195 research outputs found
Interchain interactions and magnetic properties of Li2CuO2
An effective Hamiltonian is constructed for an insulating cuprate with
edge-sharing chains Li2CuO2.The Hamiltonian contains the nearest and
next-nearest neighboring intrachain and zigzag-type interchain interactions.The
values of the interactions are obtained from the analysis of the magnetic
susceptibility, and this system is found to be described as coupled frustrated
chains.We calculate the dynamical spin correlation function S(q,\omega) by
using the exact diagonalization method, and show that the spectra of
S(q,\omega) are characterized by the zigzag-type interchain interactions. The
results of the recent inelastic neutron scattering experiment are discussed in
the light of the calculated spectra.Comment: 4 pages, 3 figures, RevTe
Fracture Propagation Driven by Fluid Outflow from a Low-permeability Aquifer
Deep saline aquifers are promising geological reservoirs for CO2
sequestration if they do not leak. The absence of leakage is provided by the
caprock integrity. However, CO2 injection operations may change the
geomechanical stresses and cause fracturing of the caprock. We present a model
for the propagation of a fracture in the caprock driven by the outflow of fluid
from a low-permeability aquifer. We show that to describe the fracture
propagation, it is necessary to solve the pressure diffusion problem in the
aquifer. We solve the problem numerically for the two-dimensional domain and
show that, after a relatively short time, the solution is close to that of
one-dimensional problem, which can be solved analytically. We use the relations
derived in the hydraulic fracture literature to relate the the width of the
fracture to its length and the flux into it, which allows us to obtain an
analytical expression for the fracture length as a function of time. Using
these results we predict the propagation of a hypothetical fracture at the In
Salah CO2 injection site to be as fast as a typical hydraulic fracture. We also
show that the hydrostatic and geostatic effects cause the increase of the
driving force for the fracture propagation and, therefore, our solution serves
as an estimate from below. Numerical estimates show that if a fracture appears,
it is likely that it will become a pathway for CO2 leakage.Comment: 21 page
Finite Temperature DMRG Investigation of the Spin-Peierls Transition in CuGeO
We present a numerical study of thermodynamical properties of dimerized
frustrated Heisenberg chains down to extremely low temperatures with
applications to CuGeO. A variant of the finite temperature density matrix
renormalization group (DMRG) allows the study of the dimerized phase previously
unaccessible to ab initio calculations. We investigate static dimerized systems
as well as the instability of the quantum chain towards lattice dimerization.
The crossover from a quadratic response in the free energy to the distortion
field at finite temperature to nonanalytic behavior at zero temperature is
studied quantitatively. Various physical quantities are derived and compared
with experimental data for CuGeO such as magnetic dimerization, critical
temperature, susceptibility and entropy.Comment: LaTeX, 5 pages, 5 eps figures include
On the importance of the heterogeneity assumption in the characterization of reservoir geomechanical properties
The geomechanical analysis of a highly compartmentalized reservoir is performed to simulate
the seafloor subsidence due to gas production. The available observations over the hydrocarbon
reservoir consist of bathymetric surveys carried out before and at the end of a 10-yr
production life. The main goal is the calibration of the reservoir compressibility cM, that is,
the main geomechanical parameter controlling the surface response. Two conceptual models
are considered: in one (i) cM varies only with the depth and the vertical effective stress
(heterogeneity due to lithostratigraphic variability); in another (ii) cM varies also in the horizontal
plane, that is, it is spatially distributed within the reservoir stratigraphic units. The latter
hypothesis accounts for a possible partitioning of the reservoir due to the presence of sealing
faults and thrusts that suggests the idea of a block heterogeneous system with the number of
reservoir blocks equal to the number of uncertain parameters. The method applied here relies
on an ensemble-based data assimilation (DA) algorithm (i.e. the ensemble smoother, ES),
which incorporates the information from the bathymetric measurements into the geomechanical
model response to infer and reduce the uncertainty of the parameter cM. The outcome from
conceptual model (i) indicates that DA is effective in reducing the cM uncertainty. However,
the maximum settlement still remains underestimated, while the areal extent of the subsidence
bowl is overestimated. We demonstrate that the selection of the heterogeneous conceptual
model (ii) allows to reproduce much better the observations thus removing a clear bias of
the model structure. DA allows significantly reducing the cM uncertainty in the five blocks
(out of the seven) characterized by large volume and large pressure decline. Conversely, the
assimilation of land displacements only partially constrains the prior cM uncertainty in the
reservoir blocks marginally contributing to the cumulative seafloor subsidence, that is, blocks
with low pressure
Spin Dynamics of the One-Dimensional J-J' Model and Spin-Peierls Transition in CuGeO_3
Spin dynamics as well as static properties of the one-dimensional J-J' model
(S=1/2, J>0 and 0\le \alpha=J'/J\le 0.5) are studied by the exact
diagonalization and the recursion method of finite systems up to 26 sites.
Especially, the dynamical structure factor S(q,\omega) is investigated
carefully for various values of \alpha. As \alpha increases beyond the
gapless-gapful critical value \alpha_c=0.2411, there appear features definitely
different from the Heisenberg model but the same with the Majumdar-Ghosh model.
Some of these features depend only on the value of \alpha and not on \delta: a
parameter introduced for the coupling alternation. By comparing these results
with a recent inelastic neutron scattering spectrum of an inorganic
spin-Peierls compound CuGeO_3 [M. Arai et al.: Phys. Rev. Lett. 77 (1996)
3649], it is found that the frustration by J' in CuGeO_3 is unexpectedly strong
(\alpha=0.4-0.45), and at least \alpha must be larger than \alpha_c to some
extent. The value of J is evaluated at \sim 180K consistent with other
estimations. The coupling alternation is extremely small. This large
frustration is a primary origin of the various anomalous properties CuGeO_3
possesses. For comparison we refer also to \alpha'-NaV_2O_5.Comment: 14 pages. A hard copy of 20 figures is available on request. To be
published in J. Phys. Soc. Jpn. Vol. 66 No. 11 (1997
Strong anisotropy of superexchange in the copper-oxygen chains of La_{14-x}Ca_{x}Cu_{24}O_{41}
Electron spin resonance data of Cu^{2+} ions in La_{14-x}Ca_{x}Cu_{24}O_{41}
crystals (x=9,11,12) reveal a very large width of the resonance line in the
paramagnetic state. This signals an unusually strong anisotropy of ~10% of the
isotropic Heisenberg superexchange in the Cu-O chains of this compound. The
strong anisotropy can be explained by the specific geometry of two symmetrical
90 degree Cu-O-Cu bonds, which boosts the importance of orbital degrees of
freedom. Our data show the apparent limitations of the applicability of an
isotropic Heisenberg model to the low dimensional cuprates.Comment: 14 pages, 3 figures included, to be published in Phys. Rev. Let
Electronic States and Magnetic Propertis of Edge-sharing Cu-O Chains
The electronic states and magnetic properties for the copper oxides
containing edge-sharing Cu-O chains such as LiCuO,
LaCaCuO and CuGeO are systematically studied. The
optical conductivity and the temperature dependence of the
magnetic susceptibility for single crystalline samples LiCuO
are measured as a reference system and analyzed by using the exact
diagonalization method for small Cu-O clusters. It is shown that the spectral
distribution of is different between edge-sharing and
corner-sharing Cu-O-Cu bonds. The charge transfer gap in edge-sharing chains is
larger than that of high- cuprates. The exchange interaction between
nearest-neighbor copper ions in edge-sharing chains depends sensitively
on the Cu-O-Cu bond angles. In addition to , the exchange interaction
between next-nearest-neighbor copper ions has sufficient contribution to
the magnetic properties. We calculate and for all the copper oxides
containing edge-sharing Cu-O chains and discuss the magnetic properties.Comment: 10 pages,RevTeX,8 postscript figures. Accepted for publication in
Phys. Rev.
Quantum lattice fluctuations in a frustrated Heisenberg spin-Peierls chain
As a simple model for spin-Peierls systems we study a frustrated Heisenberg
chain coupled to optical phonons. In view of the anorganic spin-Peierls
compound CuGeO3 we consider two different mechanisms of spin-phonon coupling.
Combining variational concepts in the adiabatic regime and perturbation theory
in the anti-adiabatic regime we derive effective spin Hamiltonians which cover
the dynamical effect of phonons in an approximate way. Ground-state phase
diagrams of these models are determined, and the effect of frustration is
discussed. Comparing the properties of the ground state and of low-lying
excitations with exact diagonalization data for the full quantum spin phonon
models, good agreement is found especially in the anti-adiabatic regime.Comment: 9 pages, 7 figures included, submitted to Phys. Rev.
Electronic structure and magnetic properties of the linear chain cuprates Sr_2CuO_3 and Ca_2CuO_3
Sr_2CuO_3 and Ca_2CuO_3 are considered to be model systems of strongly
anisotropic, spin-1/2 Heisenberg antiferromagnets. We report on the basis of a
band-structure analysis within the local density approximation and on the basis
of available experimental data a careful analysis of model parameters for
extended Hubbard and Heisenberg models. Both insulating compounds show
half-filled nearly one-dimensional antibonding bands within the LDA. That
indicates the importance of strong on-site correlation effects. The bonding
bands of Ca_2CuO_3 are shifted downwards by 0.7 eV compared with Sr_2CuO_3,
pointing to different Madelung fields and different on-site energies within the
standard pd-model. Both compounds differ also significantly in the magnitude of
the inter-chain dispersion along the crystallographical a-direction: \approx
100 meV and 250 meV, respectively. Using the band-structure and experimental
data we parameterize a one-band extended Hubbard model for both materials which
can be further mapped onto an anisotropic Heisenberg model. From the
inter-chain dispersion we estimate a corresponding inter-chain exchange
constant J_{\perp} \approx 0.8 and 3.6 meV for Sr_2CuO_3 and Ca_2CuO_3,
respectively. Comparing several approaches to anisotropic Heisenberg problems,
namely the random phase spin wave approximation and modern versions of coupled
quantum spin chains approaches, we observe the advantage of the latter in the
reproduction of reasonable values for the N\'eel temperature T_N and the
magnetization m_0 at zero temperature. Our estimate of gives the
right order of magnitude and the correct tendency going from Sr_2CuO_3 to
Ca_2CuO_3. In a comparative study we also include CuGeO_3.Comment: 23 pages, 5 figures, 1 tabl
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