Electronic Raman scattering in Tl2Ba2CuO6+x: symmetry of the order parameter, oxygen doping effects, and normal state scattering

Single crystals of the optimally doped, moderately and strongly overdoped high temperature superconductor Tl2Ba2CuO6+x (Tl-2201) with Tc=80, 56 and 30K, respectively, have been investigated by polarized Raman scattering. By taking the peak position of the B_1g component of electronic Raman scattering as 2Delta_0 we found that the reduced gap value (2Delta_0/k_BT_c) strongly decreases with increasing doping. The behavior of the low frequency scattering for the B_1g and B_2g scattering components is similar for optimally doped and overdoped crystals and can be described by a w^3 - and w -law, respectively, which is consistent with a d-wave symmetry of the order parameter. In contrast to the optimally doped Tl-2201 in both, moderately and strongly overdoped Tl-2201, the relative (compared to the B_1g) intensity of the A_1g scattering component is suppressed. We suggest that the van Hove singularity is responsible for the observed changes of Raman intensity and reduced gap value with doping. Electronic Raman scattering in the normal state is discussed in the context of the scattering from impurities and compared to the existing infrared data. The scattering rate evaluated from the Raman measurements is smaller for the overdoped samples, compared to the moderately overdoped samples.Comment: 7 pages, 7 figure

Modeling Within- and Across-Customer Association in Lifetime Value with Copulas

Recent advances in linking Recency-Frequency-Monetary value (RFM) data to Customer Lifetime Value (CLV) in non-contractual settings rely on the assumption of independence between the transaction and spend processes. We propose to model jointly the inter- and intra-customer dependency between both processes using copulas, hereby accounting for the double correlation within and across customers. Applied to a unique data set of securities' transactions, we nd that modeling both associations enhances the accuracy of CLV predictions, thus improving customer valuation and selection tasks.Association;Copula;Customer Lifetime Value;Across and Within Customers

TiOCl, an orbital-ordered system?

We present first principles density functional calculations and downfolding studies of the electronic and magnetic properties of the layered quantum spin system TiOCl. We discuss explicitely the nature of the exchange pathes and attempt to clarify the concept of orbital ordering in this material. An analysis of the electronic structure of slightly distorted structures according to the phononic modes allowed in this material suggests that this system is subject to large orbital fluctuations driven by the electron-phonon coupling. Based on these results, we propose a microscopic explanation of the behavior of TiOCl near the phase transition to a spin-gapped system.Comment: Some figures are compressed, for higher quality please contact the author

Giant phonon anomalies in the pseudo-gap phase of TiOCl

We report infrared and Raman spectroscopy results of the spin-1/2 quantum magnet TiOCl. Giant anomalies are found in the temperature dependence of the phonon spectrum, which hint to unusual coupling of the electronic degrees of freedom to the lattice. These anomalies develop over a broad temperature interval, suggesting the presence of an extended fluctuation regime. This defines a pseudo-gap phase, characterized by a local spin-gap. Below 100 K a dimensionality cross-over leads to a dimerized ground state with a global spin-gap of about 2$\Delta_{spin}\approx$~430 K.Comment: 4 pages, 3 figures, for further information see http://www.peter-lemmens.d

Longitudinal magnon in the tetrahedral spin system Cu2Te2O5Br2 near quantum criticality

We present a comprehensive study of the coupled tetrahedra-compound Cu2Te2O5Br2 by theory and experiments in external magnetic fields. We report the observation of a longitudinal magnon in Raman scattering in the ordered state close to quantum criticality. We show that the excited tetrahedral-singlet sets the energy scale for the magnetic ordering temperature T_N. This energy is determined experimentally. The ordering temperature T_N has an inverse-log dependence on the coupling parameters near quantum criticality

Collective Singlet Excitations and Evolution of Raman Spectral Weights in the 2D Spin Dimer Compound SrCu2(BO3)2

We present a Raman light scattering study of the two-dimensional quantum spin system SrCu2(BO3)2 and show that the magnetic excitation spectrum has a rich structure, including several well-defined bound state modes at low temperature, and a scattering continuum and quasielastic light scattering contributions at high temperature. The key to the understanding of the unique features of SrCu2(BO3)2 is the presence of strong interactions between well-localized triplet excitations in the network of orthogonal spin dimers realized in this compound. Based on our analysis of the Heisenberg model relevant for this material, we argue that the collective excitations involving two and three-particle singlet bound states have large binding energies and are observed as well-defined peaks in the Raman spectrum.Comment: 5 pages, 2 figures. Revised version, to appear in Phys. Rev. Lett. (2000

The J_1-J_2 model revisited : Phenomenology of CuGeO_3

We present a mean field solution of the antiferromagnetic Heisenberg chain with nearest (J_1) and next to nearest neighbor (J_2) interactions. This solution provides a way to estimate the effects of frustration. We calculate the temperature-dependent spin-wave velocity, v_s(T) and discuss the possibility to determine the magnitude of frustration J_2/J_1 present in quasi 1D compounds from measurements of v_s(T). We compute the thermodynamic susceptibility at finite temperatures and compare it with the observed susceptibility of the spin-Peierls compound CuGeO_3. We also use the method to study the two-magnon Raman continuum observed in CuGeO_3 above the spin-Peierls transition.Comment: Phys. Rev.

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on $n$ letters, where $n$ is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.Comment: 36 pages, 1 fugur

Comment on "Raman spectroscopy study of NaxCoO2 and superconducting NaxCoO2 yH2O"

The effect of surface degradation of the thermolectric cobaltite on Raman spectra is discussed and compared to experimental results from Co3O4 single crystals. We conclude that on NaCl flux grown NaxCoO2 crystals a surface layer of Co3O4 easily forms that leads to the observation of an intense phonon around 700 cm-1 [Phys. Rev. B 70, 052502 (2004)]. Raman spectra on freshly cleaved crystals from optical floating zone ovens do not show such effects and have a high frequency phonon cut-off at approximately 600 cm -1 [Phys. Rev. Lett 96, 167204 (2006)]. We discuss the relation of structural dimensionality, electronic correlations and the high frequency phonon cut-off of the thermolectric cobaltite.Comment: 2 pages, 1 figure, to be published in Phys. Rev. B (2007

Infrared optical properties of the spin-1/2 quantum magnet TiOClTiOCl

We report results on the electrodynamic response of $TiOCl$, a low-dimensional spin-1/2 quantum magnet that shows a spin gap formation for T$<T_{c1}$= 67 $K$. The Fano-like shape of a few selected infrared active phonons suggests an interaction between lattice vibrations and a continuum of low frequency (spin) excitations. The temperature dependence of the phonon mode parameters extends over a broad temperature range well above $T_{c1}$, indicating the presence of an extended fluctuation regime. In the temperature interval between 200 $K$ and $T_{c1}$ there is a progressive dimensionality crossover (from two to one), as well as a spectral weight shift from low towards high frequencies. This allows us to identify a characteristic energy scale of about 430 $K$, ascribed to a pseudo spin-gap