Alkoxyallene‐Based LANCA Three‐Component Synthesis of 1,2‐Diketones, Quinoxalines, and Unique Isoindenone Dimers and a Computational Study of the Isoindenone Dimerization

A series of β‐alkoxy‐β‐ketoenamides was prepared by the well‐established LANCA three‐component reaction of lithiated 1‐(2‐trimethylsilylethoxy)‐substituted allenes, nitriles, and α,β‐unsaturated carboxylic acids. The α‐tert‐butyl‐substituted compounds were smoothly converted into the expected 1,2‐diketones by treatment with trifluoroacetic acid. A subsequent condensation of the 1,2‐diketones with o‐phenylenediamine provided the desired highly substituted quinoxalines in good overall yield. Surprisingly, the α‐phenyl‐substituted β‐alkoxy‐β‐ketoenamides investigated afford not only the expected 1,2‐diketones, but also pentacyclic compounds with an anti‐tricyclo[4.2.1.12,5]deca‐3,7‐diene‐9,10‐dione core. These interesting products are very likely the result of an isoindenone dimerization which was mechanistically studied with the support of DFT calculations. Under the strongly acidic reaction conditions, a stepwise reaction is likely leading to a protonated isoindenone as reactive intermediate. It may first form a van der Waals complex with a neutral isoindenone before the two regio‐ and diastereoselective ring forming steps occur. Interestingly, two neutral or two protonated isoindenones are also predicted to dimerize giving the observed pentacyclic product

Observation of long range magnetic ordering in pyrohafnate Nd2Hf2O7: A neutron diffraction study

We have investigated the physical properties of a pyrochlore hafnate Nd2Hf2O7 using ac magnetic susceptibility \chi_ac(T), dc magnetic susceptibility \chi(T), isothermal magnetization M(H) and heat capacity C_p(T) measurements, and determined the magnetic ground state by neutron powder diffraction study. An upturn is observed below 6 K in C_p(T)/T, however both C_p(T) and \chi(T) do not show any clear anomaly down to 2 K. The \chi_ac(T) shows a well pronounced anomaly indicating an antiferromagnetic transition at T_N = 0.55 K. The long range antiferromagnetic ordering is confirmed by neutron diffraction. The refinement of neutron diffraction pattern reveals an all-in/all-out antiferromagnetic structure, where for successive tetrahedra, the four Nd3+ magnetic moments point alternatively all-into or all-out-of the tetrahedron, with an ordering wavevector k = (0, 0, 0) and an ordered state magnetic moment of m = 0.62(1) \mu_B/Nd at 0.1 K. The ordered moment is strongly reduced reflecting strong quantum fluctuations in ordered state.Comment: 10 pages, 9 figures and 2 tables; to appear in Phys. Rev.

Robust tests for heteroskedasticity and autocorrelation in the multiple regression model: Working paper series--02-05

The standard Rao's (1948) score or Lagrange multiplier test for heteroskedasticity was originally developed assuming normality of the disturbance term [see Godfrey (1978b), and Bruesch and Pagan (1979)]. Therefore, the resulting test depends heavily on the normality assumption. Koenker (1981) suggests a studentized for which is robust to nonnormality. This approach seems to be limited because of the unavailability of a general procedure that transforms a test to a robust one. Following Bickel (1978), we use a different approach to take account of nonnormality. Our tests will be based on the score function which is defined as the negative derivitive of the log-density function with respect to the underlying random variable. To implement the test we use a nonparametric estimate of the score function. Our robust test for heteroskedasticity is obtained by running a regression of the product of the score function and ordinary least squares residuals on some exogenous variables which are thought to be causing the heteroskedasticity. We also use our procedure to develop a robust test for autocorrelation which can be computed by regressing the score function on the lagged ordinary least squares residuals and the independent variables. Finally, we carry out an extensive Monte Carlo study which demonstrates that our proposed tests have superior finite sample properties compared to the standard tests

Density of states in graphene with vacancies: midgap power law and frozen multifractality

The density of states (DoS), $\varrho(E)$, of graphene is investigated numerically and within the self-consistent T-matrix approximation (SCTMA) in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies, $n_\text{A}$ and $n_\text{B}$, in both sub-lattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The prediction of the non-linear sigma-model for this class is a Gade-type singularity $\varrho(E) \sim |E|^{-1}\exp(-|\log(E)|^{-1/x})$. Our numerical data is compatible with this result in a preasymptotic regime that gives way, however, at even lower energies to $\varrho(E)\sim E^{-1}|\log(E)|^{-\mathfrak{x}}$, $1\leq \mathfrak{x} < 2$. We take this finding as an evidence that similar to the case of dirty d-wave superconductors, also generic bipartite random hopping models may exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough. Our research suggests that graphene with (effective) vacancy disorder is a physical representative of such systems.Comment: References updated onl

Field Induced Magnetic Ordering and Single-ion Anisotropy in the Quasi-1D Haldane Chain Compound SrNi2V2O8: A Single Crystal investigation

Field-induced magnetic ordering in the Haldane chain compound SrNi$_{2}$V$_{2}$O$_{8}$ and effect of anisotropy have been investigated using single crystals. Static susceptibility, inelastic neutron scattering, high-field magnetization, and low temperature heat-capacity studies confirm a non-magnetic spin-singlet ground state and a gap between the singlet ground state and triplet excited states. The intra-chain exchange interaction is estimated to be $J \sim 8.9{\pm}$0.1 meV. Splitting of the dispersions into two modes with minimum energies 1.57 and 2.58 meV confirms the existence of single-ion anisotropy $D(S^z){^2}$. The value of {\it D} is estimated to be $-0.51{\pm}0.01$ meV and the easy axis is found to be along the crystallographic {\it c}-axis. Field-induced magnetic ordering has been found with two critical fields [$\mu_0H_c^{\perp c} = 12.0{\pm}$0.2 T and $\mu_0H_c^{\parallel c} = 20.8{\pm}$0.5 T at 4.2 K]. Field-induced three-dimensional magnetic ordering above the critical fields is evident from the heat-capacity, susceptibility, and high-field magnetization study. The Phase diagram in the {\it H-T} plane has been obtained from the high-field magnetization. The observed results are discussed in the light of theoretical predictions as well as earlier experimental reports on Haldane chain compounds

Consequences of critical interchain couplings and anisotropy on a Haldane chain

Effects of interchain couplings and anisotropy on a Haldane chain have been investigated by single crystal inelastic neutron scattering and density functional theory (DFT) calculations on the model compound SrNi$_2$V$_2$O$_8$. Significant effects on low energy excitation spectra are found where the Haldane gap ($\Delta_0 \approx 0.41J$; where $J$ is the intrachain exchange interaction) is replaced by three energy minima at different antiferromagnetic zone centers due to the complex interchain couplings. Further, the triplet states are split into two branches by single-ion anisotropy. Quantitative information on the intrachain and interchain interactions as well as on the single-ion anisotropy are obtained from the analyses of the neutron scattering spectra by the random phase approximation (RPA) method. The presence of multiple competing interchain interactions is found from the analysis of the experimental spectra and is also confirmed by the DFT calculations. The interchain interactions are two orders of magnitude weaker than the nearest-neighbour intrachain interaction $J$ = 8.7~meV. The DFT calculations reveal that the dominant intrachain nearest-neighbor interaction occurs via nontrivial extended superexchange pathways Ni--O--V--O--Ni involving the empty $d$ orbital of V ions. The present single crystal study also allows us to correctly position SrNi$_2$V$_2$O$_8$ in the theoretical $D$-$J_{\perp}$ phase diagram [T. Sakai and M. Takahashi, Phys. Rev. B 42, 4537 (1990)] showing where it lies within the spin-liquid phase.Comment: 12 pages, 12 figures, 3 tables PRB (accepted). in Phys. Rev. B (2015

Spinon Confinement in the One-Dimensional Ising-Like Antiferromagnet SrCo2V2O8

For quasi-one dimensional quantum spin systems theory predicts the occurrence of a confinement of spinon excitation due to interchain couplings. Here we investigate the system SrCo2V2O8, a realization of the weakly-coupled Ising-like XXZ antiferromagnetic chains, by terahertz spectroscopy with and without applied magnetic field. At low temperatures a series of excitations is observed, which split in a Zeeman-like fashion in an applied magnetic field. These magnetic excitations are identified as the theoretically predicted spinon-pair excitations. Using a one dimensional Schr\"odinger equation with a linear confinement potential imposed by weak interchain couplings, the hierarchy of the confined spinons can be fully described.Comment: 4 pages, 3 figure