Crystal Structure and Magnetism of the Linear-Chain Copper Oxides Sr5Pb3-xBixCuO12

The title quasi-1D copper oxides (0=< x =<0.4) were investigated by neutron diffraction and magnetic susceptibility studies. Polyhedral CuO4 units in the compounds were found to comprise linear-chains at inter-chain distance of approximately 10 A. The parent chain compound (x = 0), however, shows less anisotropic magnetic behavior above 2 K, although it is of substantially antiferromagnetic (mu_{eff}= 1.85 mu_{B} and Theta_{W} = -46.4 K) spin-chain system. A magnetic cusp gradually appears at about 100 K in T vs chi with the Bi substitution. The cusp (x = 0.4) is fairly characterized by and therefore suggests the spin gap nature at Delta/k_{B} ~ 80 K. The chain compounds hold electrically insulating in the composition range.Comment: To be published in PR

Covariantes continuas individuales dependientes del tiempo y el modelo de Cormack–Jolly–Seber

The Cormack–Jolly–Seber model provides the basic framework for analyzing the survival of animals in open populations using capture–recapture data. Extensions of this model have already been developed that allow the survival and capture probabilities to vary between individuals based on auxiliary variables, but none can allow for variables that are continuous, time–dependent, and vary among individuals. We summarize a new method for incorporating this type of variable into the Cormack–Jolly–Seber model by modelling the distribution of the unobserved values of the variable conditional on the observed values, given a few basic assumptions about how the variable changes over time. We begin with a hypothetical scenario as motivation for our model and also present the results of two examples used in developing the model.El modelo de Cormack–Jolly–Seber proporciona el marco básico para analizar la supervivencia de animales en poblaciones abiertas utilizando datos de captura–recaptura. Si bien se han desarrollado ampliaciones de este modelo que permiten variar las probabilidades de supervivencia y de captura entre individuos a partir de variables auxiliares, en ninguna de ellas es posible utilizar variables continuas, dependientes del tiempo y que varíen de un individuo a otro. El presente estudio analiza un nuevo método que permite la incorporación de este tipo de variable en el modelo de Cormack–Jolly–Seber mediante la modelación de la distribución de los valores no observados de la variable según los valores observados, tomando como referencia algunas asumciones básicas acerca de cómo la variable cambia con el tiempo. En primer lugar, presentamos un escenario hipotético con objeto de definir el modelo, para posteriormente indicar los resultados de dos ejemplos que utilizamos para su desarrollo

The susceptibility and excitation spectrum of (VO)2_2P2_2O7_7 in ladder and dimer chain models

We present numerical results for the magnetic susceptibility of a Heisenberg antiferromagnetic spin ladder, as a function of temperature and the spin-spin interaction strengths $J_\perp$ and $J_{||}$. These are contrasted with new bulk limit results for the dimer chain. A fit to the experimental susceptibility of the candidate spin-ladder compound vanadyl pyrophosphate, (VO)$_2$P$_2$O$_7$, gives the parameters $J_\perp = 7.82$ meV and $J_{||} = 7.76$ meV. With these values we predict a singlet-triplet energy gap of $E_{gap} = 3.9$ meV, and give a numerical estimate of the ladder triplet dispersion relation $\omega(k)$. In contrast, a fit to the dimer chain model leads to $J_1=11.11$ meV and $J_2=8.02$ meV, which predicts a gap of $E_{gap} = 4.9$ meV.Comment: 16 pages, 6 figures available upon request, RevTex 3.0, preprint ORNL-CCIP-94-04 / RAL-94-02

Phase Behavior of Models with Competing Interactions

Models with competing nearest-neighbor and very long-range interactions are solved exactly for several one-dimensional cases, including the usual Ising chain (lCCI) , the X Y model (XYCI) , the transverse Ising model (TICCI), and the spherical model (SCCI). For certain ratios of the competing interaction strengths, ICCI and XYCI display triple points and two critical points in a field. In addition TICCI has an apparently enclosed phase in an H-T phase diagram; however, this phase is really paramagnetic as can be seen when an extended phase diagram is used. The extended phase diagrams for ICCI, XYCI, and TICCI display tricritical points and the tricritical exponents have different values from the usual classical values. In contrast to the rich phase behavior of the preceding models, SCCI shows very simple phase behavior, which is directly related to the ground state. Finally, the introduction of a staggered field to ICCI and a simple transformation allows reinterpretation as a metamagnetic model. Using ICCI as a guide the observability of the tricritical exponents is discussed

Spin Chains in a Field: Crossover from Quantum to Classical Behavior

Extensive numerical studies have been performed on Heisenberg antiferromagnetic chains of spin (1/2) (up to N=20), spin 1 (N=14), spin (3/2) (N=10), and spin 2 (N=8). With use of the Lanczös technique, primarily, the two lowest-lying eigenvalues have been calculated for all values of wave vector q and all values of magnetization (SzT) up to saturation for each chain. From a knowledge of the eigenvector corresponding to the lowest eigenstate for each SzT, the T=0 spin-pair correlation functions have also been calculated as a function of field. We find a most unusual quantum-classical crossover phenomenon. It shows up in greatest detail in the field-dependent dispersion spectra, but the consequences are consistently manifested in the behavior of the T=0 magnetization isotherms and in the correlations both in real space and the Fourier transforms in q space. The additional data relevant to behavior in a field have allowed us to extend previous numerical studies of Heisenberg antiferromagnetic chains with higher spin whose purpose was to examine the validity of the Haldane conjecture. The Haldane conjecture implies that Heisenberg antiferromagnetic chains with integer spin have a gap in their excitation spectrum whereas chains with half-integer spin do not. While no feature of our extended investigations is in conflict with the conjecture, unusual features associated apparently with very slow convergence make the outcome less than conclusive. It appears that calculations on significantly longer chains are required to observe with confidence the large-N asymptotic limiting behavior

Excitation Spectrum and Thermodynamic Properties of the Ising-Heisenberg Linear Ferromagnet

New analytic results are presented for the low-T thermodynamics of the Ising-Heisenberg linear ferromagnetic in a magnetic field H0. For small H0 the thermodynamic functions show unexpected and interesting structure as a function of H0 and the anisotropy Δ. The thermal and magnetic energy gaps have singularities, not necessarily at the same Δ−H0 location, as changes occur in the type of excitation dominating the low-T behavior. The results may relate to quantum solitons in the linear ferromagnet

Comparison of spin anisotropy and exchange alternation

Quasi‐1‐D magnetic systems with on the one hand an Ising‐Heisenberg type spin anisotropy and on the other hand an alternating (dimerized) character have many interesting features in common and a few interesting differences in their phase behavior and general magnetic properties. This report reviews results rather scattered in the literature in addition to presenting new results. These rather complex quantum models present a theoretical challenge. It is also hoped that this work will be helpful to magnetochemists interested in identifying the underlying magnetic character of their systems, and to experimentalists in general

Spin Gap of S=1/2 Heisenberg Model on Distorted Diamond Chain

We study the spin gap of the S=1/2 Heisenberg model on the distorted diamond chain, which is recently proposed to represent magnetic properties of Cu_3 Cl_6 (H_2 O)_2 2H_8 C_4 SO_2. This model is composed of stacked trimers and has three kinds of exchange interactions J_1, J_2 and J_3. Using the numerical diagonalization, we obtain a contour map of the spin gap in the J_2/J_1-J_3/J_1 plane. We argue possible values of the exchange constants based on the contour map and the observed value of the spin gap.Comment: 2 pages, 4 figure

Spin gap in the Quasi-One-Dimensional S=1/2 Antiferromagnet: Cu2(1,4-diazacycloheptane)2Cl4

Cu_{2}(1,4-diazacycloheptane)_{2}Cl_{4} contains double chains of spin 1/2 Cu^{2+} ions. We report ac susceptibility, specific heat, and inelastic neutron scattering measurements on this material. The magnetic susceptibility, $\chi(T)$, shows a rounded maximum at T = 8 K indicative of a low dimensional antiferromagnet with no zero field magnetic phase transition. We compare the $\chi(T)$ data to exact diagonalization results for various one dimensional spin Hamiltonians and find excellent agreement for a spin ladder with intra-rung coupling $J_1 = 1.143(3)$ meV and two mutually frustrating inter-rung interactions: $J_2 = 0.21(3)$ meV and $J_3 = 0.09(5)$ meV. The specific heat in zero field is exponentially activated with an activation energy $\Delta = 0.89(1)$ meV. A spin gap is also found through inelastic neutron scattering on powder samples which identify a band of magnetic excitations for $0.8 < \hbar\omega < 1.5$ meV. Using sum-rules we derive an expression for the dynamic spin correlation function associated with non-interacting propagating triplets in a spin ladder. The van-Hove singularities of such a model are not observed in our scattering data indicating that magnetic excitations in Cu_{2}(1,4-diazacycloheptane)_{2}Cl_{4} are more complicated. For magnetic fields above $H_{c1} \simeq 7.2$ T specific heat data versus temperature show anomalies indicating a phase transition to an ordered state below T = 1 K.Comment: 9 pages, 8 postscript figures, LaTeX, Submitted to PRB 8/4/97, e-mail Comments to [email protected]

Renormalization group and other calculations for the one‐dimensional spin‐1/2 dimerized Heisenberg antiferromagnet

A zero-temperature renormalization group (RG) approach is applied to the one-dimensional, spin-1/2 anti ferromagnetic Heisenberg dimerized (alternating) chain. Specifically, the ground state energy and lowest-lying spectral excitations are examined. The calculation indicates the existence of a gap in the spectrum of the dimerized chain which vanishes only in the limit of a uniform spin chain in contrast to a recent Green\u27s function approach. The RG results are in reasonable agreement with numerical extrapolations on the exact eigenvalue spectrum of finite chains of up to 12 spins. Both methods are compared with several other approximate treatments of the Heisenberg system. and tested by comparison with exact results for the spin-1/2 XY dimerized chain