High-temperature phase transitions in the improper ferroelectric KIO3

The ac conductivity (σ_ac) and dielectric permittivity (?) are determined in the temperature range 300?K?T3 compound. The results indicated that the compound behaves as an improper ferroelectric and undergoes a ferroelectric phase transition from a high temperature rhombohedral phase I to a low temperature monoclinic phase II at T _c?=?(486?±?1)?K. A second structural phase transition was observed around 345?K. The conductivity varies with temperature range and for T?>?428?K intrinsic conduction prevails. Different activation energies in the different temperature regions were calculated. The frequency dependence of σ(ω) was found to follow the universal dynamic response [σ(ω)∝(ω) ^s(T)]. The thermal behaviour of the frequency exponent s(T) suggests the hopping over the barrier model rather than the quantum mechanical tunneling model for the conduction mechanism.     

Absence of renormalization group pathologies near the critical temperature. Two examples

We consider real-space renormalization group transformations for Ising-type systems which are formally defined by $$\exp \left[ { - H'(\sigma ')} \right] = \sum\limits_\sigma {T(\sigma ,\sigma ')} \exp \left[ { - H(\sigma )} \right]$$ whereT(σ, σ′) is a probability kernel, i.e., ∑_σ′ T(σ,σ′) = 1 for every configuration σ. For each choice of the block spin configuration σ′, let σ′, let μ_σ′ be the measure on spin configurations σ which is formally given by taking the probability of σ to be proportional toT(σ, σ′) exp[?H(σ)]. We give a condition which is sufficient to imply that the renormalized HamiltonianH′ is defined. Roughly speaking, the condition is that the collection of measures μ_σ′ is in the high-temperature phase uniformly in the block spin configuration σ′. The proof of this result uses methods of Olivieri and Picco. We use our theorem to prove that the first iteration of the renormalization group transformation is defined in the following two examples: decimation with spacingb = 2 on the square lattice with β < 1.36β _c and the Kadanoff transformation with parameterp on the trian gular lattice in a subset of the β,p plane that includes values of β greater than β _c .     

Raman measurements of the superionic conductor AgI

Using the Raman technique, we have observed large abrupt reversible changes in the phonon spectrum at the transition temperature, T_c = 147°C, of the superionic conductor AgI. The defect nature of the high temperature phase completely breaks down the selection rules and allows the Raman measurements to give a measure of the frequency dependent conductivity, σ(ω), assuming a frequency independent matrix element. Similarities as well as differences in σ(ω) above and below T_c are shown.     

Thermally assisted hopping transport in disordered systems

The response to an external field of localized electrons coupled to phonons is investigated. The low frequency (ω<T) linear response function is shown to obey a kinetic equation. The transition probabilities (including multiphonon contributions) can be expressed in terms of the dynamical correlation functions(k, ?) of the phonons. The low temperature d.c. conductivity in three dimensions obeys a law σ(0)=σ₀ · exp(? (T ₀/T)^1/4). By a combined variational and “nearest neighbor” approximation upper limits for the exponential as well as the pre-exponential factor are obtained. In two dimensions the 1/4 in the exponent has to be replaced by 1/3. The one-dimensional case requires separate considerations which do not simply lead to an exponent 1/2. An expression for the thermopower in the hopping regime is derived and evaluated.     

Measurement of the γ-V coupling constants and σT (Vd) from coherent γ-d interactions at 7.5 GeV

We have measured the total and differential cross-sections for coherently photoproduced ?, ω and ?′ on deuterium at 7.5 GeV. Using VDM relations, we have obtained γ_ω²/γ_?² = 7.1 ± 1.5, σ_T(?d) = (54 ± 2) mb and σ_T(ωd) = (56 ± 5) mb. Assuming the amplitude for ?′ production via an intermediate ?⁰ to be small and that the amplitudes for ?p and ?′p elastic scattering are comparable, we found γ_?′²/γ_?² = 6.0 ± 1.2 and σ_T(?′d) = (47 ± 6) mb.     

Proton conductivity and ferroelectric phase transition in hydrogen-bonded ferroelectric NH4IO3

We report on the ac dielectric permittivity (ε) and the electric conductivity (σ_ω), as function of the temperature 300?K?T4IO₃. The main feature of our measured parameters is that, the compound undergoes a ferroelectric phase transition of an improper character, at (368?±?1)K from a high temperature paraelectric phase I (Pm2₁ b) to a low temperature ferroelectric phase II (Pc21n). The electric conduction seems to be protonic. The frequency dependent conductivity has a linear response following the universal power law (σ_{( ω )}?=?A(T)ω ^{s (T)}). The temperature dependence of the frequency exponent s suggests the existence of two types of conduction mechanisms.     

Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses

Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permitivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (σ_m(ω)) has been found to be higher than σ_dc at low temperatures whereas at high temperature σ_m(ω) becomes equal to σ_dc at all frequencies. The ac conductivity obeys the relation σ_ac(ω)=Aω ^S over a considerable range of low temperatures. Values of exponent S are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level (N(E _F)) have been evaluated at 80 K assuming values of electron wave function decay constant α to be 0.5 (Å)^?1. Values of N(E _F) have the order 10²⁰ which are well within the range suggested for localized states. Present values of N(E _F) are smaller than those for tungsten phosphate glasses.     

Exact solution for the extended Debye theory of dielectric relaxation of nematic liquid crystals

The exact solution for the transverse (i.e. in the direction perpendicular to the director axis) component α_⊥(ω) of a nematic liquid crystal and the corresponding correlation time T_⊥ is presented for the uniaxial potential of Martin et al. [Symp. Faraday Soc. 5 (1971) 119]. The corresponding longitudinal (i.e. parallel to the director axis) quantities α_⊥(ω), T_⊥ may be determined by simply replacing magnetic quantities by the corresponding electric ones in our previous study of the magnetic relaxation of single domain ferromagnetic particles Coffey et al. [Phys. Rev. E 49 (1994) 1869]. The calculation of α_⊥(ω) is accomplished by expanding the spatial part of the distribution function of permanent dipole moment orientations on the unit sphere in the Fokker-Planck equation in normalised spherical harmonics. This leads to a three term recurrence relation for the Laplace transform of the transverse decay functions. The recurrence relation is solved exactly in terms of continued fractions. The zero frequency limit of the solution yields an analytic formula for the transverse correlation time T_⊥ which is easily tabulated for all nematic potential barrier heights σ. A simple analytic expression for T_∥ which consists of the well known Meier-Saupe formula [Mol. Cryst. 1 (1966) 515] with a substantial correction term which yields a close approximation to the exact solution for all σ, and the correct asymptotic behaviour, is also given. The effective eigenvalue method is shown to yield a simple formula for T_⊥ which is valid for all σ. It appears that the low frequency relaxation process for both orientations of the applied field is accurately described in each case by a single Debye type mechanism with corresponding relaxation times (T_∥, T_⊥).     

The determination of hopping rates and carrier concentrations in ionic conductors by a new analysis of ac conductivity

The a.c. conductivity σ(ω) of ionic materials takes the form, σ(ω) = σ(0) + Aωⁿ. The carrier hopping rate, ω_p, is obtained from the new expression σ(0) = A ω_pⁿ and the carrier concentration is estimated from σ(0). The contribution of creation and migration terms to the activation energy for conduction may be determined from the thermal activation of σ(0) and ω_p and the corresponding entropy terms quantified. Data have been analyzed for four widely different ionic materials: single crystal Na β-alumina, polycrystalline Li₄SiO₄, Ag₇l₄AsO₄ glass and Ca(NO₃)₂/KNO₃ glass and melt. For each, the carrier concentration and hopping rates have been obtained.     

Measurement of elastic ω photoproduction at HERA ZEUS Collaboration

The reaction γp →ωp(ω → π⁺π^?π⁰ and π⁰ → γ γ) has been studied in ep interactions using the ZEUS detector at photon-proton centre-of-mass energies between 70 and 90GeV and ∣t∣ < 0.6GeV², where t is the squared four momentum transferred at the proton vertex. The elastic ω photoproduction cross section has been measured to be σ_{γp → ωp} = 1.21 ±0.12 ±0.23 μb. The differential cross section dσ_γp→ωp/d¦t¦ has an exponential shape e^?b∣t∣ with a slope b =10.0 ± 1.2 ± 1.3 GeV^?2. The angular distributions of the decay pions are consistent with s-channel helicity conservation. When compared to low energy data, the features of ω photoproduction as measured at HERA energies are in agreement with those of a soft diffractive process. Previous measurements of the ρ⁰ and ? photoproduction cross sections at HERA show a similar behaviour.     

Pressure effect on magnetization for (CoTm)90Zr10 (Tm = Cr,Mo) amorphous alloys

Temperature dependences of the forced volume magnetostriction dω/dH and the saturation magnetization σ_s for (CoTm)₉₀Zr₁₀ (Tm = Cr, Mo) amorphous alloys have recently been measured by the 3-terminal capacitance method and a vibrating sample magnetometer and magnetic balance at temperatures from 77 K to the Curie temperature T_c or the crystallization temperature. The pressure coefficient of σ_s0 at 0 K, d ln σ_s0/dp, is estimated from (dω/dH)₀ extrapolated to 0 K using the thermodynamical relation. The values of d ln σ_s0/dp increase in negative value with increasing Tm concentration. The relation between d ln σ_s0/dp and the pressure coefficient of T_c, d ln T_c/dp, estimated indirectly from dω/dH is discussed.     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

Critical spin relaxation in GdCl3

In the critical region of the insulating, uniaxial ferromagnet GdCl₃ the real part of the uniform susceptibility χ(q = 0, ω; T) has been measured by means of a frequency counting method in the ranges $\text{1.7 MHz ?}\text{ω}\text{2π}\text{? 720 MHz, 0.003 ? (}\text{T}\text{T}{}_{\mathrm{c}}\text{? 1 ≡ ?) ? 0.5}$. Parallel to the easy direction at all temperatures, χ′(ω) has a lorentzian shape, its amplitude being equal to the static susceptibility, χ_T. The half-widths τ^?1 exhibit s critical slowing down: above ?_c = 0.03 they are proportional to χ^?1_T, while at ?_c a change-over to $\text{τ}{}^{\mathrm{?1}}\text{∝ χ}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{T}}$ occurs, the origin of which is uncertain.     

On the problem of high temperature superconductivity

This article is a brief review of the present situation in theoretical investigations of high temperature superconductivity. The main subject is a discussion of the formula for a critical temperature T_c for a homogeneous and isotropic substance with arbitrary permeability ?(q, ω). The problem of the maximum possible value of T_c is discussed. It is concluded that at present there are no grounds to consider that values of T_c ? 100°K to be impossible. The paper ends with some remarks on the exciton mechanism of superconductivity for the case of superconductors with a plane geometry.     

Relaxationserscheinungen im 63 P 2-Zustand des Quecksilber-Isotops199Hg bei Stößen mit Quecksilberatomen im Grundzustand

The decay ofrf resonance signals (Δm _F =± 1, ΔF=0) in the hfs-states (F=3/2, 5/2) of the 6³ P ₂-state of¹⁹⁹Hg has been observed by means of a sampling method. By comparing the relaxation times to those of the even isotopes, the cross section σ₂(F) for the destruction of an alignment in the hfs-states by collisions with ground state Hg-atoms could be measured. The following ratios were obtained: σ₂(F=3/2)/σ₂=1.04±0.06 and σ₂(F=5/2)/σ₂=0.90± 0.03. The cross section σ₂ for the even isotopes was found to be (2.620±0.265) 10^?14cm². Assuming total decoupling of nuclear spinI and electronic angular momentumJ during the collision, the cross sections for the destruction of an orientation (σ₁) and an “octupolarisation” (σ₃) could be calculated. For the even isotopes the following ratios were derived: σ₁/σ₂=0.76 ± 0.07 and σ₃/σ₂=1.08 ± 0.09.     

Kotani theory for one dimensional stochastic Jacobi matrices

We consider families of operators,H _ω, on ?₂ given by (H _ω u)(n)=u(n+1)+u(n?1)+V _ω(n)u(n), whereV _ω is a stationary bounded ergodic sequence. We prove analogs of Kotani's results, including that for a.e. ω,σ_ac(H _ω) is the essential closure of the set ofE where γ(E) the Lyaponov index, vanishes and the result that ifV _ω is non-deterministic, then σ_ac is empty.     

Anisotropy of microwave conductivity in the superconducting and normal states of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7</Subscript>−<Emphasis Type="Italic">x</Emphasis>: 3D-2D crossover

The imaginary parts of microwave conductivity σ″(T<T_c) and resistivity ρ (_T)=1/σ(T>T_c) along (σ _ab ^″ and ρ_ab) and across and (σ _c ^″ and ρ_c the cuprate ab planes of a YBa₂Cu₃O_7?x crystal with the oxygen doping level x varying from 0.07 to 0.47 were measured in the temperature range 5≤ T≤200 K. In the superconducting state, the σ _ab ^″ (T)/σ _ab ^″ (0) and σ _c ^″ (T/σ _c ^″ (0) curves coincide for an optimally doped (x=0.07) crystal, but, with an increase in x, the slopes of the σ _c ^″ (T)/σ _c ^″ (0) curves decrease noticeably at T<T_c/3, on the background of small changes happening to the σ _ab ^″ (T/σ _ab ^″ (0) curves. The two-dimensional (2D) transport along the ab planes in the normal state of YBa₂Cu₃O_7?x is always metallic, but there is a crossover (at x=0.07) from the Drude to hopping (at x>0.07) conductivity along the c axis. This is confirmed both by the estimates of the lowest metallic and the highest tunneling conductivities along the c axis and by quantitative comparison of the measured ρ_c(T) curves with the curves calculated in the polaron model of quasiparticle transport along the c axis.     

Super-linear frequency dependence of ac conductivity of disordered Ag2S–Sb2S3 at cryogenic temperatures

The ac conductivity of a new class of disordered solids, i.e. mechanochemically synthesized amorphous fast ion conducting Ag₂S–Sb₂S₃ materials, has been investigated in the audio frequency range (10–10⁷?Hz) down to cryogenic temperatures (～10?K). The conductivity spectra exhibit the usual signature of a disordered system at higher temperatures, well described by the Jonscher power law (JPL) i.e., σ′(ω)?=?σ _dc?+?A(T)ω*, although the frequency exponent (n?<?1) is found to be a weak function of temperature. However, as the temperature is lowered, the frequency width of the σ _dc region decreases gradually and that of the JPL region increases. Eventually, the σ _dc region disappears and the JPL region alone dominates the spectrum. However, at the lowest temperatures, both the σ _dc and JPL regions disappear and σ′(ω) obeys a super-linear power law (SPL) (σ′?∝?ω^m , m?≥?1). It is observed that the SPL has strikingly similar characteristics to the well-established nearly-constant-loss (NCL) behaviour corresponding to m?=?1. Both SPL and NCL appear in the same time–temperature (low-temperature/low-frequency) domain. Furthermore, in both cases the conductivity is a distinctly weak function of temperature but quite sensitive to frequency, and the SPL/NCL?→?JPL crossover frequency is thermally activated with almost the same energy as the ac activation energy. The presence of the SPL is further manifested in the form of a well-defined minimum in the dielectric loss, ε″(ω), spectra. It is therefore proposed that the entire low-temperature/low-frequency spectra can be described by a modified Jonscher power law, σ′(ω)?=?σ _dc(T)?+?A(T) ωⁿ ?+?B(T)ω^m , m?=?1 (NCL), m?>?1 (SPL), where the second term with n?<?1 accounts for the JPL and the third term with m?≥?1 accounts for SPL/NCL. The results and some other low-temperature/low-frequency conductivity data are consistent with an asymmetric double well potential (ADWP) model.     

Manifestation of multiband optical properties of MgB2

The optical conductivity of MgB₂ has been determined on a dense polycrystalline sample in the spectral range 6 meV–4.6 eV using a combination of ellipsometric and normal incidence reflectivity measurements. σ₁(ω) features a narrow Drude peak with anomalously small plasma frequency (1.4 eV) and a very broad ‘dome’ structure, which comprises the bulk of the low-energy spectral weight. This fact can be reconciled with the results of band structure calculations by assuming that charge carriers from the 2D σ-bands and the 3D π-bands have principally different impurity scattering rates and negligible interband scattering. This also explains a surprisingly small correlation between the defect concentration and T_c, expected for a two-gap superconductor. The large 3D carrier scattering rate suggests their proximity to the localization limit.