Ideal soft mode-type quantum phase transition and phase coexistence at quantum critical point in 18O-exchanged SrTiO3

The quantum ferroelectric phase transition of 18O-exchanged SrTiO3 (x% exchanged SrTiO3 is abbreviated as STO18-x) was investigated by Raman scattering as a function of x. The result indicates the ideal soft mode-type quantum ferroelectric phase transition of STO18-x, where the 18O exchange enhances the softening of the soft mode by the suppression of quantum fluctuation. In the vicinity of the quantum critical point (x approximately xc=33%), the system results in the ferroelectric-paraelectric phase coexistence state, in clear contrast to the homogeneous ferroelectric phase in STO18-x, whose x is sufficiently larger than xc. Simultaneously, the softening of the soft mode becomes strongly rounded with the underdamped oscillation. The present result indicates that the sensitivity of the soft phonon vibration to the mass disorder is dramatically enhanced in the vicinity of the quantum critical point.     

Ferroelectric domains and the condensed soft mode in gadolinium molybdate

Results of lattice dynamical calculations of the high temperature phase of gadolinium molybdate (GMO) support the view that the phase transition in GMO arises from a softening of a doubly degenerate zone edge mode. We find a close correlation between the displacements associated with these soft modes and the difference in the structure of the two phases, suggesting that, at the transition one or other set of soft mode displacements is ‘condensed’, or ‘frozen in’ to the structure. On this basis we can explain the ferroelectric switching.     

Order-disorder component in the phase transition mechanism of 18O enriched strontium titanate

Ti and Sr nuclear magnetic resonance spectra of 18O enriched SrTiO3 (STO-18) provide direct evidence for Ti disorder already in the cubic phase and show that the ferroelectric transition at T(C)=24 K occurs in two steps. Below 70 K rhombohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below T(C). This shows that the elusive ferroelectric transition in STO-18 is indeed connected with local symmetry lowering and implies the existence of an order-disorder component in addition to the displacive soft mode one. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric state of STO-16 as well. The concentration of the rhombohedral clusters is, however, not high enough to allow for percolation.     

钽酸锂铁电相变的喇曼光谱研究

本文测定了钽酸锂晶体从室温到居里温度以上(20—800℃)的喇曼光谱。没有观察到软模现象。我们发现在居里点附近,铁电相和顺电相的喇曼光谱十分一致,经过居里点喇曼光谱不发生变化。根据这个新的实验结果和文献上关于用中子衍射测定的晶体结构资料,我们做出了钽酸锂的铁电相变为有序无序型的推论。 关键词：     

Propagation of longitudinal ultrasonic waves in RbH2PO4 near its ferroelectric phase transition temperature

Ferroelectric phase transition in RbH₂PO₄ has been investigated using propagation of longitudinal acoustic waves along the polar axis near the transition temperature. The velocity of this mode is continuous across the transition temperature. Velocity data in the ferroelectric phase are analyzed in terms of coupled soft modeacoustic mode model of Pytte to obtain the temperature dependence of the soft mode frequency. The attenuation data in the ferroelectric phase show power law dependence. It follows scaling behaviour of the type predicted by Kawasaki from the mode-mode coupling theory and the dynamical scaling.     

“Soft” mode and coupled modes in the ferroelectric phase of KDP

Measurements of the pressure dependence of the Raman spectra in the ferroelectric phase of KDP have allowed us to identify the soft mode of the phase transition and to demonstrate that it is coupled to an optic mode of the lattice in this phase. The measured frequencies are compared with frequencies calculated from the microscopic parameters for the coupled-mode system.     

Comments on the paper ‘The origin of the ferroelectric phase transition in ammonium sulphate’

The ‘soft mode’ theory of ferroelectric phase transition in ammonium sulphate reported recently by Sawada and co-workers has been criticised on the basis of experimental and theoretical facts known to-date about the crystal. It has been pointed out that the ‘soft mode’ responsible for the phase transition should have appropriate mixing of the internal modes of SO^2-₄ ion.     

Phase transitions in barium–strontium titanate films on MgO substrates with various orientations

A comparative study of the lattice dynamic upon phase transitions in a polycrystalline Ba_0.8Sr_0.2TiO₃ (BST) film on a Pt substrate and in epitaxial BST films grown on various sections of an MgO substrate has been performed by Raman spectroscopy. It has been found that different sequences of phase transitions take place in these films. The BST/Pt films demonstrate the same sequence of phase transitions that is observed in the bulk ceramics. The hardening of a soft mode in BST/(001)MgO and BST/Pt films shows that the transition from the tetragonal ferroelectric phase to the paraelectric phase has features of the displacement-type phase transition and also the order–disorder phase transition. When approaching the ferroelectric transition temperature, the soft mode in the BST/(111)MgO film is softened, following the Cockran law, which indicates the displacement-type phase transition.     

KTa_(1-x)Nb_xO_3单晶的相变软模(英文)

用Ｒａｍａｎ散射研究了四方钽铌酸钾单晶的顺电 铁电结构相变,在相变时发现和分析了一个凝聚的软晶格振动模ｖ５,它是产生于Ｏ２ Ｏ３键的对称弯曲振动。     

Raman scattering in a ferroelectric sodium nitrite crystal

Raman spectra of the ferroelectric sodium nitrite are recorded over a wide spectral range at different temperatures, including the ferroelectric phase transition interval. The room-temperature Raman spectrum reveals the overdamped А₁(z) soft mode which is attributed to the ferroelectric phase transition.     

利用慢度曲面研究立方晶系晶体的铁弹相变

讨论了慢度曲面与声学模软化之间的关系.立方晶系晶体声学模的软化即对应其在某一方向上的最大慢度,软模的本征矢的方向即为与最大慢度相对应的声学模的偏振化方向.通过求解Christoffel方程可找到某些方向上的最大慢度和与它们对应的声学模的偏振化方向.从而晶体在本征铁弹相变前后结构对称性的变化可以通过分析Christoffel方程的解及利用居里原理来确定.     

New type of far-infrared soft mode in ferroelectric gadolinium molybdate

A new type of soft mode has been observed in far infrared transmission spectra of ferroelectric Gd₂(MoO₄)₃ in 40–50 cm^-1 region. The soft mode is split and its oscillator strength decreases towards the phase transition. Its contribution to the static dielectric constant is essentially temperature independent in the ferroelectric phase and amounts only to 0.034 ± 0.008.     

Soft modes and phonon interactions in studied by neutron scattering

The low frequency lattice dynamics and its relationship to the second order paraelectric-to-ferroelectric transition in Sn₂P₂S₆ is studied. The dispersion branches of the acoustic and lowest lying optical phonons in the a^*-c^* plane have been obtained in the ferroelectric phase, for x-polarized phonons. Close to the phase transition a considerable softening is found for the lowest optical mode (P_x), comparable to the behaviour observed in previous Raman investigations. As found previously in Sn₂P₂Se₆, a strong coupling between the TO(P_x) and TA(u_xz) phonons is observed, although, apparently, not strong enough to lead to an incommensurate phase. The soft TO(P_x) mode at the zone center is observed. The temperature dependence of its frequency and damping shows that the transition is not entirely displacive. At low temperatures an unusual apparent negative LO-TO splitting is observed which is shown to arise from the coupling of the x-polarized soft mode to the nearby z-polarized optical phonon. For comparison, the soft TO(P_x) dispersion in the a^*-b^* plane is measured in both the paraelectric and ferroelectric phases. Consistent frequency changes and LO-TO splitting are observed, revealing a significant interaction between the TA(u_yx) and LA(u_xx) acoustics branches and the TO and LO soft optic branches, respectively. In contrast, the nearby y-polarized optic branch shows almost no temperature dependence. Finally, the influence of piezoelectric effects on the limiting acoustic slopes in the ferroelectric phase is discussed. Received: 11 May 1998 / Revised and Accepted: 15 June 1998     

Quantum and classical mode softening near the charge-density-wave-superconductor transition of CuxTiSe2

Temperature- and x-dependent Raman scattering studies of the charge-density-wave (CDW) amplitude modes in Cu(x)TiSe(2) show that the amplitude mode frequency omega(0) exhibits identical power-law scaling with the reduced temperature T/T(CDW) and the reduced Cu content x/x(c), i.e., omega(0) approximately (1-p)(0.15) for p=T/T(CDW) or x/x(c), suggesting that mode softening is independent of the control parameter used to approach the CDW transition. We provide evidence that x-dependent mode softening in Cu(x)TiSe(2) is associated with the reduction of the electron-phonon coupling constant, and that x-dependent "quantum" (T approximately 0) mode softening suggests the presence of a quantum critical point within the superconductor phase of Cu(x)TiSe(2).     

Investigation of specific features of the lattice dynamics and the ferroelectric transition in perovskite crystals

The specific features of diffuse X-ray scattering in BaTiO₃, KNbO₃, and PbTiP₃ perovskite crystals have been investigated. The former two perovskite compounds in cubic, tetragonal, and orthorhombic phases exhibit anomalous sheets due to diffuse X-ray scattering, whereas no similar sheets are observed in the case of diffuse X-ray scattering in PbTiO₃. For these compounds, the phonon spectra are calculated in the quasi-harmonic approximation within the polarizable-shell model, and the mechanism of stabilization of the soft mode above the temperature of the phase transition to the ferroelectric state is considered. It is demonstrated that, in the cubic phase of BaTiO₃ and KNbO₃ crystals, there exist quasi-one-dimensional “soft” modes of vibrations of ions in M-O-M-O- chains, where M = Ti or Nb. In PbTiO₃, this feature of the soft mode has not been revealed. The pair correlation functions of simultaneous atomic displacements in BaTiO₃, KNbO₃, and PbTiO₃ are determined and used to calculate the intensity of diffuse X-ray scattering. The results obtained are in good agreement with experimental data. This is a strong argument in support of the hypothesis that the specific features of diffuse scattering are associated with the existence of quasi-one-dimensional correlations of atomic displacements in the soft optical mode and that the ferroelectric transition in perovskites is a displacive ferroelectric phase transition. The possible influence of the specific features revealed in the phonon spectra of the perovskite crystals on the processes of nuclear magnetic resonance and X-ray absorption (extended X-ray absorption fine structure spectra) is briefly discussed.     

Nonlinear dielectric susceptibility of dipole impurities dissolved in the lattice of quantum paraelectrics

A general relation is derived for calculating the nonlinear dielectric susceptibility of a system placed in an external ac magnetic field, which consists of tunneling and interacting dipole impurities described by the Hamiltonian of the transverse Ising model and a lattice of ions whose dynamics is specified in the soft-mode model with the possible ferroelectric phase transition suppressed by zero-point quantum oscillations. It is shown that the relaxation peaks in the dielectric response can be enhanced several times through relaxator interaction with the soft mode. A general expression is obtained to describe the deviation from the Arrhenius law in this case. The results of this work can be employed for interpretation of recent experiments that revealed a strong effect of isovalent impurities at extremely low concentrations on the macroscopic properties of incipient ferroelectrics.     

Inelastic Light Scattering Near the Ferroelectric Phase-Transition Point in Bismuth Vanadate Crystals

The Raman and Brillouin spectra in bismuth vanadate crystals near the ferroelectric phase-transition point are studied. The intensity maximum corresponding to the soft mode in light scattering spectra is found. This mode is responsible for the instability of the bismuth vanadate crystal lattice in the vicinity of the ferroelectric phase-transition point. Strong interaction of the soft optical mode with an acoustic mode of the corresponding symmetry is revealed by an analysis of the Raman and Brillouin spectra observed. The theory of light scattering by coupled lattice modes based on the model of two strongly coupled oscillators is developed. The introduction of an additional oscillator strongly interacting with the fundamental soft mode is shown to result in a temperature shift of the structural phase transition to higher temperatures. The results obtained confirm the possibility of changing the phase-transition temperature by modification of the vibrational spectrum through introduction of additional degrees of freedom or comminution of the macroscopic sample with formation of the ordered superdispersed structure (globular crystal). These results are general and can be subsequently used to increase the phase-transition temperature in ferroelastics, ferroelectrics, and superconductors.     

Off-center displacements and hydrostatic pressure induced phase transition in perovskites

Pressure has a profound effect on the paraelectric and ferroelectric properties of perovskite crystals. In this paper we theoretically investigate the effect of pressure on the cubic-to-tetragonal phase transition and on the soft mode dynamics of some classical perovskite crystals: BaTiO(3), PbTiO(3), and KNbO(3). We use a model consisting of three subsystems: electrons, phonons, and off-center displacements treated as spins. Experiments show that pressure has a large effect on the tunneling and hopping of the off-center displacements, that in turn strongly affect the pressure dependence of the transition temperature and the soft mode frequency. This model, with a very small number of adjustable parameters, accounts quantitatively for the experimentally measured nonlinear pressure dependence of the cubic-to-tetragonal phase transition temperature, up to the critical pressure where the transition temperature is zero. It also accounts quantitatively for the pressure dependence of the soft mode frequency, which is finite at the phase transition in spite of the fact that the phase transition at elevated pressures is second order, and for the pressure dependence of the electronic gap energy.     

Incomplete ferroelectricity in SrTi 18O 3

Motivated by recent experiments demonstrating suppression of ferroelectricity with pressure in SrTi¹⁸O₃, the dynamics of the phase transition mechanism are reinvestigated within a nonlinear polarizability model. For temperatures far above the phase transition polar micro domains are formed which increase in size with decreasing temperature to freeze out at T_c without forming long range order. Experimentally, soft mode dynamics are simultaneously observed, evidencing that displacive and order/disorder features coexist. In the ferroelectric phase both components persist whereby an incomplete and inhomogeneous ferroelectric state is formed.