Study of the ferroelectric phase transition of TlGaSe2 by dielectric,calorimetric, infrared and X-ray diffraction measurements

The real part of the dielectric constant , the heat capacityc _p, the infrared reflectivity, and the X-ray diffraction of TlGaSe₂ have been measured in the temperature range from 12 K (30K) to 300 K. Both andc _p show two anomalies at about 110 K and 120 K. A study of the hysteresis loop as well as an investigation of the dielectric dispersion in the microwave region show that the phase below 110 K is ferroelectric. The crystal structure remains nearly unchanged in the course of the phase transition. The loss of the symmetry (C2/cCc) results from small positional shifts of the T1 atoms in the ab plane accompanied by a discontinuity in the axial ratios. We suggest, that the ferroelectricity is caused by the stereochemically active electron lone pair configuration of the Tl⁺ ion. Thus TlGaSe₂ may provide the first example for ferroelectricity caused by this mechanism.     

Soft mode dynamics and spatio-temporal symmetry breaking in a thermo-convective system

Using neutron scattering we have studied the behaviour of an oscillatory soft mode in a thermoconvective liquid crystal. As a function of an applied vertical temperature difference T the behaviour of the soft-mode frequency defines four regimes, separated by cross-over values at which spatio-temporal symmetry is broken. Breaking of time symmetry manifests itself in different phase relations among localized oscillators. Incomplete softening at the convection threshold T _c is interpreted as anharmonic coupling to low-energy, internal director fluctuations in the nematic. Subtracting the anharmonic contribution, the renormalized frequency squared gives a susceptibility critical index for each of the four regimes. The values range between 1.1 and 2.7, indicative of a change of the spatial dimensionality as TT _c. The widths in T of the regimes converge as the Feigenbaum ratio (4.6), and the meaning of this is discussed.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Transition temperature and isotope effect near an extended van Hove singularity

Using Eliashberg theory and a model density for ² F the transition temperatureT _c and the isotope effect are calculated near an extended van Hove singularity. We show that, at least in the one-particle and the Migdal approximation, even the considered strong van Hove singularity cannot yield large enhancements ofT _c and strong reductions of of the kind observed in experiment around optimal doping.     

High-resolution measurements of thermal expansion along the uniqueb-axis of squaric acid

The thermal expansion of squaric acid along the uniqueb-axis was measured between 323 K and 418 K with a resolution of 2·10^–7 in strain and 5·10^–4 K in temperature using a capacitance dilatometer. The anomaly associated with the antiferro-electric phase transition occuring atT _c=373.5 K was observed over the rangeT _c–50 K<T<T _c+7 K. The regular lattice expansion follows a generalized Grüneisen's law with a Debye-temperature _D =660 K and a uniaxial pressure-dependence of _D /p _b . The critical behaviour close toT _c was studied with a sweep rate of 36 mK/h. A hyteresis loop of width 23 mK was observed in the strain curve, indicating a 1st order transition. However, no discontinuity in dilatation was observed, and therefore the transition is close to a multicritical point. The anomalous increase in the expansion coefficient can be described with critical exponents ==0.56 in the interval 0.4 K<|T–T _c|<12 K. Closer toT _c the divergence is stronger. A generalized Pippard relation between the expansion coefficient and specific heat holds to within 1 K from the transition point. The inconsistencies apparent closer toT _c are interpreted as a consequence of a weak 1st order transition.     

Simultaneous determination of specific heat,thermal conductivity and thermal diffusivity at low temperature via the photopyroelectric technique

The photopyroelectric effect has been used to measure simultaneously specific heat (c), thermal conductivity (k) and thermal diffusivity () at low temperatures. A calibration procedure which allows the use of a pyroelectric transducer at low temperatures is described. Simultaneous measurements of c, k, and over a high T _c superconducting phase transition are reported.     

Spectral theory,zeta functions and the distribution of periodic points for Collet-Eckmann maps

We study unimodal interval mapsT with negative Schwarzian derivative satisfying the Collet-Eckmann condition |DT ⁿ (Tc)|K _c ⁿ for some constantsK>0 and _c>1 (c is the critical point ofT). We prove exponential mixing properties of the unique invariant probability density ofT, describe the long term behaviour of typical (in the sense of Lebesgue measure) trajectories by Central Limit and Large Deviations Theorems for partial sum processes of the form , and study the distribution of typical periodic orbits, also in the sense of a Central Limit Theorem and a Large Deviations Theorem.This is achieved by proving quasicompactness of the Perron Frobenius operator and of similar transfer operators for the Markov extension ofT and relating the isolated eigenvalues of these operators to the poles of the corresponding Ruelle zeta functions.Supported by an Alexander von Humboldt grant     

Spatio-temporal Fourier components and soft modes in thermal convection: A neutron scattering study

In a nematic liquid crystal subjected to a vertical temperature difference T in a vertical slab container, we find, using real-time and real-space neutron scattering, that the spatiotemporal pattern can be indexed on a two-dimensional lattice with selection rule (h+k)=2n. Higher index modes are sequentially activated as T increases from the convection threshold T _c . The frequency softening as TT _c and asTT ₀, the super-cooling limit of the nematic, is discussed.     

Y1Ba2Cu3O7-δ thin films from KrF laser ablation with substrate heating and in situ patterning by CO2 laser radiation

Y₁Ba₂Cu₃O_7– thin films were deposited by KrF laser ablation while replacing conventional contact heating by cw CO₂ laser irradiation of the substrate front surface. The HTSC films obtained on (100)ZrO₂ showed T _c(R=0)=90 K, T(90–10%)=0.5 K, j _c=2.5 × 10⁶ A/cm², a sharp transition in the ac susceptibility X(T), and pure c-axis orientation. Micrographs of thin films (< 0.5 m) showed a smooth morphology while thick films (>1 m) contained many crystallites sticking in the bulk material. Furthermore, in situ patterning was achieved during deposition by local laser heating of a selected substrate surface area. The resulting planar films contained amorphous, semiconducting parts only 1 mm or less apart from crystalline material showing the above HTSC quality.Presented at LASERION '91, June 12–14, 1991, München (Germany)     

A lower bound for the memory capacity in the Potts-Hopfield model

We consider Potts-Hopfield networks of sizeN. We prove the result: _c >0 such that for all 0<< _c we can find, >0 in such a way that, whenN, we can store N patterns, all of them being sorrounded by -energy barriers at distance.     

Dynamics of the one dimensional randomly dilute Ising ferromagnet

The effect of randomly dilute impurities in the percolation limit on the relaxation of magnetization M(t) and on the way the time-dependent correlation function M(t)M(0) decays in a one dimensional Ising ferromagnet is considered, as is the behaviour of the dynamic susceptibility. It is found that the decay of the magnetization is hardly altered except for small faster decaying boundary effects. However, the correlation function is drastically altered, decaying in general faster asymptotically than the pure system. The dynamical susceptibility also changes, showing a breaking in the simple relaxational scaling form of the pure system. Crossover behaviour with non-critical slowing down (apart from the critical slowing down asTT _c=0) is also observed in the transition from the pure ferromagnetic to randomly dilute behaviour.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

Contribution of quantum corrections and superconducting fluctuations to the magnetic field and temperature dependence of the conductivity in amorphous CuTi and CuZr alloys

We report conductivity measurements on Cu _x Ti_100–x and Cu _x Zr_100–x glasses as a function of magnetic field (0B6T) and temperature (1.5–5. At low temperatures the measured conductivity(T,B)= ₀+(T)+(B,T) is compared quantitatively with the predictions of diagrammatic perturbation theories including quantum interference effects, spin-orbit scattering and electron-electron interaction. We obtain a set of characteristic fields for inelastic and spin orbit scattering from both the magnetic field and the temperature dependence of the measured (T, B). Below about 4K the Coulomb interaction determines (T) in consistence with the Hall effect, whereas quantum interference processes and spin-orbit scattering dominate the magnetic field dependence. In case of Cu _x Zr_100–x , (B, T) can be explained by taking into account superconducting fluctuations (Maki-Thompson and Aslamasov-Larkin parts) in addition. Superconducting fluctuations dominate the temperature dependence as well. For high magnetic fields and lower temperatures (B/T>1T/K) we find discrepancies between experiment and calculations from perturbation theory.     

On the hole spectral function of the Emery model

We discuss the spectral function of a single O hole generated in a two-dimensional CuO₂-lattice at half-filling. The latter constitutes the most important structural element of high-T _c superconducting materials. The system is described by the so-called extended Hubbard or Emery model. Strong electronic correlations which are incorporated in the model prevent the usual evaluation of Green functions based on Wick's theorem and using diagram techniques. For that reason we apply a new cumulant approach to dynamical correlation functions introduced recently. As a result we find that the local one-O hole excitation spectrum has two structured absorption regions around the bare O energy _p and around _p + due to charge fluctuations of Cu holes. Here is the bare charge transfer gap. The width of the absorption regime around _p is of the order of several timest _pd ² /, wheret _pd is the hopping integral between Cu and O holes.     

Low temperature self-ion irradiation of pure and granular aluminium-films

Al-films, evaporated at room temperature under different oxygen partial pressures, were irradiated with self-ions (500 keV, Al⁺⁺) at low temperature (<7 K). The observed increase of the resistivity and of the superconducting transition temperatureT _c depends strongly on the oxygen contentc ₀ present in the layers. A qualitative different behaviour of the above quantities was found for different fluence ranges of the bombarding ions. For high fluences in all cases an oxygen stabilized disorder state was obtained with correspondingT _c-increases betweenT _c=0.2 K for the purest films (c ₀0.5 at %) andT _c =1.2 K for films with c ₀=40 at %. The annealing behaviour of the irradiated films is also dependent on the oxygen contentc ₀.     

Upper bounds onT c for one-dimensional Ising systems

We present upper bounds on the critical temperature of one-dimensional Ising models with long-range,l/n interactions, where 1<2. In particular for the often studied case of =2 we have an upper bound onT _c which is less than theT _c found by a number of approximation techniques. Also for the case where is small, such as =1.1, we obtain rigorous bounds which are extremely close, within 1.0%, to those found by approximation methods.     

Thermal fluctuations in high-temperature superconductors

The effect of fluctuations and anisotropy on the transition from the normal to the superconducting state are studied. Neglecting magnetic fluctuations, which is justified as long as the Ginzburg-Landau parameter 1, the critical behavior belongs to thexy-universality class including superfluid helium. Since (t)=₀ t ^2/3, wheret=1-T/T _c , upon approachingT _c further, the intrinsic fluctuating magnetic field might change the nature of the transition. Concentrating on thexy-regime, we derive with the aid of the helicity modulus a universal relation betweenT _c and the amplitudes of the phase correlation length and penetration depth. We also extend the universal critical point amplitude relations to the case of superconductors with uniaxial mass anisotropy. Our analysis of recent specific heat and excess dc conductivity measurement suggest that for both static and dynamic properties three-dimensional critical behavior has been observed. The -like specific heat singularity points to criticalxy-behavior. Further evidence is provided in terms of the universal amplitude relations, providing estimates for the amplitudes of the correlation lengths for the magnitude and phase of the order parameter and the London penetration depth. We find remarkable agreement with experiment and the correlation volume is comparable to that in superfluid helium.     

Relationship between T c and electronegativity differences in compound superconductors

The electronegativity differences, N, between the anions and the cations in suggested resonating elements of some representative high-temperature superconductors with T _c - 10 K are evaluated adopting Pauling's scale. The relationship between N and T _c was found to separate all the examined high-T _csuperconductors onto two curves: One for the cuprate superconductors having two-dimensional layered structures was a straight line, T _c=29.8+4.1N; the other correlation curve representing the remaining compound superconductors including the doped 113 perovskite and the perovskite-related 214 structures was at lower T _c values but also suggested that increasing electronegativity differences was related to increasing T _c.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098     

Strong-coupling effects in high-T c superconductors

It is conceivable that the high-T _c superconducting perovskites are conventional electronphonon superconductors. In this case one expects significant strong-coupling effects because of the unusually high ratiok _B T _c / of the order 0.1 and greater. We use a set of reasonable models for the Eliashberg function ² F() (which takes into account available information on the phonon spectra and which fit the measuredT _c 's) and calculate strong-coupling effects in the specific heatc _s (T)/T _c , the ratio ₀/k _B T _c , the critical fieldsH _c (T) andH _c2 (T) including Pauli limiting, and other measurable quantities. Strongcoupling corrections turn out to be in the range of 0 to about 100%, depending on the quantity of interest. We discuss the perspectives of using strong-coupling effects as indicators for conventional electron-phonon superconductivity in the new materials.     

On the Bose-Einstein condensation of free relativistic bosons with or without mass

The Bose-Einstein condensation of free relativistic particles [=(M ² c ⁴ +c ² p ² ) ^1/2 –Mc ² ] is studied rigorously. For massless bosons (=cp), the condensation transition of third (second) order occurs in2 (3) dimensions (D). The molar heat capacity follows the T ² (T ³ ) law below the condensation temperature T_c [k ^B T_c=(2 ² c ² n/1.645) ^1/2 [( ^{2 3} c ³ n/1.202) ^1/3 ], reaches4.38 (10.8) R at T=T_c, and approaches the high-temperature-limit value2 (3) R with no jump (a jump equal to6.75R) in2 (3)D. For finite-mass (M) bosons, the phase transition occurs only in3D with the condensation temperature T_c always smaller than that of the corresponding nonrelativistic bosons [=(2M) ^–1 p ² ]. If the mass M is reduced to zero, the condensation temperature T_c grows monotonically and reaches eventually that of massless relativistic bosons. This mass-dependence of T_c is therefore distinct from the case of nonrelativistic bosons, where T_c grows to infinity as M 0. A brief discussion is given for a possible connection with the normal-to-super transition of the independently moving Cooper pairs (bosons).     

Spectral behavior of quasi periodic potentials

Spectral properties of Schrödinger operators of the typeH =–+V, where is the Laplacian,V a quasiperiodic potential and a coupling constant, are developed.V is taken to be finite sum of exponentials with generic frequencies. For small a strong stability is shown. On the other hand, examples (in the finite diffeence case) are given, for which a transition in the type of spectrum occurs, as is increased.Research supported in part by grant NSF MCS 7900813