Magnetic structure of the edge-sharing copper oxide chain compound NaCu2O2

Single-crystal neutron diffraction has been used to determine the incommensurate magnetic structure of NaCu2O2, a compound built up of chains of edge-sharing CuO4 plaquettes. Magnetic structures compatible with the lattice symmetry were identified by a group-theoretical analysis, and their magnetic structure factors were compared to the experimentally observed Bragg intensities. In conjunction with other experimental data, this analysis yields an elliptical helix structure in which both the helicity and the polarization plane alternate among copper-oxide chains. This magnetic ground state is discussed in the context of the recently reported multiferroic properties of other copper-oxide chain compounds

Dipole-active optical phonons in YTiO_3: ellipsometry study and lattice-dynamics calculations

The anisotropic complex dielectric response was accurately extracted from spectroscopic ellipsometry measurements at phonon frequencies for the three principal crystallographic directions of an orthorhombic (Pbnm) YTiO_3 single crystal. We identify all twenty five infrared-active phonon modes allowed by symmetry, 7B_1u, 9B_2u, and 9B_3u, polarized along the c-, b-, and a-axis, respectively. From a classical dispersion analysis of the complex dielectric functions \tilde\epsilon(\omega) and their inverses -1/\tilde\epsilon(\omega) we define the resonant frequencies, widths, and oscillator strengths of the transverse (TO) and longitudinal (LO) phonon modes. We calculate eigenfrequencies and eigenvectors of B_1u, B_2u, and B_3u normal modes and suggest assignments of the TO phonon modes observed in our ellipsometry spectra by comparing their frequencies and oscillator strengths with those resulting from the present lattice-dynamics study. Based on these assignments, we estimate dynamical effective charges of the atoms in the YTiO_3 lattice. We find that, in general, the dynamical effective charges in YTiO_3 lattice are typical for a family of perovskite oxides. By contrast to a ferroelectric BaTiO_3, the dynamical effective charge of oxygen related to a displacement along the c-axis does not show the anomalously large value. At the same time, the dynamical effective charges of Y and ab-plane oxygen exhibit anisotropy, indicating strong hybridization along the a-axis.Comment: 8 pages, 7 figure

Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds

We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold, where the L^2 norm of all second derivatives of the function involving horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian. Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE in non-divergence form with bounded measurable coefficients. The method of proof is through a Bochner technique. The Heisenberg group is seen to be en extremal manifold for our inequality in the class of manifolds whose Ricci curvature is non-negative.Comment: 13 page

Magnetic excitations and phonons in the spin-chain compound NaCu2O2

We report an inelastic light scattering study of single-crystalline NaCu$_2$O$_2$, a spin-chain compound known to exhibit a phase with helical magnetic order at low temperatures. Phonon excitations were studied as a function of temperature and light polarization, and the phonon frequencies are compared to the results of ab-initio lattice dynamical calculations, which are also reported here. The good agreement between the observed and calculated modes allows an assignment of the phonon eigenvectors. Two distinct high-energy two-magnon features as well as a sharp low-energy one-magnon peak were also observed. These features are discussed in terms of the magnon modes expected in a helically ordered state. Their polarization dependence provides evidence of substantial exchange interactions between two closely spaced spin chains within a unit cell. At high temperatures, the spectral features attributable to magnetic excitations are replaced by a broad, quasielastic mode due to overdamped spin excitations

Dispersion of the odd magnetic resonant mode in near-optimally doped Bi2Sr2CaCu2O8+d

We report a neutron scattering study of the spin excitation spectrum in the superconducting state of slightly overdoped Bi2Sr2CaCu2O8+d system (Tc=87 K). We focus on the dispersion of the resonance peak in the superconducting state that is due to a S=1 collective mode. The measured spin excitation spectrum bears a strong similarity to the spectrum of the YBa2Cu3O6+x system for a similar doping level i.e. x= 0.95-1), which consists of intersecting upward- and downward-dispersing branches. A close comparison of the threshold of the electron-hole spin flip continuum, deduced from angle resolved photo-emission measurements in the same system, indicates that the magnetic response in the superconducting state is confined, in both energy and momentum, below the gapped Stoner continuum. In contrast to YBa2Cu3O6+x, the spin excitation spectrum is broader than the experimental resolution. In the framework of an itinerant-electron model, we quantitatively relate this intrinsic energy width to the superconducting gap distribution observed in scanning tunnelling microscopy experiments. Our study further suggests a significant in-plane anisotropy of the magnetic response.Comment: 10 figure

Competing magnetic fluctuations in Sr3Ru2O7 probed by Ti doping

We report the effect of nonmagnetic Ti4+ impurities on the electronic and magnetic properties of Sr3Ru2O7. Small amounts of Ti suppress the characteristic peak in magnetic susceptibility near 16 K and result in a sharp upturn in specific heat. The metamagnetic quantum phase transition and related anomalous features are quickly smeared out by small amounts of Ti. These results provide strong evidence for the existence of competing magnetic fluctuations in the ground state of Sr3Ru2O7. Ti doping suppresses the low temperature antiferromagnetic interactions that arise from Fermi surface nesting, leaving the system in a state dominated by ferromagnetic fluctuations.Comment: 5 pages, 4 figures, 1 tabl

Helicoidal magnetic order in a clean copper oxide spin chain compound

We report susceptibility, specific heat, and neutron diffraction measurements on NaCu$_2$O$_2$, a spin-1/2 chain compound isostructural to LiCu$_2$O$_2$, which has been extensively investigated. Below 13 K, we find a long-range ordered, incommensurate magnetic helix state with a propagation vector similar to that of LiCu$_2$O$_2$. In contrast to the Li analogue, substitutional disorder is negligible in NaCu$_2$O$_2$. We can thus rule out that the helix is induced by impurities, as was claimed on the basis of prior work on LiCu$_2$O$_2$. A spin Hamiltonian with frustrated longer-range exchange interactions provides a good description of both the ordered state and the paramagnetic susceptibility.Comment: 4 pages, 4 figures Improved Fig.1 and 4. Minor rephrasing. Reference adde

On the Alexandrov Topology of sub-Lorentzian Manifolds

It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation function. Both lead to the definition of the Alexandrov topology, which is linked to the property of strong causality of a space-time. We studied three possible ways to define the Alexandrov topology on sub-Lorentzian manifolds, which usually give different topologies, but agree in the Lorentzian case. We investigated their relationships to each other and the manifold's original topology and their link to causality.Comment: 20 page