperature ~620 K, a GHz relaxation ascribed to flipping of the PNDs emerges from the soft mode response, slows down and broadens, remaining quite strong towards the cryogenic temperatures, where it can be assigned to fluctuations of the PND boundaries.

The three dimensional distribution of the X-ray diffuse scattering intensity of BaTiO$_3$ has been recorded in a synchrotron experiment and simultaneously computed using molecular dynamics simulations of a shell-model. Together these have allowed the details of the disorder in paraelectric BaTiO$_3$ to be clarified. The narrow sheets of diffuse scattering, related to the famous anisotropic longitudinal correlations of Ti ions, are shown to be caused entirely by the overdamped anharmonic soft phonon branch. This finding demonstrates that the occurrence of narrow sheets of diffuse scattering agrees with a displacive picture of the cubic phase of this textbook ferroelectric material., Comment: 5 pages, 4 figures

Phase-field simulations demonstrate that the polarization order-parameter field in the Ginzburg-Landau-Devonshire model of rhombohedral ferroelectric BaTiO3 allows for an interesting linear defect, stable under simple periodic boundary conditions. This linear defect, termed here as Ising line, can be described as about 2 nm thick intrinsic paraelectric nanorod acting as a highly mobile borderline between finite portions of Bloch-like domain walls of the opposite helicity. These Ising lines play the role of domain boundaries associated with the Ising-to-Bloch domain wall phase transition., Comment: 5 figures

Polarized Raman, IR and time-domain THz spectroscopy of orthorhombic lead zirconate single crystals yielded a comprehensive picture of temperature-dependent quasiharmonic frequencies of its low-frequency phonon modes. It is argued that these modes primarily involve vibration of Pb and/or oxygen octahedra librations and their relation to particular phonon modes of the parent cubic phase is proposed. Counts of the observed IR and Raman active modes belonging to distinct irreducible representations agree quite well with group-theory predictions. The most remarkable finding is the considerably enhanced frequency renormalization of the y-polarized polar modes, resulting in a pronounced low temperature dielectric anisotropy. Results are discussed in terms of contemporary phenomenological theory of antiferroelectricity.

Cylindrical BaTiO3 nanorods embedded in (100)-oriented SrTiO3 epitaxial film in a brush-like configuration are investigated in the framework of the Ginzburg-Landau-Devonshire model. It is shown that strain compatibility at BaTiO3/SrTiO3 interfaces keeps BaTiO3 nanorods in the rhombohedral phase even at room temperature. Depolarization field at the BaTiO3/SrTiO3 interfaces is reduced by an emission of the 109-degree or 71-degree domain boundaries. In case of nanorods of about 10-80 nm diameter, the ferroelectric domains are found to form a quadruplet with a robust flux-closure arrangement of the in-plane components of the spontaneous polarization. The out-of-plane components of the polarization are either balanced or oriented up or down along the nanorod axis. Switching of the out-of-plane polarization with coercive field of about $5.10^6$ V/m occurs as a collapse of a 71-degree cylindrical domain boundary formed at the curved circumference surface of the nanorod. The remnant domain quadruplet configuration is chiral, with the $C_4$ macroscopic symmetry. More complex stable domain configurations with coexisting clockwise and anticlockwise quadruplets contain interesting arrangement of strongly curved 71-degree boundaries., Comment: Erratta - corrected error in Fig. 1

Broadband dielectric spectroscopy from Hz up to the infrared (IR) range and temperature interval 10-300 K was carried out for xBaZrO3-(1-x)BaTiO3 (BZT-x, x = 0.6, 0.7, 0.8) solid solution ceramics and compared with similar studies for x = 0, 0.2, 0.4, 1 ceramics published recently (Phys. Rev. B 86, 014106 (2012)). Rather complex IR spectra without appreciable mode softening are ascribed to Last-Slater transverse optic (TO) phonon eigenvector mixing and possible two-mode mixed crystal behavior. Fitting of the complete spectral range requires a relaxation in the 100 GHz range for all the samples. Below 1 GHz another relaxation appears, which is thermally activated and obeys the same Arrhenius behavior for all the relaxor BZT samples. The frequently reported Vogel-Fulcher behavior in BZT relaxors is shown to be an artifact of the evaluation from the permittivity or loss vs. temperature dependences instead of its evaluation from loss vs. frequency maxima. The relaxation is assigned to local hopping of the off-centered Ti4+ ions in the frozen BTO clusters, whose size is rather small and cannot grow on cooling. Therefore BZT is to be considered as a dipolar glass rather than relaxor ferroelectric., Comment: subm. to Ferroelectrics

The paper draws the attention to the spatiotemporal symmetry of various vector-like physical quantities. The symmetry is specified by their invariance under the action of symmetry operations of the Opechowski nonrelativistic space-time rotation group O(3).{1, 1'}= O'(3), where 1' is time-reversal operation. It is argued that along with the canonical polar vector, there are another 7 symmetrically distinct classes of stationary physical quantities, which can be - and often are - denoted as standard three-components vectors, even though they do not transform as a static polar vector under all operations of O'(3). The octet of symmetrically distinct "directional quantities" can be exemplified by: two kinds of polar vectors (electric dipole moment P and magnetic toroidal moment T, two kinds of axial vectors (magnetization M and electric toroidal moment G), two kinds of chiral "bi-directors" C and F (associated with the so-called true and false chirality, resp.) and still another two achiral "bi-directors" N and L, transforming as the nematic liquid crystal order parameter and as the antiferromagnetic order parameter of the hematite crystal alpha-Fe2O3, respectively., Comment: 5 pages, 2 figures

Domain structures of 320 nm thin epitaxial films of ferroelectric PbTiO3 grown by MOCVD technique in identical conditions on SmScO3 and TbScO3 perovskite sub- strates have been investigated by Raman spectroscopy and piezoresponse force microscopy techniques. Phonon frequency shifts and typical domain structure motifs are discussed. The results reveal strikingly different domain structure architecture: domain structures of the PbTiO3 film grown on SmScO3 have dominantly a-domain orientation while strongly preferential c-domain orientation was found in the PbTiO3 film grown on the TbScO3 substrate. Differences between the two cases are traced back to the film-substrate lattice mismatch at the deposition temperature.

The paper describes heterostructures spontaneously formed in PMN-PT single crystals cooled under bias electric field applied along [001]pc and then zero-field-heated in the vicinity of the so-called depoling temperature. In particular, formation of lamellar structures composed of tetragonal-like and rhombohedral-like layers extending over macroscopic (mm) lengths is demonstrated by optical observations and polarized Raman investigations.

Hyper-Raman scattering experiments allowed collecting the spectra of the lowest F1u-symmetry mode of PbTiO3 crystal in the paraelectric phase up to 930K as well as down to about 1K above the phase transition. It is realized that this mode is fully responsible for the Curie-Weiss behavior of its dielectric permittivity above Tc. Near the phase transition, this phonon frequency softens down to 17 cm-1 and its spectrum can be well modeled as a response of a single damped harmonic oscillator. It is concluded that PbTiO3 constitutes a clean example of a soft mode-driven ferroelectric system.

Ferroelectric phase transition in the semiconductor Sn2P2S6 single crystal has been studied by means of neutron scattering in the pressure-temperature range adjacent to the anticipated tricritical Lifshitz point (p=0.18GPa, T=296K). The observations reveal a direct ferroelectric-paraelectric phase transition in the whole investigated pressure range (0.18 - 0.6GPa). These results are in a clear disagreement with phase diagrams assumed in numerous earlier works, according to which a hypothetical intermediate incommensurate phase extends over several or even tens of degrees in the 0.5GPa pressure range. Temperature dependence of the anisotropic quasielastic diffuse scattering suggests that polarization fluctuations present above TC are strongly reduced in the ordered phase. Still, the temperature dependence of the (200) Bragg reflection intensity at p=0.18GPa can be remarkably well modeled assuming the order-parameter amplitude growth according to the power law with logarithmic corrections predicted for a uniaxial ferroelectric transition at the tricritical Lifshitz point.

THz-range dielectric spectroscopy and first-principle-based effective-Hamiltonian molecular dynamics simulations were employed to elucidate the dielectric response in the paraelectric phase of (Ba,Sr)TiO3 solid solutions. Analysis of the resulting dielectric spectra suggests the existence of a crossover between two different regimes: a higher-temperature regime governed by the soft mode only versus a lower-temperature regime exhibiting a coupled soft mode/central mode dynamics. Interestingly, a single phenomenological coupling model can be used to adjust the THz dielectric response in the entire range of the paraelectric phase (i.e., even at high temperature). We conclude that the central peak is associated with thermally activated processes, and that it cannot be discerned anymore in the dielectric spectra when the rate of these thermally activated processes exceeds certain characteristic frequency of the system.

Complementary diffuse and inelastic synchrotron X-ray scattering measurements of lead zirconate-titanate single crystals with composition near the morphotropic phase boundary (x=0.475) are reported. In the temperature range 293 K < T < 400 K a highly anisotropic quasielastic diffuse scattering is observed. Above 400 K this scattering disappears. Its main features can be reproduced by model of inhomogeneous lattice deformations caused by inclusions of a tetragonal phase into a rhombohedral or monoclinic phase. This observation supports the idea that PZT at its morphotropic phase boundary is essentially structurally inhomogeneous., Comment: 4 pages, 4 figures

Compressively strained epitaxial (001) EuTiO3 thin films of tetragonal symmetry have been deposited on (001) (LaAlO3)_0.29-(SrAl_{1/2}Ta_{1/2}O3)_0.71 (LSAT) substrates by reactive molecular-beam epitaxy. Enhancement of the Neel temperature by 1 K with 0.9% compressive strain was revealed. The polar phonons ofthe films have been investigated as a function of temperature and magnetic field by means of infrared reflectance spectroscopy. All three infrared active phonons show strongly stiffened frequencies compared to bulk EuTiO3 in accordance with first principles calculations. The phonon frequencies exhibit gradual softening on cooling leading to an increase in static permittivity. A new polar phonon with frequency near the TO1 soft mode was detected below 150 K. The new mode coupled with the TO1 mode was assigned as the optical phonon from the Brillouin zone edge, which is activated in infrared spectra due to an antiferrodistortive phase transition and due to simultaneous presence of polar and/or magnetic nanoclusters. In the antiferromagnetic phase we have observed a remarkable softening of the lowest-frequency polar phonon under an applied magnetic field, which qualitatively agrees with first principles calculations. This demonstrates the strong spin-phonon coupling in EuTiO3, which is responsible for the pronounced dependence of its static permittivity on magnetic field in the antiferromagnetic phase., Comment: Submitted to Phys. Rev. B

Mechanically compatible and electrically neutral domain walls in tetragonal, orthorhombic and rhombohedral ferroelectric phases of BaTiO3 are systematically investigated in the framework of the phenomenological Ginzburg-Landau-Devonshire (GLD) model with parameters of Ref. [Hlinka and Marton, Phys. Rev. 74, 104104 (2006)]. Polarization and strain profiles within domain walls are calculated numerically and within an approximation leading to the quasi-one-dimensional analytic solutions applied previously to the ferroelectric walls of the tetragonal phase [W. Cao and L.E. Cross, Phys. Rev. 44, 5 (1991)]. Domain wall thicknesses and energy densities are estimated for all mechanically compatible and electrically neutral domain wall species in the entire temperature range of ferroelectric phases. The model suggests that the lowest energy walls in the orthorhombic phase of BaTiO3 are the 90-degree and 60-degree walls. In the rhombohedral phase, the lowest energy walls are the 71-degree and 109-degree walls. All these ferroelastic walls have thickness below 1 nm except for the 90-degree wall in the tetragonal phase and the 60-degree S-wall in the orthorhombic phase, for which the larger thickness of the order of 5 nm was found. The antiparallel walls of the rhombohedral phase have largest energy and thus they are unlikely to occur. The calculation indicates that the lowest energy structure of the 109-degree wall and few other domain walls in the orthorhombic and rhombohedral phases resemble Bloch-like walls known from magnetism., Comment: 12 pages, 9 figures

Ferroelectric soft mode properties in ceramics and thin films are reviewed and compared with single crystals. In general, the permittivity in ceramics and thin films is markedly reduced compared to the single crystals mainly because of low-permittivity grain boundaries - dead layers - (sometimes also nano-cracks) present in the samples. In SrTiO3 and BaTiO3, this dielectric reduction is fully explained by stiffening of the soft mode frequency. In most other ferroelectrics, the soft mode accounts only partly for such a permittivity reduction, since the transition is only partially driven by the phonon mode softening. In these cases, additional relaxational dispersion below the optical phonon range (central mode) accounts for the main part of the dielectric anomaly near Tc. Influence of nano-cracks on reduced permittivity near Tc and related stiffening of the central mode is manifested in the antiferroelectric PbZrO3 ceramics., Comment: New developments in advanced functional ceramics. Ed. L. Mitoseriu, Indian Series of Appl. Phys., Trivandrum, Transworld Research Network, in press

The paper suggests to treat the infrared reflectivity spectra of single crystal perovskite relaxors as fine-grained ferroelectric ceramics: locally frozen polarization makes the dielectric function strongly anisotropic in the phonon frequency range and the random orientation of the polarization at nano-scopic scale requires to take into account the inhomogeneous depolarization field. Employing a simple effective medium approximation (Bruggeman symmetrical formula) to dielectric function describing the polar optic modes as damped harmonic oscillators turns out to be sufficient for reproducing all principal features of room temperature reflectivity of PMN. One of the reflectivity bands is identified as a geometrical resonance entirely related to the nanoscale polarization inhomogeneity. The approach provides a general guide for systematic determination of the polar mode frequencies split by the inhomogeneous polarization at nanometer scale., Comment: 5 pages, 2 figures

The paper presents infrared reflectivity and micro-Raman scattering spectra of LiBC powder pellets. The experiment allowed assignment of frequencies of all infrared and Raman active zone center modes. Results are compared with available ab-initio calculations; prediction of large Born effective charges on the nodes of B-C graphene sheets is confirmed., Comment: 4 pages, 5 figures (change: Fig 2 replaced)

Inelastic neutron scattering study of the perovskite relaxor ferroelectric PZN:8%PT elucidates the origin of the previously reported unusual kink on the low frequency transverse phonon dispersion curve (known as "waterfall" effect). We show that its position depends on the choice of the Brillouin zone and that the relation of its position to the size of the polar nanoregions is highly improbable. The observation is explained in the framework of a simple model of coupled damped harmonic oscillators representing the acoustic and optic phonon branches., Comment: 4 pages, 6 figures, LaTeX

The paper presents polarized Raman scattering study on a few-micron-size crystallite of LiBC with natural faces. The experiment on as grown sample has revealed a four lattice modes with frequencies at 1276 cm^-1, 830 cm^-1, 546 cm^-1 and 170 cm^-1, respectively. The number of observed Raman lines and their selection rules are incompatible with the assumed D6h symmetry. The modes at 1276 cm^-1 and 170 cm^-1 correspond to the expected Raman active modes. In contrast with the superconducting compound MgB2, the B-C bond stretching mode (at 1276 cm^-1) has rather small damping. The two "forbidden" modes (at 830 cm^-1 and 546 cm^-1) disappeared after subsequent thermal treatment., Comment: 4 pages, LaTeX, complementary experimental result

The elastostatic Green function tensor approach, which was recently used to treat electrostriction in numerical simulation of domain structure formation in cubic ferroelectrics, is reviewed and extended to the crystals of hexagonal and orthorhombic symmetry. The tensorial kernels appearing in the expressions for effective nonlocal interaction of electrostrictive origin are derived explicitly and their physical meaning is illustrated on simple examples. It is argued that the bilinear coupling between the polarization gradients and elastic strain should be systematically included in the Ginzburg-Landau free energy expansion of electrostrictive materials., Comment: 4 pages

The paper presents detailed Raman scattering study of the unusually broad E2g phonon mode in MgB2 crystal. For the first time, it is shown by the polarized Raman scattering on few-micron-size crystallites with natural faces that the observed broad Raman feature really does obey the selection rules of an E2g mode. Raman spectra on high quality polycrystalline superconducting MgB2 wires reveal a very symmetric E2g phonon line near 615 1/cm with the room temperature linewidth of 260 1/cm only. Additional scattering of different polarization dependence, observed in certain crystallites is interpreted as weighted phonon density of states induced by lattice imperfections., Comment: 4 pages + 7 figures

The phase transition in a 3D array of classical anharmonic oscillators with harmonic nearest-neighbour coupling (discrete $\phi^4$ model) is studied by Monte Carlo (MC) simulations and by analytical methods. The model allows to choose a single dimensionless parameter a determining completely the behaviour of the system. Changing a from 0 to $+\infty$ allows to go continuously from the displacive to the order-disorder limit. We calculate the transition temperature $T_c$ and the temperature dependence of the order parameter down to T=0 for a wide range of the parameter a. The $T_c$ from MC calculations shows an excellent agreement with the known asymptotic values for small and large a. The obtained MC results are further compared with predictions of the mean-field and independent-mode approximations as well as with predictions of our own approximation scheme. In this approximation, we introduce an auxiliary system, which yields approximately the same temperature behaviour of the order parameter, but allows the decoupling of the phonon modes. Our approximation gives the value of $T_c$ within an error of 5% and satisfactorily describes the temperature dependence of the order parameter for all values of a., Comment: 7 Figures