Soft Mode Frequency Research Articles

Spectrum of Elementary Excitations of Mixed-Valence Molecular Crystals

The spectrum of elementary excitations of molecular crystals comprising mixed-valence d1–d2 clusters has been investigated. Depending on the number of phase transitions arising in the systems under consideration two types of temperature behaviour of the soft mode frequency are shown to be possible. An anomalous temperature dependence of the elastic modulus is predicted.

Polarization dependence of Born effective charge and dielectric constant in KNbO3.

The Born effective charge Z^{*} and dielectric tensor \epsilon_{\infty} of KNbO_3 are found to be very sensitive to the atomic geometry, changing by as much as 27% between the paraelectric cubic and ferroelectric tetragonal and rhombohedral phases. Subtracting the bare ionic contribution reveals changes of the dynamic component of Z^{*} as large as 50%, for atomic displacements that are typically only a few percent of the lattice constant. Z^{*}, \epsilon_{\infty} and all phonon frequencies at the Brillouin zone center were calculated using the {\it ab initio} linearized augmented plane-wave linear response method with respect to the reference cubic, experimental tetragonal, and theoretically determined rhombohedral ground state structures. The ground state rhombohedral structure of KNbO_3 was determined by minimizing the forces on the relaxed atoms. By contrast with the cubic structure, all zone center phonon modes of the rhombohedral structure are stable and their frequencies are in good agreement with experiment. In the tetragonal phase, one of the soft zone center modes in the cubic phase is stablized. In view of the small atomic displacements involved in the ferroelectric transitions, it is evident that not only the soft mode frequencies but also the Born effective charge and dielectric constants are very sensitive to the atomic geometry.

Raman Scattering Study of Cubic to Tetragonal Phase Transitions in Mixed System AxBa1-xTiO3

The ferroelectric phase transition with the point group change from m3m to 4 mm in the mixed system Ax Ba1-x TiO3 (A=Pb, Sr) was studied by Raman scattering measurements. The low frequency spectra show strong dependence on both composition and temperature. The square of the soft mode frequency shows a linear dependence on T c. While, in temperature dependence, the soft mode of Pb0.14Ba0.86TiO3 slightly decreases towards T c on heating, but the softening is suppressed near T c. Peak frequencies higher than 100 cm-1 are insensitive to both composition and temperature. The mode intensity gradually decreases with increasing temperature. In spite of the fact that all optical modes should be Raman inactive above T c, a few modes are still observed in the spectra.

High-pressure dielectric and lattice vibration studies of the phase transition in lithium thallium tartrate monohydrate (LTT)

A substantial increase of the ferroelectric phase transition temperature with hydrostatic pressure was observed for lithium thallium tartrate monohydrate single crystals. The temperature dependence of the permittivity shows an unusual shape exhibiting a broad plateau in below . It follows from our hysteresis loop measurements that the domain wall motion freezes approximately 5 - 15 K (this value is pressure dependent) below and causes the drop in . The temperature and pressure dependence of the soft-mode frequency was measured by far-infrared as well as Raman spectroscopy at 10 - 300 K and 0.1 - 440 MPa. The soft mode softens only incompletely because of its strong coupling with a transverse acoustic mode.

Microwave Dielectric Dispersion in Deuterated Betaine Phosphite

The dielectric behaviour of ferroelectric hydrogen-bonded deuterated betaine phosphite crystals is investigated in the frequency range up to 4 GHz. The dielectric dynamics of Debye type shows a critical slowing-down of the polarization fluctuations. The frequency of the relaxational soft mode in the para-electric phase varies according to v s = 0.2(T - 295.8) GHz and decreases to 0.55 GHz at T C = 298 K.

Dynamics of ferroelectric thin films described by the transverse Ising model

The dynamic properties of thin films described by the Ising model in a transverse field (TIM) have been studied under the random-phase approximation. The frequencies of soft modes and surface modes have been obtained. For films with reduced surface interaction (compared to the bulk), the soft mode corresponds to a surface-like mode in the ferroelectric phase but to a bulk-like mode in the paraelectric phase. Conversely, for films with an enhanced surface interaction, the soft mode is a bulk-like mode in the ferroelectric phase and a surface-like mode in the paraelectric phase. The number of surface-like modes in the ferroelectric phase can be greater than one; the number increases as the temperature approaches the Curie temperature, and does not depend on the in-plane wavevector for a given temperature in the ferroelectric phase. However, there is only one surface-like mode in the paraelectric phase, and its character becomes bulk-like at large wavevector. The surface modes can be clearly seen from the frequency dependence of the dynamic susceptibility; the surface mode pole increases in strength with decreasing film thickness. The frequency dependences of optical reflectivity coefficients have also been obtained. The reflection peaks due to the surface modes lie below the bulk reststrahl band in the ferroelectric phase of films with reduced surface ferroelectricity, and also in the paraelectric phase of films with enhanced surface ferroelectricity; otherwise, they lie within the reststrahl band.

Soft mode observation in paraelectric SbSBr

From the temperature dependence of the Raman spectra in the paraelectric SbSBr, the B 1u soft mode was observed in the X(ZZ)Y configuration as the state density, which became Raman active due to strong electron-phonon coupling. The soft mode frequency was obtained from the minimum energy of the state density and the temperature dependence of Ω( T) 2 = 500 + 4.8 × ( T − T c), T c = 22.8 K cm −2. This mode led to an A 1 soft mode with strong intensity in the ferroelectric phase.

Successive phase transitions of hexagonal barium titanate: soft acoustic mode and coupled acoustic-soft optic mode

The successive phase transitions at T 0 (222 K) and T C (74 K) of hexagonal BaTiO 3 have been studied by Brillouin scattering. An intense central peak was found near T 0 and was identified as a result of scattering from the coupled soft optic and acoustic mode. The coupled mode model was employed in order to explain the observed spectral changes. The ω 0 2Γ 0 ratio of the soft optic mode frequency ω 0 and the damping constant Γ 0, and the square of bilinear coupling constant A show linear dependence on temperature difference T − T 0, indicating the mean field behavior. The clear softening of c 66 shear acoustic mode was found near T C. The square of frequency of c 66 mode depends linearly on T − T C around the transition temperature. The results conclusively show that the phase transition at T C is the proper ferroelastic transition with the order parameter strain s 6.

Raman spectroscopy of quantum paraelectric SrTiO 3 fine particles

Size effects of quantum paraelectric SrTiO 3 particles were studied by Raman scattering. The particles were synthesized by a sol-gel method. The particle sizes were controlled by the firing temperatures and determined by the X-ray analysis to range from 12 to 44 nm in diameter. The soft mode frequencies of the smaller particles were higher than those of the larger particles in the low temperature. The soft mode behavior was conforming with dielectric results of the Lyddane-Sachs-Teller relation.

Raman scattering and the evolution of polar order in Li-doped and Nb-doped KTaO3.

A comparative study of first-order Raman scattering in ${\mathrm{K}}_{0.984}$${\mathrm{Li}}_{0.016}$Ta${\mathrm{O}}_{3}$ and K${\mathrm{Ta}}_{0.976}$${\mathrm{Nb}}_{0.024}$${\mathrm{O}}_{3}$ single crystals has been performed. The soft-phonon line shows marked differences in the two systems, revealing a distinctive behavior with regard to the scale of polar order. Analysis of the low-frequency spectrum allows for an estimate of the polar correlation length in the Li-doped sample; this is limited to the nanometric scale, in agreement with the view of a dipole-glass transition. No evidence of a similar situation is found in the Nb-doped sample, where the general trend of soft-mode frequencies and intensities suggests a transition to a state of long-range order, for the quoted concentration. The intensities of the hard-phonon spectra and the T${\mathrm{O}}_{4}$ linewidth are shown to confirm the different evolution of the polar transition in the two systems.

Pressure dependence of the soft modes in the model ferroelastics Hg2I2

The pressure dependence of the soft modes in the paraphase (boundary of the Brillouin zone, X point) and the ferrophase (center of the Brillouin zone, Γ point) is studied in the model ferroelastic crystals Hg2I2. An anomalous linear pressure dependence of the soft-mode frequency in the paraphase (p<pc) is observed. The results obtained and the nature of the ferroelastic phase transition induced in Hg2I2 crystals by a high hydrostatic pressure are discussed.

The soft mode behaviour and electron correlation effect in the pseudo Jahn-Teller system

The relationship between electron correlation and lattice instability is discussed in this paper. A exciton Hamiltonian coupled with lattice motion is proposed to include the many body effect of the electron correlation. In strong coupling case we can limit our discussion to an effective Hamiltonian in which only the ground state and the low excited state is included. A pseudo spin representation is introduced, and the Green function technique is used to calculate the frequency of the soft mode. Our result implies that electron correlation will greatly enhance the lattice instability.

Nonlinear dynamics of a two-dimensional lattice

The dynamics of the nonlinear excitations in a two-dimensional (2D) φ4-diatomic lattice, with nonlinear on-site electron-phonon coupling at the polarizable ion site has been presented, without considering the self consistent phonon approximation. One of the major results obtained from our calculations is in the understanding of continuous structural phase transition, where we have obtained the minimum in soft mode frequency at a soft mode temperatureT s (>T c), not at critical temperatureT c. This occurs due to the anisotropy of such 2D systems.

Hyper-Raman study of Li-induced polarization clusters in K1-xLixTaO3

The low-frequency hyper-Raman spectrum of K1-xLixTaO3(x=0.011,0.016, and 0.036) is measured as a function of temperature between 10 and 200 K. At each Li concentration x and temperature T, the spectrum in the wavenumber range below 150 cm-1 is adequately described by the sum of a damped harmonic oscillator lineshape and a central delta function representing the soft-mode and hyper-Rayleigh scattering, respectively. The x and T dependence of the hyper-Rayleigh intensity IHRL(x,T) reflects the growth and coalescence of polarization clusters induced in the incipiently unstable host lattice by the off-centre displacements of the Li ions. The concept of a cluster coalescence temperature Tcc(x) is introduced and verified for IHRL(x,T). From the increase of IHRL(x,T) between Tcc(x) and 10 K, the low-temperature limit of the dipolar correlation radius is estimated. While IHRL(x,T) is a smooth and single-valued function of temperature for x=0.011 and 0.016, it exhibits a thermal hysteresis loop with rather steep edges for x=0.036, in accordance with a previous conjecture that the condensation of the Li subsystem changes its character at a crossover concentration around 0.022. In contrast to IHRL(x,T), the soft-mode frequency Omega 0(x,T) turns out to be insensitive to the coalescence of polarization clusters because it monitors quadrupolar rather than dipolar correlations. Up to x=0.036, the Li-induced increase of the soft-mode damping constant y(x,T) cannot be explained in terms of an unresolved soft-mode splitting due to the tetragonal symmetry of the polarization clusters. Instead, the influence of symmetry reduction and disorder on the selection rules of multiphonon damping processes has to be considered. As in IHRL(x,T), new features are observed in y(x,T) when passing from x=0.016 to x=0.036.

Brillouin scattering study of hexagonal BaTiO3

Abstract The successive phase transitions at T 0 (222 K) and T c (74 K) of hexagonal BaTiO3 have been studied by Brillouin scattering. The anomalous central peak was found near T 0, and drastic changes in spectral shape and intensity were observed below T 0. The coupled-mode model for a soft optic and acoustic mode was employed to fit the experimental data in order to explain the observed spectral changes. The ω2 0/Γ0 ratio of soft optic mode frequency ω0 and damping constant Γ0 and the square of bilinear coupling constant show linear dependence on T - T 0, indicating the mean-field behavior. The complete softening of c66 shear acoustic mode was found near T c . The square of the frequency of c66 shear acoustic mode depends linearly on the temperature T –- T c . The results suggest that the phase transition at T c is the proper ferroelastic transition with the order parameter strain s6.

Refined treatment of the model of linearly coupled anharmonic oscillators and its application to the temperature dependence of the zone-center soft-mode frequencies of KTaO3 and SrTiO3.

The temperature behavior of the zone-center soft modes of ${\mathrm{KTaO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$ is remeasured betwen 5 and 300 K by the technique of hyper-Raman spectroscopy, the experimental errors of soft-mode frequency and damping constant being reduced to below \ifmmode\pm\else\textpm\fi{}1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The results are taken as a stimulus to a refined treatment of the prototype dynamical model of a ferroelectric crystal, i.e., a lattice of anharmonic oscillators randomly driven by a heat bath and coupled to each other by a dipolarlike intercell interaction. While the intercell coupling is described as previously in terms of a molecular-field approximation, the pseudoharmonic frequency of the anharmonic oscillator at each lattice site is calculated as exactly as possible within the framework of the statistical-linearization approach. The effective classical potential method is used to test a variety of local anharmonic-oscillator potentials. In the case of ${\mathrm{KTaO}}_{3}$ excellent fits to the experimental values of the soft-mode frequency ${\mathrm{\ensuremath{\Omega}}}_{0}$(T) are obtained on the basis of only three parameters characterizing globally the harmonic limit, the anharmonicity, and the dipolar interaction, respectively. In the case of ${\mathrm{SrTiO}}_{3}$ some uncertainty arises from the unknown dependence of these parameters on the octahedral rotation in the antiferrodistortive phase below 105 K. In both materials ${\mathrm{\ensuremath{\Omega}}}_{0}$(T) turns out to be too smooth for deducing details of the local anharmonic-oscillator potential like its anisotropy and the ratio of sextic and quartic anharmonicity parameters. On the other hand, local potentials of the multiple-well type with quartic anharmonicities and negative harmonic terms can definitely be excluded.

Soft modes and structural phase transitions in La 2CuO 4

The structural sequence HTT(D 4h 17)→LTO(D 2h 18)→LTO2(D 4h 16)→LTT(D 4h 16) in doped La 2CuO 4 is considered with the Landau-type thermodynamic potential proposed by J.D. Axe et al. [Phys. Rev. Lett. 62 (1989) 2751]. The temperature dependence of the soft mode frequencies associated with instability of these phases is calculated. It is shown that the mode frequencies are not equal to zero at the temperature of transformation LTO2→LTT if the order parameter susceptibilities are considered to be elastically clamped. The inverse sequence HTT→LTT→LTO2→LTO which is theoretically possible is also treated.

Examination of order-disorder and soft modes in perovskite ferroelectrics by impulsive stimulated Raman scattering

The dynamics of low frequency soft modes and order-disorder modes in the orthorhombic phase of KNbO3 and the tetragonal phase of BaTiO3 have been examined using a time-domain technique, impulsive stimulated Raman scattering (ISRS). There was no evidence in either crystal for an order-disorder mode with the same symmetry as the soft mode. Order-disorder modes were found to have different symmetry from the soft modes. Excellent agreement was found in both crystals between capacitance measurements and the LST value of the component of the low frequency dielectric constant which depends on the soft mode frequency. These results are consistent with the predictions of the eight-site model for the crystals and their transitions.

STABILISATION OF PARAELECTRIC PHASE BY STRONG CUBIC AND QUARTIC PHONON ANHARMONICITIES IN KDP CRYSTAL

Considering cubic and quartic phonon anharmonic interactions into the pseudospinphonon coupled mode model of Kobayashi6 expressions for shift, width, soft mode frequency and hence Curie temperature, dielectric susceptibility, Curie-Weiss constant and dielectric (tangent) loss have been evaluated for ferroelectric KDP. The method of retarded double-time thermal Green’s function and the treatment of Dyson’s equation have been used in the development. It is shown that cubic and quartic phonon anharmonic interactions render real value to the soft mode frequency in the para-phase. Results are in agreement with the experimental results of others.

Measurement of soft mode damping in SrTiO 3 by FIR surface waves

The results of investigation of low-frequency modes in SrTiO 3 crystals by FIR surface electromagnetic waves (SEW) are presented. Amplitude and phase spectroscopy methods, including SEW heterodying for the complex SEW refraction index n ef measurements at temperatures of 80–300 K were applied. The SEW method appears to be convenient for the soft mode (SM) frequency and damping measurements and advantages against other method are discussed. The possible reasons of disagreement of SEW damping values at v = 84 cm −1 obtained by us and others are discussed. Sharp increase of SEW damping at this frequency when temperature increases was explained by transition of Fano type mode ( v < v TO) to Zenneck-Sommerfeld one ( v > v TO) with sufficiently larger damping. At liquid N temperature SM frequency take the value of 43 cm −1. It sufficiently well agrees with the one obtained by hyper-Raman and IRR methods. YBa 2Cu 3O 7 − x thin films Preliminary experiments with ferroelectric Ba x Sr 1 − x TiO 3 and superconducting on SrTiO 3 showed the SEW sensitivity to the phase transitions of films. The maximum of SEW damping in Ba x Sr 1 − x TiO 3 at the phase transition temperature was obtained. The plasma frequency v p as well as electron collisional frequency v τ in YBa 2Cu 3O 7 − x was obtained ( v p = 10 4cm −1, v t = 3000 cm −1 at 300 K).