Modified kagome physics in the natural spin-1/2 kagome lattice systems - kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2

The recently discovered natural minerals Cu3Zn(OH)6Cl2 and Cu3Mg(OH)6Cl2 are spin 1/2 systems with an ideal kagome geometry. Based on electronic structure calculations, we develop a realistic model which includes couplings across the kagome hexagons beyond the original kagome model that are intrinsic in real kagome materials. Exact diagonalization studies for the derived model reveal a strong impact of these couplings on the magnetic ground state. Our predictions could be compared to and supplied with neutron scattering, thermodynamic and NMR data.Comment: 5 pages, 5 figures, 1 tabl

Coupled frustrated quantum spin-1/2 chains with orbital order in volborthite Cu3V2O7(OH)2(H2O)2

We present a microscopic magnetic model for the spin-liquid candidate volborthite Cu3V2O7(OH)2(H2O)2. The essentials of this DFT-based model are (i) the orbital ordering of Cu(1) 3d 3z2-r2 and Cu(2) 3d 3x2-y2, (ii) three relevant couplings J_ic, J_1 and J_2, (iii) the ferromagnetic nature of J_1 and (iv) frustration governed by the next-nearest-neighbor exchange interaction J_2. Our model implies magnetism of frustrated coupled chains in contrast to the previously proposed anisotropic kagome model. Exact diagonalization studies reveal agreement with experiments.Comment: 5 pages, 4 figures + supplementar

Large quantum fluctuations in the strongly coupled spin-1/2 chains of green dioptase: a hidden message from birds and trees

The green mineral dioptase Cu6Si6O18(H2O)6 has been known since centuries and plays an important role in esoteric doctrines. In particular, the green dioptase is supposed to grant the skill to speak with trees and to understand the language of birds. Armed with natural samples of dioptase, we were able to unravel the magnetic nature of the mineral (presumably with hidden support from birds and trees) and show that strong quantum fluctuations can be realized in an essentially framework-type spin lattice of coupled chains, thus neither frustration nor low-dimensionality are prerequisites. We present a microscopic magnetic model for the green dioptase. Based on full-potential DFT calculations, we find two relevant couplings in this system: an antiferromagnetic coupling J_c, forming spiral chains along the hexagonal c axis, and an inter-chain ferromagnetic coupling J_d within structural Cu2O6 dimers. To refine the J_c and J_d values and to confirm the proposed spin model, we perform quantum Monte-Carlo simulations for the dioptase spin lattice. The derived magnetic susceptibility, the magnetic ground state, and the sublattice magnetization are in remarkably good agreement with the experimental data. The refined model parameters are J_c = 78 K and J_d = -37 K with J_d/J_c ~ -0.5. Despite the apparent three-dimensional features of the spin lattice and the lack of frustration, strong quantum fluctuations in the system are evidenced by a broad maximum in the magnetic susceptibility, a reduced value of the Neel temperature T_N ~ 15 K >> J_c, and a low value of the sublattice magnetization m = 0.55 Bohr magneton. All these features should be ascribed to the low coordination number of 3 that outbalances the three-dimensional nature of the spin lattice.Comment: Dedicated to Stefan-Ludwig Drechsler on the occasion of his 60th birthday (9 pages, 6 figures

Fully Analyzing an Algebraic Polya Urn Model

This paper introduces and analyzes a particular class of Polya urns: balls are of two colors, can only be added (the urns are said to be additive) and at every step the same constant number of balls is added, thus only the color compositions varies (the urns are said to be balanced). These properties make this class of urns ideally suited for analysis from an "analytic combinatorics" point-of-view, following in the footsteps of Flajolet-Dumas-Puyhaubert, 2006. Through an algebraic generating function to which we apply a multiple coalescing saddle-point method, we are able to give precise asymptotic results for the probability distribution of the composition of the urn, as well as local limit law and large deviation bounds.Comment: LATIN 2012, Arequipa : Peru (2012

Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs

General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph H, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and Schur triples in random subsets of integers. In the second part of the paper we return to the subgraph counts in random graphs and provide upper tail estimates in the rooted case.Comment: 15 page

Magnetism of CuX2 frustrated chains (X = F, Cl, Br): the role of covalency

Periodic and cluster density-functional theory (DFT) calculations, including DFT+U and hybrid functionals, are applied to study magnetostructural correlations in spin-1/2 frustrated chain compounds CuX2: CuCl2, CuBr2, and a fictitious chain structure of CuF2. The nearest-neighbor and second-neighbor exchange integrals, J1 and J2, are evaluated as a function of the Cu-X-Cu bridging angle, theta, in the physically relevant range 80-110deg. In the ionic CuF2, J1 is ferromagnetic for theta smaller 100deg. For larger angles, the antiferromagnetic superexchange contribution becomes dominant, in accord with the Goodenough-Kanamori-Anderson rules. However, both CuCl2 and CuBr2 feature ferromagnetic J1 in the whole angular range studied. This surprising behavior is ascribed to the increased covalency in the Cl and Br compounds, which amplifies the contribution from Hund's exchange on the ligand atoms and renders J1 ferromagnetic. At the same time, the larger spatial extent of X orbitals enhances the antiferromagnetic J2, which is realized via the long-range Cu-X-X-Cu paths. Both, periodic and cluster approaches supply a consistent description of the magnetic behavior which is in good agreement with the experimental data for CuCl2 and CuBr2. Thus, owing to their simplicity, cluster calculations have excellent potential to study magnetic correlations in more involved spin lattices and facilitate application of quantum-chemical methods

Intrinsic peculiarities of real material realizations of a spin-1/2 kagome lattice

Spin-1/2 magnets with kagome geometry, being for years a generic object of theoretical investigations, have few real material realizations. Recently, a DFT-based microscopic model for two such materials, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, was presented [O. Janson, J. Richter and H. Rosner, arXiv:0806.1592]. Here, we focus on the intrinsic properties of real spin-1/2 kagome materials having influence on the magnetic ground state and the low-temperature excitations. We find that the values of exchange integrals are strongly dependent on O--H distance inside the hydroxyl groups, present in most spin-1/2 kagome compounds up to date. Besides the original kagome model, considering only the nearest neighbour exchange, we emphasize the crucial role of the exchange along the diagonals of the kagome lattice.Comment: 4 pages, 4 figures. A paper for the proceedings of the HFM 2008 conferenc

Decorated Shastry-Sutherland lattice in the spin-1/2 magnet CdCu2(BO3)2

We report the microscopic magnetic model for the spin-1/2 Heisenberg system CdCu2(BO3)2, one of the few quantum magnets showing the 1/2-magnetization plateau. Recent neutron diffraction experiments on this compound [M. Hase et al., Phys. Rev. B 80, 104405 (2009)] evidenced long-range magnetic order, inconsistent with the previously suggested phenomenological magnetic model of isolated dimers and spin chains. Based on extensive density-functional theory band structure calculations, exact diagonalizations, quantum Monte Carlo simulations, third-order perturbation theory, as well as high-field magnetization measurements, we find that the magnetic properties of CdCu2(BO3)2 are accounted for by a frustrated quasi-2D magnetic model featuring four inequivalent exchange couplings: the leading antiferromagnetic coupling J_d within the structural Cu2O6 dimers, two interdimer couplings J_t1 and J_t2, forming magnetic tetramers, and a ferromagnetic coupling J_it between the tetramers. Based on comparison to the experimental data, we evaluate the ratios of the leading couplings J_d : J_t1 : J_t2 : J_it = 1 : 0.20 : 0.45 : -0.30, with J_d of about 178 K. The inequivalence of J_t1 and J_t2 largely lifts the frustration and triggers long-range antiferromagnetic ordering. The proposed model accounts correctly for the different magnetic moments localized on structurally inequivalent Cu atoms in the ground-state magnetic configuration. We extensively analyze the magnetic properties of this model, including a detailed description of the magnetically ordered ground state and its evolution in magnetic field with particular emphasis on the 1/2-magnetization plateau. Our results establish remarkable analogies to the Shastry-Sutherland model of SrCu2(BO3)2, and characterize the closely related CdCu2(BO3)2 as a material realization for the spin-1/2 decorated anisotropic Shastry-Sutherland lattice.Comment: 16 pages, 13 figures, 2 tables. Published version with additional QMC dat

Environmental effects on progesterone profile measures of dairy cow fertility

Environmental effects on fertility measures early in lactation, such as the interval from calving to first luteal activity (CLA), proportion of samples with luteal activity during the first 60 days after calving (PLA) and interval to first ovulatory oestrus (OOE) were studied. In addition, traditional measurements of fertility, such as pregnancy to first insemination, number of inseminations per service period and interval from first to last insemination were studied as well as associations between the early and late measurements. Data were collected from an experimental herd during 15 years and included 1106 post-partum periods from 191 Swedish Holsteins and 325 Swedish Red and White dairy cows. Individual milk progesterone samples were taken twice a week until cyclicity and thereafter less frequently. First parity cows had 14.8 and 18.1 days longer CLA (LS-means difference) than second parity cows and older cows, respectively. Moreover, CLA was 10.5 days longer for cows that calved during the winter season compared with the summer season and 7.5 days longer for cows in tie-stalls than cows in loose-housing system. Cows treated for mastitis and lameness had 8.4 and 18.0 days longer CLA, respectively, compared with healthy cows. OOE was affected in the same way as CLA by the different environmental factors. PLA was a good indicator of CLA, and there was a high correlation (−0.69) between these two measurements. Treatment for lameness had a significant influence on all late fertility measurements, whereas housing was significant only for pregnancy to first insemination. All fertility traits were unfavourably associated with increased milk production. Regression of late fertility measurements on early fertility measurements had only a minor association with conception at first AI and interval from first to last AI for cows with conventional calving intervals, i.e. a 22 days later, CLA increased the interval from first to last insemination by 3.4 days. Early measurements had repeatabilities of 0.14–0.16, indicating a higher influence by the cow itself compared with late measurements, which had repeatabilities of 0.09–0.10. Our study shows that early fertility measurements have a possibility to be used in breeding for better fertility. To improve the early fertility of the cow, there are a number of important factors that have to be taken into account

Microscopic magnetic modeling for the SS=1/2 alternating chain compounds Na3_3Cu2_2SbO6_6 and Na2_2Cu2_2TeO6_6

The spin-1/2 alternating Heisenberg chain system Na$_3$Cu$_2$SbO$_6$ features two relevant exchange couplings: $J_{1a}$ within the structural Cu$_2$O$_6$ dimers and $J_{1b}$ between the dimers. Motivated by the controversially discussed nature of $J_{1a}$, we perform extensive density-functional-theory (DFT) calculations, including DFT+$U$ and hybrid functionals. Fits to the experimental magnetic susceptibility using high-temperature series expansions and quantum Monte Carlo simulations yield the optimal parameters $J_{1a}$ = $-$217 K and $J_{1b}$ = 174 K with the alternation ratio $\alpha = J_{1a}/J_{1b} \simeq$ $-$1.25. For the closely related system Na$_2$Cu$_2$TeO$_6$, DFT yields substantially enhanced $J_{1b}$, but weaker $J_{1a}$. The comparative analysis renders the buckling of the chains as the key parameter altering the magnetic coupling regime. Numerical simulation of the dispersion relations of the alternating chain model clarify why both antiferromagnetic and ferrromagnetic $J_{1a}$ can reproduce the experimental magnetic susceptibility data.Comment: published version: 11 pages, 8 figures, 5 tables + Supplemental materia