Compensated Half-metallicity in the Trigonally Distorted Perovskite-type NiCrO3_3

Using first principles calculations, we investigate the electronic and magnetic properties of the trigonally distorted (R-3c) perovskite-derived NiCrO$_3$. Within the local spin density approximation (LSDA), our calculations show that this system is an exactly compensated half-metal (CHM). The local spin moments of Cr 2.04, and antialigned Ni -1.41 and three oxygens -0.63 (in the units of $\mu_B$), indicate high spin S=3/2 Cr$^{3+}$ and S=3/2 (NiO$_3$)$^{3-}$ units. Considering reasonable values of the on-site Coulomb repulsion U on both Ni and Cr ions with LDA+U approach, this system becomes an insulator (as reported by Chamberland and Cloud) having a narrow gap in the spin-up channel, whereas the other channel has a large gap of ~3 eV. Although inclusion of U seemingly leads to the transition Ni$^{2+} --> high spin S=3/2 Ni$^{3+}$, consistent with the experimentally observed effective moment, the zero net moment remains unchanged due to either reduction of oxygen local moments or enhancement of Cr local moment. Compression of volume by 10to CHM even when correlation effects are included.These results suggest the possibility of a CHM state in NiCrO$_3$ and provide another route to search for CHM, which is a property sought by many.Comment: 5 pages, 5 embedded figures, (To be published in PRB rapid Commun.

Charge and Spin Ordering in Insulating Na0.5_{0.5}CoO2_2: Effects of Correlation and Symmetry

Ab initio band theory including correlations due to intra-atomic repulsion is applied to study charge disproportionation and charge- and spin-ordering in insulating Na$_{0.5}$CoO$_2$. Various ordering patterns (zigzag and two striped) for four-Co supercells are analyzed before focusing on the observed "out-of-phase stripe" pattern of antiferromagnetic Co$^{4+}$ spins along charge-ordered stripes. This pattern relieves frustration and shows distinct analogies with the cuprate layers: a bipartite lattice of antialigned spins, with axes at 90 degree angles. Substantial distinctions with cuprates are also discussed, including the tiny gap of a new variant of "charge transfer" type within the Co 3d system.Comment: 5 pages, 3 figure

Hardness of Graph Pricing through Generalized Max-Dicut

The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games Conjecture (UGC). We show that it is NP-hard to approximate within a factor better than 1/4 under the UGC, so that the simple combinatorial algorithm might be the best possible. We also prove that for any $\epsilon > 0$, there exists $\delta > 0$ such that the integrality gap of $n^{\delta}$-rounds of the Sherali-Adams hierarchy of linear programming for Graph Pricing is at most 1/2 + $\epsilon$. This work is based on the effort to view the Graph Pricing problem as a Constraint Satisfaction Problem (CSP) simpler than the standard and complicated formulation. We propose the problem called Generalized Max-Dicut($T$), which has a domain size $T + 1$ for every $T \geq 1$. Generalized Max-Dicut(1) is well-known Max-Dicut. There is an approximation-preserving reduction from Generalized Max-Dicut on directed acyclic graphs (DAGs) to Graph Pricing, and both our results are achieved through this reduction. Besides its connection to Graph Pricing, the hardness of Generalized Max-Dicut is interesting in its own right since in most arity two CSPs studied in the literature, SDP-based algorithms perform better than LP-based or combinatorial algorithms --- for this arity two CSP, a simple combinatorial algorithm does the best.Comment: 28 page

Charge Disproportionation and Spin Ordering Tendencies in Na(x)CoO2

The strength and effect of Coulomb correlations in the (superconducting when hydrated) x~1/3 and ``enhanced'' x~2/3 regimes of Na(x)CoO2 are evaluated using the correlated band theory LDA+U method. Our results, neglecting quantum fluctuations, are: (1) allowing only ferromagnetic order, there is a critical U_c = 3 eV, above which charge disproportionation occurs for both x=1/3 and x=2/3, (2) allowing antiferromagnetic order at x=1/3, U_c drops to 1 eV for disproportionation, (3) disproportionation and gap opening occur simultaneously, (4) in a Co(3+)-Co(4+) ordered state, antiferromagnetic coupling is favored over ferromagnetic, while below U_c ferromagnetism is favored. Comparison of the calculated Fermi level density of states compared to reported linear specific heat coefficients indicates enhancement of the order of five for x~0.7, but negligible enhancement for x~0.3. This trend is consistent with strong magnetic behavior and local moments (Curie-Weiss susceptibility) for x>0.5 while there no magnetic behavior or local moments reported for x<0.5. We suggest that the phase diagram is characterized by a crossover from effective single-band character with U >> W for x>0.5 into a three-band regime for x U_eff <= U/\sqrt(3) ~ W and correlation effects are substantially reduced.Comment: 10 pages, 8 figures, corrected a few typos and changed reference

Chemical Differences between K and Na in Alkali Cobaltates

K$_x$CoO$_2$ shares many similarities with Na$_x$CoO$_2$, as well as some important differences (no hydration-induced superconductivity has been reported). At $T_{c2}$=20 K, K$_{0.5}$CoO$_2$ becomes an insulator with a tiny optical gap as happens in Na$_{0.5}$CoO$_2$ at 52 K. This similarity, with a known common structure, enables direct comparisons to be made. Using the K-zigzag structure recently reported and the local density approximation, we compare and contrast these cobaltates at x=0.5. Although the electronic structures are quite similar as expected, substantial differences are observed near the Fermi level. These differences are found to be attributable mostly to the chemical, rather than structural difference: although Na is normally considered to be fully ion, K has somewhat more highly ionic character than does Na in these cobaltates.Comment: 5 paper

Boron Spectral Density and Disorder Broadening in B-doped Diamond

Comparison of periodic B dopants with a random alloy of substitional boron in diamond is carried out using several supercells and the coherent potential approximation (CPA) for the random alloy case. The main peak in the B local density of states is shifted to lower binding energy compared to the corresponding C peak in intrinsic diamond. In supercells, this shows up as strongly B-character bands split from bulk C bands away from the zone center,in an energy region around -1 eV. Even for a 4*4*4 supercell (BC$_{127}$), effects of the dopant order are evident in the form of primarily B-character bands just below the Fermi level at the supercell zone boundary. The bands resulting from the CPA are of continuous mixed C-B character. They resemble virtual crystal bands, but broadened somewhat reflecting the disorder-induced lifetime, and are consistent with angle-resolved photoemission band maps. The B character is 1.7 times larger than for C (per atom) near the top of the valence bands for CPA, and roughly the same for supercells. CPA results are particularly useful since they characterize the wavevector and energy dependence of disorder broadening.Comment: 8 pages and 9 embedded figures (To appear in PRB

Oregon's nutria problem

The nutria or coypu, Myocastor coypus, is a large semi-aquatic rodent that superficially resembles an overgrown muskrat or a stunted beaver. They were introduced into Oregon from about 1930 to the 1950's. At one time Oregon had more than 600 fur farmers raising these animals for fur; now there are none. Some animals escaped and many others were released into the wild when it became apparent that pelt values were nonexistent and production costs greatly exceeded profits. Being prolific and quite mobile, the nutria quickly spread through much of western Oregon. By the 1960's damage to agricultural crops was common to severe in western Oregon. Crops damaged included seed, grain, forage, hay and trees. Burrowing damage to stream banks, field borders, and farm ponds was reported in many areas. Growth and reproduction data for Oregon nutria are included. Methods for controlling feral nutria including the use of prolin, red squill, strychnine alkaloid, and zinc phosphide are reported. Fur trapping and adverse weather as factors in population reduction are discussed