Temperature and pressure dependences of the properties and phase transition in paratellurite (TeO2: Ultrasonic,dielectric and Raman and Brillouin scattering results

The effects of temperature and pressure on the ultrasonic propagation properties, dielectric constants and the Raman and Brillouin spectra in paratellurite (TeO₂) were investigated with emphasis on the behavior in the vicinity of the newly-discovered, pressure-induced phase transition. The transition is found to be second-order and purely strain-induced, driven by a soft shear acoustic mode propagating along a <110〉 and polarized along a (110) crystal direction. Such pure-strain transitions were previously discussed by Anderson and Blount and the transition in paratellurite is the first observation of this kind of transition. No evidence was found for any coupling of the soft mode to any other acoustic or optic mode, although small anomalies associated with lattice strains accompanying the transition were observed in some of the elastic and dielectric constants. Analysis of the effective elastic constant C, governing the soft mode velocity indicates that, within experimental uncertainty, the transition can be described by mean-field theory. Although the apparent attenuation of the soft mode increased significantly near the transition, it is concluded that this effect is probably due to the fact that the phase and group velocities are not parallel rather than to intrinsic dissipative processes in the crystal. With the exception of C₄₄, the remaining elastic constants and Raman-active phonon frequencies displayed normal increases with pressure. No soft Raman-active modes were observed in either phase. The static dielectric constants ?₁ are large, due to the large electronic polarizability of TeO₂, and the anisotropy in ? results almost entirely from the anisotropy in the optical dielectric constants ?_∞. In the low pressure tetragonal phase both ?_a and ?_c exhibit normal temperature dependences and ?_c decreases with pressure; however, ?_a exhibits an anomalous increase with pressure. Temperature, pressure and uniaxial stress measurements are combined to evaluate the various contributions to the temperature and pressure dependences of ?. Combining the ? data with available i.r. measurements demonstrated that the generalized Lyddane-Sachs-Teller relation is well obeyed for TeO₂. Finally, the Szigetti effective charge ratios were determined for the lowest frequency IR-active modes. These ratios were found to be quite low, being 0.27 and 0.18 for the a-axis responses, respectively, indicating that the bonding is highly covalent.     

Dielectric and optical behaviors in relaxor ferroelectric Pb(In1/2Nb1/2)1−xTixO3 crystal

Dielectric permittivities (ε′,ε″) have been measured as functions of temperature (140-535 K) and frequency (500 Hz-2.0 MHz) in a (001)-cut Pb(In_1/2Nb_1/2)_0.7Ti_0.3O₃ (PINT30%) single crystal grown by the modified Bridgman method with Pb(Mg_1/3Nb_2/3)_0.71Ti_0.29O₃ (PMNT29%) seed crystal. A diffused phase transition was observed in the temperature region of ∼430-460 K with strong frequency dispersion. Above the Burns temperature T_B≅510 K, the dielectric permittivity was found to follow the Curie-Weiss behavior, ε′=C/(T−T_C), with parameters C=3.9×10⁵ and T_C=472 K. Below T_B≅510 K, polar nanoclusters are considered to appear and are responsible for the diffused dielectric anomaly. Optical transmission, refractive indices, and the Cauchy equations were obtained as a function of wavelength at room temperature. The unpoled crystal shows almost no birefringence, indicating that the average structural symmetry is optically isotropic. The crystal exhibits a broad transparency in the wavelength range of ∼0.4-6.0 μm.     

X-ray diffraction investigation of the thermochromic phase transition in an [NH2(C2H5)2]2CuCl4 crystal

The unit cell parameters of an [NH₂(C₂H₅)₂]₂CuCl₄ crystal are determined using x-ray diffraction analysis, and the thermal expansion coefficients along the principal crystallographic directions are calculated in the temperature range 100–330 K. The behavior of the intensities of the diffraction reflections from the (100), (010), and (001) crystallographic planes is studied in the vicinity of the thermochromic phase transition temperature. The occurrence of a first-order phase transition in the [NH₂(C₂H₅)₂]₂CuCl₄ crystal at T ≈ 324 K is confirmed experimentally.     

Structure and phase transitions in chloroantimonate(V) crystals: [(C2H5)3NH]SbCl6 and [(C2H5)3NH]SbCl6·1/2[(C2H5)3NH]Cl

New triethylammonium salts: [(C₂H₅)₃NH]SbCl₆ (TCA) and [(C₂H₅)₃NH]SbCl₆·1/2[(C₂H₅)₃NH]Cl (TCAT) have been synthesized. The compounds crystallise in monoclinic symmetry: space groups P2₁/n and P2₁/c, for TCA at 293 K and TCAT at 100 K, respectively. The crystal structure of [(C₂H₅)₃NH]SbCl₆ consists of discrete ionic pairs—triethylammonium cations and hexachloroantimonate anions—linked via the bifurcated N-H?Cl hydrogen bonds. The crystal structure of [(C₂H₅)₃NH]SbCl₆·1/2[(C₂H₅)₃NH]Cl is composed of three symmetrically independent triethylammonium cations, chlorine anion and two symmetrically independent hexachloroantimonate anions. TCA undergoes a structural phase transition at 336 K (on heating) into the orthorhombic C222 space group, whereas TCAT reveals a structural phase transition at 332 K. The phase transitions are of the first order type. TCA shows a ferroelastic domain structure below 336 K. Differential scanning calorimetry, dilatometric, dielectric dispersion and Raman scattering measurements have been used to study the phase transition mechanisms in these triethylammonium salts.     

Charge and lattice dynamics of ordered state in La1/2Ca1/2MnO3: infrared reflection spectroscopy study

We report an infrared reflection spectroscopy study of La_1/2Ca_1/2MnO₃ over a broad frequency range and temperature interval which covers the transitions from the high temperature paramagnetic to ferromagnetic and, upon further cooling, to antiferromagnetic phase. The structural phase transition, accompanied by a ferromagnetic ordering at T_C=234 K, leads to enrichment of the phonon spectrum. A charge ordered antiferromagnetic insulating ground state develops below the Néel transition temperature T_N=163 K. This is evidenced by the formation of charge density waves and opening of a gap with the magnitude of 2Δ₀=(320±15) cm⁻¹ in the excitation spectrum. Several of the infrared active phonons are found to exhibit anomalous frequency softening. The experimental data suggest coexistence of ferromagnetic and antiferromangetic phases at low temperatures.     

Phase transition, order parameter, and their manifestation in optical spectra of Hg2Cl2

This paper reports on a high-precision study of the effects induced by the phase transition in Raman spectra of Hg₂Cl₂ crystals. The odd (acoustic and IR-active) phonons, including the soft modes, from the Brillouin zone (BZ) X points of the paraphase of these crystals, which are induced by the phase transition, unit cell doubling, and the X ?? ?? BZ folding, have been investigated both theoretically and experimentally. The temperature dependences of the intensities of these phonons, complemented by a theoretical analysis, have yielded the first information on the behavior of the transition order parameter. The corresponding critical exponents have been derived, which correlate in magnitude with the data obtained from X-ray diffraction measurements and, thus, imply the closeness of the phase transition in these crystals to the tricritical point.     

Acoustic anomalies and relaxation dynamics of relaxor ferroelectric Na1/2Bi1/2TiO3 single crystals studied by using Brillouin spectroscopy

Acoustic anomalies of relaxor ferroelectric Na_1/2Bi_1/2TiO₃ single crystals were investigated over a wide temperature range from −196 °C to 900 °C by using Brillouin spectroscopy. The longitudinal sound velocity, the acoustic absorption coefficient and the elastic constant C₁₁ were determined for the acoustic phonon mode propagating in the [100] direction. Two acoustic anomalies, weaker ones at the cubic-tetragonal phase transition temperature of ~540 °C and more pronounced ones at temperatures near 315 °C near the dielectric maximum temperature, were investigated and discussed in relation with the relevant order parameters coupled to the acoustic waves. The relaxation dynamics in the cubic phase were studied based on the flattening of the mode frequency and the half width, which was observed for the first time, and a modified Arrhenius law.     

Effect of electric field on the smeared phase transition in crystals PbIn1/2Nb1/2O3-28PbTiO3 and PbIn1/2Nb1/2O3-37PbTiO3

The effect of a direct-current electric field (0 < E < 3 kV/cm) on the smearing of the phase transition and the Curie-Weiss exponent (γ) for two PbIn_1/2Nb_1/2O₃-28PbTiO₃ and PbIn_1/2Nb_1/2O₃-37PbTiO₃ crystals lying at different distances from the morphotropic phase boundary has been investigated. The universal Curie-Weiss law has been used to approximate the temperature dependences of the dielectric permittivity. It has been shown that the more remote is the crystal from the morphotropic phase boundary, the larger is the exponent γ and, consequently, the more smeared is the phase transition (in the zero field, γ = 1.67 and 1.49 for PbIn_1/2Nb_1/2O₃-28PbTiO₃ and PbIn_1/2Nb_1/2O₃-37PbTiO₃, respectively). It has been found that a weak electric field (no greater than 2–3 kV/cm) in the case of the more smeared phase transition almost does not affect the Curie-Weiss exponent, whereas for the PbIn_1/2Nb_1/2O₃-37PbTiO₃ crystal, this exponent decreases with increasing electric field strength and approaches γ = 1, which is characteristic of the conventional ferroelectric.     

Doping and temperature dependence of inversion symmetry breaking in La2−xSrxCuO4

The doping dependence of the Raman spectra of high quality La_2−xSr_xCu^16,18O₄ polycrystalline compounds has been investigated at low temperatures. It is shown that symmetry forbidden bands peaked at ∼150 cm⁻¹, ∼280 cm⁻¹, and ∼370 cm⁻¹ are activated in the (xx/yy) polarization Raman spectra due to the local breaking of the inversion symmetry mainly at low temperatures and for doping concentrations for which the compound is superconducting. The apparent A₁-character of the activated modes in the symmetry reduced phase indicates a reduction from the D_2h to C_2v or D₂ crystal symmetries, which associates the observed modes to specific IR-active phonons with eigenvectors mainly along the c-axis. The temperature and doping dependence of this inversion symmetry breaking and the superconducting transition temperature are very similar, though the symmetry reduction occurs at significantly higher temperatures.     

Analysis of the relationship between temperature dependence of the libration mode and dielectric relaxation in NaNO2

The behavior of the low frequency dielectric constant of NaNO₂ as function of frequency and temperature is consistently correlated to the temperature behavior of the frequencies and linewidths of the phonons of B₁ symmetry in the crystal. The frequency of the librational ‘soft’ mode closely related to the ferroelectric-paraelectric phase transition does not go to zero but tends to a hard core value at the transition temperature. The behavior of the dielectric constant as function of temperature and frequency is explained by assuming a dielectric relaxation mechanism proposed by Mason and not by Cochran's soft phonon model.     

Inelastic neutron scattering from transverse acoustic modes in K2SnCl6

In cubic K₂SnCl₆ the dispersion curve für q q; [110] of [1$\text{1}$0] polarized acoustic phonons has been measured at three temperatures near the phase transition temperature T_c1. The acoustic branch shows no temperature dependence in the low wave vector region and stiffens slightly near the X-point of the fcc-Brillouin zone as the temperature approaches the phase transition T_c1= 262 K from above. The results support a previously developed model on acoustic anomalies in this compound.     

Nonlinear dielectric response in the mixed K0.91(NH4)0.09H2PO4 crystal

The influence of bias and variable electric fields on the dielectric response of the K_0.91(NH₄)_0.09H₂PO₄ single crystal has been studied in the vicinity of the ferroelectric phase transition temperature T _C. Below T _C, the nonlinear response is caused mainly by the domain mechanism. This is confirmed, in particular, by observations of chaotic oscillations in a series RLC-circuit containing the studied sample as a capacitor C and excited by a sinusoidal voltage. Peculiarities of the behavior of the dielectric nonlinearity are found near the Curie temperature, which are explained by the emergence of an intermediate heterophase state.     

Magnetic and transport properties of the charge-ordered manganite Pr2/3Ca1/3MnO3

The transport properties, ac susceptibility χ, and EPR spectra have been studied for the insulator polycrystalline manganite Pr_2/3Ca_1/3MnO₃ undergoing the orbital (O) and charge (C) orderings below T _CO ～ 250 K that lead to antiferromagnetic (AF) ordering below T _N ≈ 155 K. Above T _C ～ 110 K, the χ′(T) dependence indicates that the sample contains a phase undergoing a second-order transition from the paramagnetic to ferromagnetic state. In the vicinity of T _C , the colossal magnetoresistance effect is observed. The EPR spectrum characteristics are sensitive to the development of the O/C and AF orderings, and they show peculiarities at T _CO and T _N . Between T _CO and T _N , the temperature dependence of the g factor exhibits a characteristic point that can be related to the appearance of the electric polarization revealed in manganites of this class.     

Anomalous reduced sound velocity of multiferroic TbMn2O5

The anomalous reduced sound velocity of multiferroic TbMn₂O₅ (TMO) has been studied using Green's function technique. To achieve this aim, the anharmonic phonon-phonon interaction and the spin-phonon interaction were used. It was shown that the reduced velocity of sound of TMO exhibits a kink at the ferroelectric phase transition temperature T_C. This can be explained as an effect of vanishing ferroelectric ordering above T_C. It was found that the reduced sound velocity increases with increasing V⁽³⁾ (the third-order atomic force constants of the anharmonic phonons) in the interval T?<?T_C, whereas the reduced sound velocity remains unchanged in the interval T_C?<?T?<?T_N. It was also found that the reduced sound velocity increases with the increase of V⁽⁴⁾ (the fourth-order atomic force constants of the anharmonic phonons) in the interval T?<?T_N. In addition, the ferroelectric phase transition temperature T_C decreases when V⁽⁴⁾ increases in the interval T?<?T_N. Those theoretical results are in agreement with the experimental data.     

Nonadiabatic interaction of acoustic phonons with spins <Emphasis Type="Italic">S</Emphasis>=1/2 in the two-dimensional Heisenberg model

The ground state of a two-dimensional antiferromagnet having spins S=1/2 and interacting with acoustic phonons is investigated in the nonadiabatic approximation using the quantum-mechanical Monte Carlo method. The critical parameters of the spin-phonon coupling, corresponding to the formation of bound spin-phonon excitations, crystal symmetry lowering, and the emergence of a gap in the spin excitation spectrum, as well as the antiferromagnet-quantum spin liquid transition, are determined. The orthorhombicity parameter, the sublattice magnetization, the violation of the spherical symmetry of spin-spin correlation functions, and the magnetic moment in Gd₂CuO₄ and Eu₂CuO₄ are calculated.     

Acoustic properties of multiferroic PbFe1/2Ta1/2O3

The longitudinal acoustic wave velocity and attenuation in PbFe_1/2Ta_1/2O₃ ceramics have been measured by pulse-echo technique in the temperature range from 4.2 to 530 K. The anomalies observed in the sound velocity and attenuation behavior versus temperature were correlated with Burns temperature, temperature range of the coexistence of relaxor ferroelectric and antiferromagnetic states, and a suggested second antiferromagnetic phase transition at low temperatures.     

Second order resonant Raman scattering at the E1 and E1 + Δ1 edges of germanium

The resonance of the 2TO phonon second order Raman band of germanium was investigated in the vicinity of the E₁, E₁ + Δ₁ gaps. The peak reported earlier for 2TO phonons at Γ is interpreted as due to a resonant process of the iterative type, involving two first order electron-phonon vertices. The rest of the 2TO band is interpreted as a process involving a second order electron-two phonon interaction vertex. From these measurements three phonon coupling constants for the electron-two phonon interaction are obtained.     

Optical and acoustic properties of 33PbIn1/2Nb1/2O3-35PbMg1/3Nb2/3O3-32PbTiO3 single crystals in an electric field

The influence of different conditions of applying a dc electric field (0 < E < 4 kV/cm) on the behavior of optical transmission and on the acoustic parameters (sound velocity and attenuation) in the [001]- and [011]-oriented single crystals 33Pb(In_1/2Nb_1/2)O₃-35PbMg_1/3Nb_2/3O₃-32PbTiO₃ existing near the morphotropic phase boundary has been investigated. It has been found that the optical transmission, sound velocity, and attenuation sharply change near the phase transition in a narrow range of electric fields for any method of their applying. In the field applied along [001], the change in the sound velocity due to the phase transition is 1.5 times greater than that in the field applied along [011]. This is caused by a larger contribution of the piezoelectric effect to the elastic modulus determining the sound velocity along [001] as compared to [011]. It has been shown that the number, symmetry, and stability of the phases formed in the field depend on the conditions of applying the field.     

Isotopic effect in Brillouin light-scattering spectra of a Cs5H3(SO4)4 · xH2O crystal

A Brillouin scattering study of the behavior of hypersonic longitudinal acoustic phonons in crystalline pentacesium trihydrogen tetrasulfate Cs₅H₃(SO₄)₄ · xH₂O (PCHS) and its deuterated analog Cs₅D₃(SO₄)₄ · xD₂O (DPCHS) at temperatures ranging from 420 to 120 K is reported. The effect of deuteration on the crystal lattice dynamics is investigated. The differences in the behavior of hypersonic acoustic phonons in the PCHS and DPCHS crystals suggest the existence of a hydrogen isotope effect in both the high-and low-temperature phases. A possible model of the isotopic effect in the high-temperature phase is discussed. An analysis is made of the acoustic response of the PCHS and DPCHS crystals in the region of the transition to the glasslike phase.