Quenching of the Haldane gap in LiVSi<Subscript>2</Subscript>O<Subscript>6</Subscript> and related compounds

We report results of susceptibility χ and ⁷Li NMR measurements on LiVSi₂O₆. The temperature dependence of the magnetic susceptibility χ(T) exhibits a broad maximum, typical for low-dimensional magnetic systems. Quantitatively it is in agreement with the expectation for an S=1 spin chain, represented by the structural arrangement of V ions. The NMR results indicate antiferromagnetic ordering below T_N=24 K. The intra- and interchain coupling J and J_p for LiVSi₂O₆, and also for its sister compounds LiVGe₂O₆, NaVSi₂O₆ and NaVGe₂O₆, are obtained via a modified random phase approximation which takes into account results of quantum Monte Carlo calculations. While J_p is almost constant across the series, J varies by a factor of 5, decreasing with increasing lattice constant along the chain direction. The comparison between experimental and theoretical susceptibility data suggests the presence of an easy-axis magnetic anisotropy, which explains the formation of an energy gap in the magnetic excitation spectrum below T_N, indicated by the variation of the NMR spin-lattice relaxation rate at T≪T_N.     

Bixbyite- and anatase-type phases in the system Sc-Ta-O-N

The aim of our study was to modify the basis compound ß-TaON, which crystallizes in the monoclinic baddeleyite-type, by incorporation of appropriate dopant ions, in order to obtain anion-deficient cubic fluorite-type phases, which are of interest as solids with mobile nitrogen ions. For this purpose, scandium-doped tantalum oxide nitrides were prepared by ammonolysis of amorphous oxide precursors. An unexpected variety of phases with different structural features was observed: bixbyite-type phases of general composition Sc_xTa_1−x(O,N)_y with 0.33≤x≤1 and 1.7≤y≤1.9, yellow colored metastable anatase-type phases such as Sc_0.1Ta_0.9O_1.2N_0.8 or Sc_0.15Ta_0.85O_1.3N_0.7 and, additionally, anosovite-type phases Sc_xTa_3−xO_2xN_5−2x with 0≤x≤1.05. Selected phases were investigated by UV/vis spectroscopy. Anatase- and anosovite-type compounds show brilliant colors. In the anatase-type phase, a possible anion ordering was examined by theoretical methods. Additionally, energy calculations on phase stability were performed for Sc_xTa_1−xO_1+2xN_1−2x in the baddeleyite, rutile, and anatase structure types with varying amounts of dopants.     

A lattice point problem on the regular tree

Huber (1956) [8] considered the following problem on the hyperbolic plane H. Consider a strictly hyperbolic subgroup of automorphisms on H with compact quotient, and choose a conjugacy class in this group. Count the number of vertices inside an increasing ball, which are images of a fixed point x∈H under automorphisms in the chosen conjugacy class, and describe the asymptotic behaviour of this number as the size of the ball goes to infinity. We use a well-known analogy between the hyperbolic plane and the regular tree to solve this problem on the regular tree.     

Random on-site interactions versus random potential in ultra cold atoms in optical lattices

We consider the physics of lattice bosons in the presence of either disordered on-site chemical potential or disordered on-site interparticle interactions. By means of analytical results using strong-coupling expansion, and numerical results based on quantum Monte Carlo calculations, we show that important qualitative changes in the zero temperature phase diagram are observed when comparing both cases. Although for both types of disorder superfluid, Mott-insulator and Bose-glass phases may be found, we show that in the case of random interactions the Mott-insulating regions shrink and eventually vanish for any finite disorder strength beyond a sufficiently large filling factor. Furthermore, at low values of the chemical potential both the superfluid and Mott insulator are stable towards the formation of a Bose-glass, leading to a possibly non-trivial tricritical point. We discuss possible experimental realizations of both types of disorder in the context of ultra cold atomic gases in optical lattices. PACS 03.75.Lm; 03.75.Ss; 05.30.Jp; 32.80.Pj