Ferromagnetic ordering of linearly coordinated Co ions in LiSr2_2[CoN2_2]

LiSr$_2$[CoN$_2$] single crystals were successfully grown out of Li-rich flux. Temperature- and field-dependent measurements of the magnetization in the range of $T = 2 - 300$ K and up to $\mu_{0}\textit{H} = 7$ T as well as measurements of the heat capacity are presented. Ferromagnetic ordering emerges below $T_C = 44$ K and comparatively large coercivity fields of $\mu_0H = 0.3$ T as well as pronounced anisotropy are observed upon cooling. Polycrystalline samples of the Ca analog LiCa$_2$[CoN$_2$] were obtained and investigated in a similar way. In both compounds Co manifests orbital contributions to the magnetic moment and large single-ion anisotropy that is caused by second-order Spin-orbit coupling. Quantum chemistry calculations reveal a magnetic anisotropy energy of 7 meV, twice as large as the values reported for similar Co $d^{8}$ systems.Comment: 21 pages, 6 figures, 5 table

From 'nothing' to inflation and back again

A procedure for solving Wheeler-DeWitt equation in Euclidean region, following step by step the construction of tunneling wave function in nonrelativistic quantum mechanics by Banks, Bender and Wu, is proposed. Solutions for a universe satisfying no-boundary condition and a universe created from 'nothing' are compared to the corresponding solutions for a particle in a two-dimensional potential well, and effects of indefiniteness of metric and zero energy in Wheeler-DeWitt equation are discussed.Comment: 8 pages, presented at the conference Relativity and Gravitation, 100 years after Einstein in Prague (Prague 2012

Effective relational dynamics

We provide a synopsis of an effective approach to the problem of time in the semiclassical regime. The essential features of this new approach to evaluating relational quantum dynamics in constrained systems are illustrated by means of a simple toy model.Comment: 4 pages, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS

Effective approach to the problem of time: general features and examples

The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the quantum constrained system can be truncated to finite size and solved by the reduced phase space or gauge-fixing methods. In particular, the classical feasibility of local internal times is directly generalized to quantum systems, overcoming the main difficulties associated with the general problem of time in the semiclassical realm. The key features of local internal times and the procedure of patching global solutions using overlapping intervals of local internal times are described and illustrated by two quantum mechanical examples. Relational evolution in a given choice of internal time is most conveniently described and interpreted in a corresponding choice of gauge at the effective level and changing the internal clock is, therefore, essentially achieved by a gauge transformation. This article complements the conceptual discussion in arXiv:1009.5953.Comment: 42 pages, 9 figures; v2: streamlined discussions, more compact manuscrip

Single crystal growth and anisotropic magnetic properties of Li2Sr[Li1 − xFexN]2

Up to now, investigation of physical properties of ternary and higher nitridometalates was severely hampered by challenges concerning phase purity and crystal size. Employing a modified lithium flux technique, we are now able to prepare sufficiently large single crystals of the highly air and moisture sensitive nitridoferrate $\rm Li_2Sr[Li_{1-x}Fe_xN]_2$ for anisotropic magnetization measurements. The magnetic properties are most remarkable: large anisotropy and coercivity fields of 7 Tesla at $T = 2$ K indicate a significant orbital contribution to the magnetic moment of iron. Altogether, the novel growth method opens a route towards interesting phases in the comparatively recent research field of nitridometalates and should be applicable to various other materials.Comment: 10 pages, 5 figures, published open access in Inorganics, minor typos correcte

Micro-cantilever testing of diamond - silicon carbide interfaces in silicon carbide bonded diamond materials produced by reactive silicon infiltration

SiC-bonded diamond materials produced by pressureless reactive infiltration of diamond preforms with silicon show high hardness and wear resistance. These properties are due to the relatively high diamond volume content of approximately 50 vol% and the mechanically strong interface between diamond and SiC. To determine the bending strength of individual interfaces between diamond and SiC, micro-cantilevers were prepared by focused ion beam milling at 13 grain boundaries and in-situ bending tests were carried out in a scanning electron microscope. The determined strength of cantilevers showing interface fracture was 10.4 ± 4.0 GPa. Fracture surfaces were analyzed to verify the fracture behavior and initiation. In addition to fracture at the interface diamond/SiC, fracture occurred inside the SiC grains and at the SiC/silicon interface at comparable strength values. The results prove the high diamond/SiC-interface bonding strength

On Exceptional Vertex Operator (Super) Algebras

We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We show that the genus one partition function and characters for simple ordinary modules must satisfy modular linear differential equations. We show the rationality of the central charge and module lowest weights, modularity of solutions, the dimension of each graded space is a rational function of the central charge and that the lowest weight primaries generate the algebra. We also discuss conditions on the reducibility of the lowest weight primary vectors as a module for the automorphism group. Finally we analyse solutions for exceptional vertex operator algebras with primary vectors of lowest weight up to 9 and for vertex operator superalgebras with primary vectors of lowest weight up to 17/2. Most solutions can be identified with simple ordinary modules for known algebras but there are also four conjectured algebras generated by weight two primaries and three conjectured extremal vertex operator algebras generated by primaries of weight 3, 4 and 6 respectively.Comment: 37 page

Three-dimensional AdS gravity and extremal CFTs at c=8m

We note that Witten's proposed duality between extremal c=24k CFTs and three-dimensional anti-de Sitter gravity may possibly be extended to central charges that are multiples of 8, for which extremal self-dual CFTs are known to exist up to c=40. All CFTs of this type with central charge 24 or higher, provided that they exist, have the required mass gap and may serve as candidate duals to three-dimensional gravity at the corresponding values of the cosmological constant. Here, we compute the genus one partition function of these theories up to c=88, we give exact and approximate formulas for the degeneracies of states, and we determine the genus two partition functions of the theories up to c=40.Comment: 17 pages, harvmac; v2: references added, version accepted in JHE

Worldwide evidence of a unimodal relationship between productivity and plant species richness

The search for predictions of species diversity across environmental gradients has challenged ecologists for decades. The humped-back model (HBM) suggests that plant diversity peaks at intermediate productivity; at low productivity few species can tolerate the environmental stresses, and at high productivity a few highly competitive species dominate. Over time the HBM has become increasingly controversial, and recent studies claim to have refuted it. Here, by using data from coordinated surveys conducted throughout grasslands worldwide and comprising a wide range of site productivities, we provide evidence in support of the HBM pattern at both global and regional extents. The relationships described here provide a foundation for further research into the local, landscape, and historical factors that maintain biodiversity