Magnetic properties of undoped Cu2O fine powders with magnetic impurities and/or cation vacancies

Fine powders of micron- and submicron-sized particles of undoped Cu2O semiconductor, with three different sizes and morphologies have been synthesized by different chemical processes. These samples include nanospheres 200 nm in diameter, octahedra of size 1 micron, and polyhedra of size 800 nm. They exhibit a wide spectrum of magnetic properties. At low temperature, T = 5 K, the octahedron sample is diamagnetic. The nanosphere is paramagnetic. The other two polyhedron samples synthesized in different runs by the same process are found to show different magnetic properties. One of them exhibits weak ferromagnetism with T_C = 455 K and saturation magnetization, M_S = 0.19 emu/g at T = 5 K, while the other is paramagnetic. The total magnetic moment estimated from the detected impurity concentration of Fe, Co, and Ni, is too small to account for the observed magnetism by one to two orders of magnitude. Calculations by the density functional theory (DFT) reveal that cation vacancies in the Cu2O lattice are one of the possible causes of induced magnetic moments. The results further predict that the defect-induced magnetic moments favour a ferromagnetically coupled ground state if the local concentration of cation vacancies, n_C, exceeds 12.5%. This offers a possible scenario to explain the observed magnetic properties. The limitations of the investigations in the present work, in particular in the theoretical calculations, are discussed and possible areas for further study are suggested.Comment: 20 pages, 5 figures 2 tables, submitted to J Phys Condense Matte

An exact general remeshing scheme applied to physically conservative voxelization

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems. We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal the corresponding integral over the output mesh. We refer to this as "physically conservative voxelization". At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara (1994), who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain. We also address practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3

Relation between the weak itinerant magnetism in A2A_2Ni7_7 compounds (AA = Y, La) and their stacked crystal structures

The weak itinerant magnetic properties of $A_2$Ni$_7$ compounds with $A$ = {Y, La} have been investigated using electronic band structure calculations in the relation with their polymorphic crystal structures. These compounds crystallizes in two structures resulting from the stacking of two and three blocks of [$A_2$Ni$_4$ + 2 $A$Ni$_5$] units for hexagonal $2H$-La$_2$Ni$_7$ (Ce$_2$Ni$_7$ type) and rhombohedral $3R$-Y$_2$Ni$_7$ (Gd$_2$Co$_7$ type) respectively. Experimentally, $2H$-La$_2$Ni$_7$ is a weak itinerant antiferromagnet whereas $3R$-Y$_2$Ni$_7$ is a weak itinerant ferromagnet. From the present first principles calculation within non-spin polarized state, both compounds present an electronic density of state with a sharp and narrow peak centered at the Fermi level corresponding to flat bands from $3d$-Ni. This induces a magnetic instability and both compounds are more stable in a ferromagnetic (FM) order compared to a paramagnetic state ($\Delta E \simeq$ -35 meV/f.u.). The magnetic moment of each of the five Ni sites varies with their positions relative to the [$A_2$Ni$_4$] and [$A$Ni$_5$] units: they are minimum in the [$A_2$Ni$_4$] unit and maximum at the interface between two [$A$Ni$_5$] units. For $2H$-La$_2$Ni$_7$, an antiferromagnetic (AFM) structure has been proposed and found with an energy comparable to that of the FM state. This AFM structure is described by two FM unit blocks of opposite Ni spin sign separated by a non-magnetic layer at z = 0 and $\frac12$. The Ni ($2a$) atoms belonging to this intermediate layer are located in the [La$_2$Ni$_4$] unit and are at a center of symmetry of the hexagonal cell ($P6_3/mmc$) where the resultant molecular field is cancelled. Further non-collinear spin calculations have been performed to determine the Ni moment orientations which are found preferentially parallel to the $c$ axis for both FM and AFM structures.Comment: 19 pages, 7 figures, 2 table

Sub-Critical Closed String Field Theory in D Less Than 26

We construct the second quantized action for sub-critical closed string field theory with zero cosmological constant in dimensions $2 \leq D < 26$, generalizing the non-polynomial closed string field theory action proposed by the author and the Kyoto and MIT groups for $D = 26$. The proof of gauge invariance is considerably complicated by the presence of the Liouville field $\phi$ and the non-polynomial nature of the action. However, we explicitly show that the polyhedral vertex functions obey BRST invariance to all orders. By point splitting methods, we calculate the anomaly contribution due to the Liouville field, and show in detail that it cancels only if $D - 26 + 1 + 3 Q ^ 2 = 0$, in both the bosonized and unbosonized polyhedral vertex functions. We also show explicitly that the four point function generated by this action reproduces the shifted Shapiro-Virasoro amplitude found from $c=1$ matrix models and Liouville theory in two dimensions. LATEX file.Comment: 28 pages, CCNY-HEP-93-

NaIrO3 - A pentavalent post-perovskite

Sodium iridium(V) oxide, NaIrO3, was synthesized by a high pressure solid state method and recovered to ambient conditions. It is found to be isostructural with CaIrO3, the much-studied structural analogue of the high-pressure post-perovskite phase of MgSiO3. Among the oxide post-perovskites, NaIrO3 is the first example with a pentavalent cation. The structure consists of layers of corner- and edge-sharing IrO6 octahedra separated by layers of NaO8 bicapped trigonal prisms. NaIrO3 shows no magnetic ordering and resistivity measurements show non-metallic behavior. The crystal structure, electrical and magnetic properties are discussed and compared to known post-perovskites and pentavalent perovskite metal oxides.Comment: 22 pages, 5 figures. Submitted to Journal of Solid State Chemistr

Software for Exact Integration of Polynomials over Polyhedra

We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software implementation and provide benchmark computations. The computation of integrals of polynomials over polyhedral regions has many applications; here we demonstrate our algorithmic tools solving a challenge from combinatorial voting theory.Comment: Major updat

On the equivalence between the cell-based smoothed finite element method and the virtual element method

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D

Inverse pressure-induced Mott transition in TiPO4_4

TiPO$_4$ shows interesting structural and magnetic properties as temperature and pressure are varied, such as a spin-Peierls phase transition and the development of incommensurate modulations of the lattice. Recently, high pressure experiments for TiPO$_4$ reported two new structural phases appearing at high pressures, the so-called phases IV and V [M. Bykov et al., Angew. Chem. Int. Ed. 55, 15053]. The latter was shown to include the first example of 5-fold O-coordinated P-atoms in an inorganic phosphate compound. In this work we characterize the electronic structure and other physical properties of these new phases by means of ab-initio calculations, and investigate the structural transition. We find that the appearance of phases IV and V coincides with a collapse of the Mott insulating gap and quenching of magnetism in phase III as pressure is applied. Remarkably, our calculations show that in the high pressure phase V, these features reappear, leading to an antiferromagnetic Mott insulating phase, with robust local moments