Critical behaviour of Sn2P2S6 and Sn2P2(Se0.28S0.72)6 crystals under high hydrostatic pressures

Basing on the temperature dependences of optical birefringence for Sn₂P₂S₆ and Sn₂P₂(Se_0.28S_0.72)₆ crystals subjected to hydrostatic pressures, we prove unambiguously that Sn₂P₂S₆ reveals a tricritical point on its (p, T)-phase diagram with the coordinates (p, T) = (4.3 kbar, 259 K), so that the second-order phase transition transforms into the first-order one whenever the pressure increases above 4.3 kbar. We also find that increasing hydrostatic pressure applied to Sn₂P₂(Se_0.28S_0.72)₆ leads to the change in the phase transition character from tricritical to first order. Further increase in the pressure up to ~2.5 kbar imposes splitting of the first-order paraelectric-to-ferroelectric phase transition into two phase transitions, a second-order paraelectric-to-incommensurate one and a first-order incommensurate-to-ferroelectric transition.     

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<p _c ) is observed. The results obtained and the nature of the ferroelastic phase transition induced in Hg₂I₂ crystals by a high hydrostatic pressure are discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 227–231 (25 February 1996)     

Acoustic wave velocities and elastic properties of Sn2P2(Se0.28S0.72)6 solid solutions

An experimental study and analysis is presented of the acoustic properties of Sn₂P₂(Se_0.28S_0.72)₆ ferroelectric crystals. Complete matrices of elastic stiffness and compliance as well as characteristic acoustic slowness surfaces have been obtained. The directions of propagation and polarisation of the slowest acoustic waves were determined. It was found that the elastic properties and the acoustic wave velocities for Sn₂P₂(Se_0.28S_0.72)₆ and Sn₂P₂S₆ crystals are almost the same at room temperature.     

Baric dependence of the fundamental absorption edge in the region of phase transitions of Sn2P2S6-type intrinsic ferroelectrics

The energy position of the fundamental absorption edge in the neighborhood of phase transitions in Sn₂P₂S₆ and (Pb_0.1Sn_0.9)₂P₂S₆ ferroelectric crystals is studied as a function of the temperature and baric dependence on the basis of direct measurements of the isoabsorption relations. Thep, T phase diagram of Sn₂P₂S₆ crystals is constructed. the temperature-dependent variation of the band gap in those crystals is due mainly to electron-phonon interaction. Uzhgorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 82–85, August, 1997.     

On the special points on the (P,T, x)-phase diagram for Sn2P2(Se x S1− x )6 crystals: acoustic studies of Sn2P2(Se0.28S0.72)6

On the basis of temperature dependences of the acoustic wave velocity and the acoustic attenuation in Sn₂P₂(Se_0.28S_0.72)₆ crystals under normal conditions and hydrostatic pressures, we show that increasing pressure causes these crystals to move away from the tricritical point and enter into the region of first-order phase transitions (PTs) in (P,?T,?x)-space. Still higher hydrostatic pressures lead to an increase in the attenuation of the acoustic wave with the velocity v ₂₂ and broadening of its anomaly in the PT region, thus hinting at splitting of the PT, with the appearance of an intermediate incommensurate phase approximately at P?=?3.3?kbar. We offer a (P,?T,?x)-phase diagram for the solid solutions Sn₂P₂(Se _x S_{1? x} )₆, which includes two special lines of PTs, tricritical and triple ones, which can intersect at the Lifshitz point at negative hydrostatic pressures. The variations of the surface of acoustic wave velocities occurring with changing temperature are obtained for Sn₂P₂(Se_0.28S_0.72)₆ crystals under the atmospheric pressure.     

Thermal expansion of the Sn2P2(Se0.28S0.72)6 solid solutions

In the present work, we have experimentally studied and analysed the dilatometric properties of Sn₂P₂(Se_0.28S_0.72)₆ crystals during ferroelectric phase transition. A complete matrix of thermal expansion tensors as well as the characteristic surface of the thermal expansion tensor has been obtained. The critical exponent for the volume thermal expansion coefficient in Sn₂P₂(Se_0.28S_0.72)₆ crystals has been determined to be equal to 0.50 ± 0.06, which is peculiar to tricritical behaviour. Non-agreement in the values of the critical exponents evaluated from the temperature dependencies of relative elongation (0.17 ± 0.01) and volume thermal expansion coefficient (0.50 ± 0.06) is shown to be due to the possible temperature rotation of the spontaneous polarisation vector.     

Splitting of the phase transition in ferroelectric solid solutions Sn2P2(SexS1−x)6 at high pressures

The influence of the temperature and hydrostatic pressure on the forbidden band width and dielectric permittivity of the ferroelectric solid solutions Sn₂P₂(Se_xS_1–x)₆ (x=0.04, 0.20, 0.30) is investigated. A change in the species and splitting of ferroelectric phase transition lines are detected for p = 0.140 and 0.026 GPa, respectively, for the solid solutions Sn₂P₂(Se_0.04S_0.96)₆ and Sn₂P₂(Se_0.20S_{0.80 6}, which is due to the existence of a Lifshits critical point separating the transitions into codimensional and noncodimensional phases on the p, T diagram. Shift coefficients with the pressure of the phase transition temperature are found for the solid solutions investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 28–32, February, 1988.     

Dielectric properties of Sn2P2S6 crystals as a function of their growth conditions

The behavior of the permittivity near a phase transition in Sn₂P₂S₆ crystals of different technological quality is studied. It is established that, in high-resistance crystals, where an internal electric field is formed by the screening of spontaneous polarization in the polar phase, long-time relaxation of ɛ is observed in a temperature range ∼2 K above T _max. This relaxation and change in the form of the maximum of ɛ′(T) at a phase transition are attributed to an internal electric field induced by the volume space charge formed in regions near the surface. It is established that the existing differences in the properties of Sn₂P₂S₆ crystals are due to deviations from stoichiometry, arising during growth and synthesis of the crystals. Fiz. Tverd. Tela (St. Petersburg) 41, 1456–1461 (August 1999)     

New phase-transformation line and intermediate phase in Sn2P2S6

A study is made of the effect of temperature and hydrostatic pressure on the permittivity, forbidden-band width, electrical conductivity, and photoconductivity of crystals of Sn₂P₂S₆. The empirical results obtained indicate that a new phase-transformation line exists on the p-T diagram of Sn₂P₂S₆ p > 0.17 GPa. This phase transformation is evidently a second-order transition, separating a paraelectric, proportionate phase from an intermediate, possibly nonproportionate phase. The results also indicate similarity of the p-T diagram of Sn₂P₂S₆ to the x-T diagrams of ferroelectric solid solutions of Sn₂P₂(Se_xS_1–x)₆.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 57–60, September, 1985.     

Acoustic attenuation in ferroelectric Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> crystals

The temperature and frequency dependencies of sound attenuation for the proper uniaxial ferroelectric Sn₂P₂S₆, which has a strong nonlinear interaction of the polar soft optic and fully symmetrical optic modes that is related to the triple well potential, were studied by Brillouin spectroscopy. It was found that the sound velocity anomaly is described in the Landau-Khalatnikov approximation with one relaxation time. For explanation of the observed temperature and frequency dependencies of the sound attenuation in the ferroelectrric phase, the accounting of several relaxation times is needed and, for quantitative calculations, the mode Gruneisen coefficients are more appropriate as interacting parameters than are the electrostrictive coefficients. Relaxational sound attenuation by domain walls also appears in the ferroelectric phase of Sn₂P₂S₆ crystals.     

Fundamental reflection spectrum and the electronic band structure of chlorine-doped CdTe

The effect of chlorine impurity on the fundamental reflection spectrum and the electronic band structure of cadmium telluride crystals has been studied. At the impurity concentration N _Cl>5.0×10¹⁹ cm^?3, a peak appears in the reflectance spectra. This peak is due to electron transitions at the X point of the Brillouin zone from the upper split valence band to Cl levels lying 0.05 eV above the Γ minimum of the conduction band. The other features in the reflectance spectra and band structure are explained as being due to the effect of spin-orbit splitting at the X point and to indirect electronic transitions from the Cl levels to the Γ minimum.     

Microwave study of the soft ferroelectric mode in Sn2P2S6 crystals

This paper presents the results of the investigation of dielectric dispersion in semiconductive ferroelectric Sn₂P₂S₆ crystals over the frequency range 1 kHz to 78.5 GHz. The main dielectric dispersion in Sn₂P₂S₆ is caused by the soft ferroelectric B_u mode and in the vicinity of the Curie point it occurs in the millimeter region. The frequency of the soft mode in the paraelectric phase varies according to v_s = 35 (T-T_c )^½ GHz on approaching the Curie point. The soft mode is strongly overdamped. Close to T_c the relative damping is y/v_s = 14. The dielectric contribution of the soft mode is equal to the static dielectric permittivity and it explains its whole temperature-dependence.     

About the existence of a Lifshitz point on the phase diagram of Sn2P2(Se x S1– x )6 solid solutions: acoustic and optical studies

On the basis of combined studies of the acoustic and optical properties of Sn₂P₂(Se _x S_{1– x} )₆ solid solutions with x?=?0 and 0.28 it is shown that two special points exist on the x,T-phase diagram of these ferroelectric crystals, a tricritical point and a triple one. With increasing Se concentration, the phase transition changes its character at x?≈?0.28 from second-order to first-order. The phase transition becomes split at x?≈?0.4, with the appearance of an intermediate incommensurate phase.     

Energy band structure and Frenkel excitons in PbGa2S4

Optical reflection spectra are measured and calculated in PbGa₂S₄ crystals in the region of resonances related to excitons with large oscillator strength and binding energy (Frenkel excitons). The splitting of the upper valence band in the center of the Brillouin zone due to crystal field (Δ_cf) and spin orbit (Δ_so) interaction are determined. Optical reflection spectra are measured and calculated according to Kramers-Kronig relations in the region of 3-6 eV in Е⊥с and Е∥с polarizations, and the optical constants n, k, ε₁ and ε₂ are determined. The observed electronic transitions in PbGa₂S₄ crystals are discussed in the frame of theoretical energy band structure calculation for thiogallate crystals.     

Optical spectra and energy band structure of AgAsS2 crystals

Ground and excited states of three exciton series are observed in the region of fundamental absorption edge of AgAsS₂ crystals. The contours of exciton reflection spectra are calculated and the main parameters of excitons and energy bands are determined in the center of Brillouin zone. The optical reflection spectra are investigated at 30 K in E∥c and E⊥c polarizations in AgAsS₂ crystals in the region of 2-6 eV. The optical functions are calculated from the reflection spectra and a scheme of electronic transitions responsible for peculiarities of reflection spectra deep into the absorption band is proposed.     

Electronic structure,topological phase transitions and superconductivity in (K,Cs)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Fe<Subscript>2</Subscript>Se<Subscript>2</Subscript>

We present LDA band structure of novel hole doped high temperature superconductors (T _c ∼ 30 K) K _x Fe₂Se₂ and Cs _x Fe₂Se₂ and compare it with previously studied electronic structure of isostructural FeAs superconductor BaFe₂As₂ (Ba122). We show that stoichiometric KFe₂Se₂ and CsFe₂Se₂ have rather different Fermi surfaces as compared with Ba122. However at about 60% of hole doping Fermi surfaces of novel materials closely resemble those of Ba122. In between these dopings we observe a number of topological Fermi surface transitions near the Γ point in the Brillouin zone. Superconducting transition temperature T _c of new systems is apparently governed by the value of the total density of states (DOS) at the Fermi level.     

Two-photon absorption and energy band structure of orthorhombic Hg2Cl2 crystals

Dependence of two-photon absorption (TPA) rate on the state of polarization of a laser beam is investigated in the low-temperature orthorhombic modification of Hg₂Cl₂ crystals. Theoretical calculations of the dependence of TPA rate on the direction of polarization vector of the beam are performed for centrosymmetric points, Y, Z, T, R andS of the Brillouin zone. The domain structure of real crystals is taken into consideration and it is shown that periodicity of the polarization dependence may indicate whether TPA is due to transitions either at, Y, Z, T orR, S points. The polarization dependence of TPA cannot, however, distinguish between points inside these two groups. Comparison of theory with a low-temperature (T 8·5 K) experimental curve of polarization dependence is discussed. It is shown that the experiment can be explained in main features by a model of noninteracting oriented linear dipoles. Further, on the basis of TPA measurements, a simple energy band structure of Hg₂Cl₂ is proposed regarding Hg₂Cl₂ crystal as a linear chain of molecules.The authors express thanks to Dr. . Barta for supplying the Hg₂Cl₂ crystals, Dr. Z. Bryknar for critical comments and Dr. B. Velický for stimulating discussion. We thank also Dr. V. Kohlová for assistance during measurement.     

Clusters in the model ferroelastic Hg2Cl2

The critical fluctuations induced by a ferroelastic phase transition and corresponding to the soft TA mode at the X point at Brillouin zone boundary have been studied in the model crystal Hg₂Cl₂ within a broad temperature and wave-vector range. Anisotropic diffuse x-ray scattering maxima associated with order-parameter fluctuations and nucleation of low-temperature orthorhombic clusters in the high-temperature tetragonal matrix have been found to exist at these points. New information has been obtained on the temperature dependence of the susceptibility and correlation length, cluster shape and anisotropy, and the critical exponents. Fiz. Tverd. Tela (St. Petersburg) 41, 148–152 (January 1999)     

New topological surface state in layered topological insulators: Unoccupied dirac cone

The unoccupied states in topological insulators Bi₂Se₃, PbSb₂Te₄, and Pb₂Bi₂Te₂S₃ are studied by the density functional theory methods. It is shown that a surface state with linear dispersion emerges in the inverted conduction band energy gap at the center of the surface Brillouin zone on the (0001) surface of these insulators. The alternative expression of ?₂ invariant allowed us to show that a necessary condition for the existence of the second $\bar \Gamma $ Dirac cone is the presence of local gaps at the time reversal invariant momentum points of the bulk spectrum and change of parity in one of these points.     

Thermal expansion of Sn2P2S6 crystals

We present the results for thermal expansion coefficients of Sn₂P₂S₆ crystals determined both in the crystallographic system and the system based on eigenvectors of thermal expansion tensor. Peculiarities of temperature evolution of the indicative surface of thermal expansion tensor for Sn₂P₂S₆ are discussed, including the region of their ferroelectric phase transition.