The definability criterions for convex projective polyhedral reflection groups

Following Vinberg, we find the criterions for a subgroup generated by reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the $n$-dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of \SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over $\mathbb{Z}$. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure

Dielectric constants of Ir, Ru, Pt, and IrO2: Contributions from bound charges

We investigated the dielectric functions $\epsilon$($\omega$) of Ir, Ru, Pt, and IrO$_2$, which are commonly used as electrodes in ferroelectric thin film applications. In particular, we investigated the contributions from bound charges $\epsilon^{b}$($\omega$), since these are important scientifically as well as technologically: the $\epsilon_1^{b}$(0) of a metal electrode is one of the major factors determining the depolarization field inside a ferroelectric capacitor. To obtain $\epsilon_1^{b}$(0), we measured reflectivity spectra of sputtered Pt, Ir, Ru, and IrO2 films in a wide photon energy range between 3.7 meV and 20 eV. We used a Kramers-Kronig transformation to obtain real and imaginary dielectric functions, and then used Drude-Lorentz oscillator fittings to extract $\epsilon_1^{b}$(0) values. Ir, Ru, Pt, and IrO$_2$ produced experimental $\epsilon_1^{b}$(0) values of 48$\pm$10, 82$\pm$10, 58$\pm$10, and 29$\pm$5, respectively, which are in good agreement with values obtained using first-principles calculations. These values are much higher than those for noble metals such as Cu, Ag, and Au because transition metals and IrO$_2$ have such strong d-d transitions below 2.0 eV. High $\epsilon_1^{b}$(0) values will reduce the depolarization field in ferroelectric capacitors, making these materials good candidates for use as electrodes in ferroelectric applications.Comment: 26 pages, 6 figures, 2 table

Putative spin liquid in the triangle-based iridate Ba3_3IrTi2_2O9_9

We report on thermodynamic, magnetization, and muon spin relaxation measurements of the strong spin-orbit coupled iridate Ba$_3$IrTi$_2$O$_9$, which constitutes a new frustration motif made up a mixture of edge- and corner-sharing triangles. In spite of strong antiferromagnetic exchange interaction of the order of 100~K, we find no hint for long-range magnetic order down to 23 mK. The magnetic specific heat data unveil the $T$-linear and -squared dependences at low temperatures below 1~K. At the respective temperatures, the zero-field muon spin relaxation features a persistent spin dynamics, indicative of unconventional low-energy excitations. A comparison to the $4d$ isostructural compound Ba$_3$RuTi$_2$O$_9$ suggests that a concerted interplay of compass-like magnetic interactions and frustrated geometry promotes a dynamically fluctuating state in a triangle-based iridate.Comment: Physical Review B accepte

Mechanism of enhanced light output in InGaN-based microlight emitting diodes

Micro-light emitting diode (LED) arrays with diameters of 4 to 20 mum have been fabricated and were found to be much more efficient light emitters compared to their broad-area counterparts, with up to five times enhancement in optical power densities. The possible mechanisms responsible for the improvement in performance were investigated. Strain relaxation in the microstructures as measured by Raman spectroscopy was not observed, arguing against theories of an increase in internal quantum efficiency due to a reduction of the piezoelectric field put forward by other groups. Optical microscope images show intense light emission at the periphery of the devices, as a result of light scattering off the etched sidewalls. This increases the extraction efficiency relative to broad area devices and boosts the forward optical output. In addition, spectra of the forward emitted light reveal the presence of resonant cavity modes [whispering gallery (WG) modes in particular] which appear to play a role in enhancing the optical output

Singe ferroelectric and chiral magnetic domain of single-crystalline BiFeO3_3 in an electric field

We report polarized neutron scattering and piezoresponse force microscopy studies of millimeter-sized single crystals of multiferroic BiFeO$_3$. The crystals, grown below the Curie temperature, consist of a single ferroelectric domain. Two unique electric polarization directions, as well as the populations of equivalent spiral magnetic domains, can be switched reversibly by an electric field. A ferroelectric monodomain with a single-$q$ single-helicity spin spiral can be obtained. This level of control, so far unachievable in thin films, makes single-crystal BiFeO$_3$ a promising object for multiferroics research.Comment: 4 figures in separate jpg file