Soft modes below the incommensurate transition in K2SeO4

A coordinated series of Raman and Brillouin scattering measurements were carried out in K₂SeO₄ with emphasis on temperatures near and below the incommensurate structural phase transition (T_i=129 K). Below the lock-in phase transition (T_c=99 K) Raman scattering from both the amplitude mode and the phase mode analog was observed. However, only the amplitude mode could be followed into the incommensurate phase. Details of the amplitude mode frequency and damping are reported for temperatures considerably closer to T_i than previously possible. Our results do not confirm the diverging linewidth extrapolated from earlier Raman work. We also report here the first Brillouin scattering results in K₂SeO₄. Although substancial interaction effects between the acoustic phonons and the soft amplitude mode are evident near T_i, the coupled mode lineshapes can be well described without the introduction of a relaxing self energy for the soft mode. Finally, limits on the characteristics of the phason are drawn from our failure to observe it directly in the incommensurate phase.     

Theoretical study of the magnetism in the incommensurate phase of TiOCl

Going beyond a recently proposed microscopic model [D. Mastrogiuseppe, A. Dobry, arXiv:0810.3018v1] for the incommensurate transition in the spin-Peierls TiOX (X=Cl, Br) compounds, in the present work we start by studying the thermodynamics of the model with XY spins and adiabatic phonons. We find that the system enters an incommensurate phase by a first order transition at a low temperature T_c1. At a higher temperature T_c2 a continuous transition to a uniform phase is found. Furthermore, we study the magnetism in the incommensurate phase by density matrix renormalization group (DMRG) calculations on a one-dimensional Heisenberg model where the exchange is modulated by the incommensurate atomic position pattern. When the wave vector q of the modulation is near π, we find local magnetized zones (LMZ) in which spins abandon their singlets as a result of the domain walls induced by the modulated distortion. When q moves far away enough from π, the LMZ disappear and the system develops incommensurate magnetic correlations induced by the structure. We discuss the relevance of this result regarding previous and future experiments in TiOCl.     

Light-scattering study of the non-zero wave vector incommensurate soft mode in K2SeO4

Observations are reported of inelastic light scattering from the non-zero wave vector soft phonon that drives the incommensurate structural phase transition in K₂SeO₄. They are shown to correlate with neutron scattering measurements of phonon frequency shifts on cooling to the incommensurate transition temperature. The observed light scattering is suggested to arise from intrinsic disorder.     

Specific heat behaviour of K2SeO4 in the 48K–800K temperature range a new phase transition

A calorimetric study performed on the ferroelectric K₂SeO₄ in the 48K–800K temperature range confirmed the existence of three phase transition and revealed the occurrence of a new one at 56.03±0.05K (T^IV_c). The critical measurements for the commensurate-incommensurate phase transition seem to show a cross-over behaviour.     

EPR lineshape study of the incommensurate phase in γ-irradiated K2SeO4

The temperature dependence of the SeO^4-₄ EPR frequencies and the asymmetric broadening of the EPR lines in the incommensurate phase of K₂SeO₄ can be explained by an incommensurate spatial modulation of the g tensors which corresponds to the “broad” phase soliton limit. A comparison between the experimental and calculated lineshape shows a ≈1% volume fraction of commensurate regions in the middle of the incommensurate phase at 110 K.     

Observation of soft-modes in a single crystal of Rb2ZnBr4 by Raman scattering

The Raman spectra of an oriented single crystal of Rb₂ZnBr₄ shows three soft modes. One of them is interpreted as the amplitude mode of the incommensurate phase. The second one, seen well below the lock-in transition temperature appears as the phase mode. Moreover, an additional soft mode is observed between T=120 K and T=20 K, in the b(c, c)a scattering geometry. By extrapolation it is found that its frequency would vanish around T₃=140 K ± 10 K. This soft mode is likely to be related to a new phase transition.     

Ferroelectricity and phase transition from incommensurate phase into commensurate one in (NH4)2ZnCl4

Phase transition has been found in (NH₄)₂ZnCl₄ at T = 266 ± 0.5 K by NQR method. There is a ferroelectric phase below T_c with a space group P2₁cn and with the trebling of the elementary lattice parameter along the axis c. Above the phase transition temperature in the crystal (NH₄)₂ZnCl₄ an incommensurate phase is realized.     

Inelastic neutron scattering study of commensurate-incommensurate phase transition in thiourea

This paper presents a study of the nature of the incommensurate lattice instability in deuterated thiourea by inelastic neutron scattering. It shows clearly a “soft mode” which condenses at the phase transition in a satellite reflexion. A study of related dispersion curves along the [O ξ O] direction shows an unusual spectral shape in a large temperature range above T_c.     

Scattering of light in a ferroelectric with incommensurate phase: K2ZnCl4

We presented and analyzed spectra of Raman scattering in various phase states of K₂ZnCl₄ crystals, including the incommensurate phase. On the basis of this analysis we determined the parameters of modes associated with internal and external motions of ions. We found that the phase mode reveals itself in the Raman scattering spectra; this mode is responsible for the instability of the crystal lattice in the vicinity of the incommensurate phase transition.     

Central peak for a scalar ϕ 4-model: mode coupling approach revisited

We reinvestigate the mode coupling approach to the central peak which occurs in the vicinity of a structural phase transition at T _c. For a scalar ? ⁴-model it is shown that the use of renormalized vertices leads to quite different results compared to recent calculations with bare vertices. Particularly, we prove that the latter are obtained in leading order of the anharmonicity constant of the on-site potential from a perturbational treatment of the renormalized vertices. Again, this mode coupling approach may yield a dynamical transition at a temperature T _c'(≥ T _c) at which the dynamics becomes nonergodic, i.e. a central peak occurs. For a ? ⁴- model with infinite range interactions our theoretical predictions are consistent with numerical results. Furthermore, if the fluctuations in the vicinity of Tc are Gaussian, no dynamical transition occurs above Tc. Therefore the temperature T ₀'obtained from the Ginzburg criterion sets an upper bound for T _c'. If a dynamical transition occurs, it is shown that the nonergodicity parameter as function of wave vector q and temperature T follows from an universal master function.     

Symmetry determination of commensurate and incommensurate phases of K2SeO4 by EPR

From a reinterpretation of EPR results on γ-irradiated K₂SeO₄ crystals, previously reported by Aiki et al., the space group symmetry for commensurate (ferroelectric) phase of K₂SeO₄ is determined to be Pna2₁. The EPR results support the modulation of polarization as the reason for disappearance of ferroelectricity in incommensurate phase.     

Far infrared and millimetre dielectric response of incommensurate and ferroelectric K2SeO4

Dielectric response of K₂SeO₄ in the spectral region 5–460cm^–1 was determined using transmissivity and reflectivity measurements as a function of temperature between 80 and 300K. The spectral features above 20cm^–1 are interpreted using results of lattice vibrational analysis in three known commensurate phases. The low-frequency dielectric anomaly in the incommensurate phase can be roughly described by critical slowing-down of a Debye relaxation given rise to by the overdamped infrared active phason mode which softens at the incommensurate-commensurate transition.     

Determination of incommensurate structures: Choice of atomic parameters

It is argued that in the diffraction diagram of an incommensurate modulated structure only the satellite reflections are sensitive to the relative phases of the atomic modulation functions. The consequences of this fact on the structure refinement and the choice of structural parameters are discussed. Taking into account these considerations, the structure of the incommensurate modulated phase of K₂SeO₄ is determined from new experimental data.     

DSC study of superionic phase transition in (NH4)4H2(SeO4)3 single crystals

DSC and complex impedance studies of the protonic conductor (NH₄)₄H₂(SeO₄)₃, which undergoes a superionic phase transition of first order at T_s = 378 K show that the activation energy of ionic conductivity d(lg σ)/dt and the ordering enthalpy ΔC_p of the crystal are proportional: d(lg σ)/dT = XΔC_p/RT_s + const, as found for MAg₄I₅ crystals undergoing a second-order superionic phase transition. Thus the short-range order environment of the species involved in fast-ion transport plays the main role in the superionic phase transition. This is also supported by the value of the entropy change at T_s, ΔS = 43 J/mole·K. A new metastable phase was found to be induced on heating the (NH₄)₄H₂(SeO₄)₃ crystal above T_s.     

The influence of phase transitions in the Rb<Subscript>2</Subscript>CdI<Subscript>4</Subscript> ferroelastic on the exciton absorption spectrum

The parameters of the long-wavelength exciton band for Rb₂CdI₄ films are investigated in the temperature range 90–410 K. It is found that the Rb₂CdI₄ films undergo a sequence of phase transitions at temperatures T_c1=380 K (paraphase → incommensurate phase), T_c2=290 K (incommensurate phase → ferroelastic phase I), and T_c3 = 210 K (ferroelastic phase I → ferroelastic phase II). The parameters of the exciton band (such as the spectral position and the half-width) measured during heating and cooling of the Rb₂CdI₄ film differ significantly. This is especially true for the incommensurate phase. Upon heating of the incommensurate phase, the domain boundaries become frozen, whereas the cooling of this phase is accompanied by the generation of solitons and their pinning, which, in turn, results in a first-order phase transition at the temperature T_c2. It is revealed that the oscillator strength of the exciton band anomalously increases in the range of existence of commensurate phase I (T_c3<-T<-T_c2) due to ordering of the Rb₂CdI₄ crystal lattice.     

X-ray diffraction study of a structural phase transition in (NbSe4)3I

The second-order structural phase transition was observed by X-ray diffraction technique in (NbSe₄)₃I. The transition temperature (T_c) was 274.2 K. No evidence of the formation of the charge-density wave was found out. Temperature dependence of the intensity of (0,5,12) reflection obeys the Landau theory of the second kind of phase transition near T_c. Temperature dependence of the integral breadth of (0,0,12) reflection indicates the effect of the soft-phonon mode below T_c. The existence of the structural phase transition, probably not associated with charge-density-wave formation, suggests the unique nature of (NbSe₄)Z₃I in the new series of compounds (MSe₄)_xI (M=Nb, Ta).     

New results in the study of Brillouin scattering in thiourea

Below T₂ = 202 K, in the incommensurate phase, a Debye relaxation appears for c₃₃; it can be attributed to a linear coupling between an acoustical mode and a phason. The relaxation time is τ = τ₀/(T₀?T) with τ₀ = 6.2 x 10^?12 sec deg and T₀ = 200.9 K. The same phenomenon appears more weakly for c₁₁. The c₆₆ elastic constant has a double discontinuity around T₁ = 169 K; this shows that in the vicinity of T₁ there are two transitions, separated by a temperature interval of 3°.     

Effect of γ irradiation on the low-temperature electrical conductivity and dielectric properties of TlGaSe2 crystals

Electrical conductivity and dielectric properties of single-crystal TlGaSe₂ have been studied as a function of γ irradiation dose in the 100–280 K range including the existence of an incommensurate phase. Anomalies in the form of maxima have been observed in the σ=f(T), tan δ=f(T), and ɛ=f(T) curves at the points of transition from the paraphase to incommensurate (IC) phase, T _i, and from the IC to commensurate phase, T _c. The increase in the quantities σ, tan δ, and ɛ observed initially with increasing irradiation dose is followed by their strong decrease and disappearance of the anomalies. It has been established that γ irradiation does not affect the phase transition temperatures T _i and T _c. Fiz. Tverd. Tela (St. Petersburg) 40, 1328–1331 (July 1998)     

Neutron evidence for an overdamped phason branch in incommensurate K2SeO4

Neutron results on the incommensurate phase of K₂SeO₄ taken near a strong satellite reflection, reveal a heavily damped inelastic feature which is identified as the phase-mode response. The damped-harmonic-oscillator analysis of the experimental spectra leads to mode-parameter values which are consistent with recent optical results.     

Ultrasonic studies of the high Tc superconductor (La1−xSrx)2CuO4−δ

We synthesized (La_1−xSr_x)₂CuO_4−δ crystals with 0 ≦ x ≦ 0.4 by the sintering method, and obtained several samples with good homogeneity, high onset superconducting transition temperature T_c ≲ 38 K and narrow transition width ΔT_c. For the sample with the maximum T_c among them, ultrasonic measurements were performed. In the curve of the sound velocity change ΔV_s(T) versus temperature T, there was observed an anomalously large decrease of sound velocity as T decreases in the range 150 K < T < 240 K. Furthermore, in the plots of the ultrasonic attenuation coefficient α(T) as a function of T, there were observed a broad and large peak located at T ∼ 100 K and a small peak located at T ∼ 200 K. These results show the existence of an optical mode of the energy ℏω_op/k_B ∼ 100 K and, probably, also of that of ∼ 200 K. On the basis of these experimental results of elastic properties, we suggest the origin of high T_c of this material.