Low Energy Singlets in the Excitation Spectrum of the Spin Tetrahedra System Cu_2Te_2O_5Br_2

Low energy Raman scattering of the s=1/2 spin tetrahedra system Cu_2Te_2O_5Br_2 is dominated by an excitation at 18 cm^{-1} corresponding to an energy E_S=0.6\Delta, with \Delta the spin gap of the compound. For elevated temperatures this mode shows a soft mode-like decrease in energy pointing to an instability of the system. The isostructural reference system Cu_2Te_2O_5Cl_2 with a presumably larger inter-tetrahedra coupling does not show such a low energy mode. Instead its excitation spectrum and thermodynamic properties are compatible with long range Neel-ordering. We discuss the observed effects in the context of quantum fluctuations and competing ground states.Comment: 5 pages, 2 figures, ISSP-Kashiwa 2001, Conference on Correlated Electron

Relation between Kitaev magnetism and structure in α\alpha-RuCl3_3

Raman scattering has been employed to investigate lattice and magnetic excitations of the honeycomb Kitaev material $\alpha$-RuCl$_3$ and its Heisenberg counterpart CrCl$_3$. Our phonon Raman spectra give evidence for a first-order structural transition from a monoclinic to a rhombohedral structure for both compounds. Significantly, only $\alpha$-RuCl$_3$ features a large thermal hysteresis, consistent with the formation of a wide phase of coexistence. In the related temperature interval of $70-170$ K, we observe a hysteretic behavior of magnetic excitations as well. The stronger magnetic response in the rhombohedral compared to the monoclinic phase evidences a coupling between the crystallographic structure and low-energy magnetic response. Our results demonstrate that the Kitaev magnetism concomitant with fractionalized excitations is susceptible to small variations of bonding geometry.Comment: 9 pages, 8 figures, To appear in PR

Dynamical Dzyaloshinsky-Moriya interaction in KCuF3: Raman evidence for an antiferrodistortive lattice instability

In the orbitally ordered, quasi-one dimensional Heisenberg antiferromagnet KCuF3 the low-energy Eg and B1g phonon modes show an anomalous softening (25% and 13%) between room temperature and the characteristic temperature T_S = 50 K. In this temperature range a freezing-in of F ion dynamic displacements is proposed to occur. In addition, the Eg mode at about 260 cm-1 clearly splits below T_S. The width of the phonon lines above T_S follows an activated behavior with an activation energy of about 50 K. Our observations clearly evidence a reduction of the structural symmetry below T_S and indicate a strong coupling of lattice and spin fluctuations for T>T_S.Comment: 7 pages, 9 figure

Positive contraction mappings for classical and quantum Schrodinger systems

The classical Schrodinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and a prior, and the law dictates a controlled path that abides by the specified marginals. Schrodinger proved that the optimal steering of the density between the two end points is effected by a multiplicative functional transformation of the prior; this transformation represents an automorphism on the space of probability measures and has since been studied by Fortet, Beurling and others. A similar question can be raised for processes evolving in a discrete time and space as well as for processes defined over non-commutative probability spaces. The present paper builds on earlier work by Pavon and Ticozzi and begins with the problem of steering a Markov chain between given marginals. Our approach is based on the Hilbert metric and leads to an alternative proof which, however, is constructive. More specifically, we show that the solution to the Schrodinger bridge is provided by the fixed point of a contractive map. We approach in a similar manner the steering of a quantum system across a quantum channel. We are able to establish existence of quantum transitions that are multiplicative functional transformations of a given Kraus map, but only for the case of uniform marginals. As in the Markov chain case, and for uniform density matrices, the solution of the quantum bridge can be constructed from the fixed point of a certain contractive map. For arbitrary marginal densities, extensive numerical simulations indicate that iteration of a similar map leads to fixed points from which we can construct a quantum bridge. For this general case, however, a proof of convergence remains elusive.Comment: 27 page

Electronic Raman scattering of Tl-2223 and the symmetry of the supercon- ducting gap

Single crystalline Tl2Ba2Ca2Cu3O10 was studied using electronic Raman scattering. The renormalization of the scattering continuum was investigated as a function of the scattering geometry to determine the superconducting energy gap 2Delta(k). The A1g- and B2g-symmetry component show a linear frequency behaviour of the scattering intensity with a peak related to the energy gap, while the B1g-symmetry component shows a characteristic behaviour at higher frequencies. The observed frequency dependencies are consistent with a dx^2-y^2-wave symmetry of the gap and yield a ratio of 2Delta/k_BT_c=7.4. With the polarization of the scattered and incident light either parallel or perpendicular to the CuO2-planes a strong anisotropy due to the layered structure was detected, which indicates an almost 2 dimensional behaviour of this system.Comment: 2 pages, Postscript-file including 2 figures. Accepted for publication in the Proceedings of the M^2SHTSC IV Conference, Grenoble (France), 5-9 July 1994. Proceedings to be published in Physica C. Contact address: [email protected]

Study of intercalation and deintercalation of Na_xCoO_2 yH_2O single crystals

Single crystals of NaxCoO2 with beta-phase (x=0.55, 0.60 and 0.65), alpha'-phase (x=0.75) and alpha-phase (x=0.9, 1.0) have been grown by the floating zone technique. The Na-extraction and hydration were carried out for the alpha'-sample to get superconducting phase of NaxCoO2.yH2O (x~0.3, y~1.3). Hydrated single crystals exhibit cracked layers perpendicular to the c-axis due to a large expansion when the water is inserted into the structure. A study of intercalation/deintercalation was performed to determine the stability of the hydrated phase and effects of hydration on the structure of the compound. X-ray diffraction and Thermogravimetric experiments are used to monitor the process of water molecules accommodated in and removed from the crystal lattice. The initial intercalation process takes place with two-water molecules corresponding to y=0.6) inserted in a formula unit, followed by a group of four (y=1.3) to form a cluster of Na(H2O)4. Thermogravimetric analysis suggests that the deintercalation occurs with the removal of the water molecules one by one from the hydrated cluster at elevated temperatures of approximately 50, 100, 200 and 300 C, respectively. Our investigations reveal that the hydration process is dynamic and that water molecule inter- and deintercalation follow different reaction paths in an irreversible way.Comment: 15 pages, 6 figures, figures with higher resolution by email request from the corresponding autho