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

Finite Temperature DMRG Investigation of the Spin-Peierls Transition in CuGeO3_3

We present a numerical study of thermodynamical properties of dimerized frustrated Heisenberg chains down to extremely low temperatures with applications to CuGeO$_3$. 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$_3$ such as magnetic dimerization, critical temperature, susceptibility and entropy.Comment: LaTeX, 5 pages, 5 eps figures include

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

Elementary excitations, exchange interaction and spin-Peierls transition in CuGeO3_3

The microscopic description of the spin-Peierls transition in pure and doped CuGeO_3 is developed taking into account realistic details of crystal structure. It it shown that the presence of side-groups (here Ge) strongly influences superexchange along Cu-O-Cu path, making it antiferromagnetic. Nearest-neighbour and next-nearest neighbour exchange constants $J_{nn}$ and $J_{nnn}$ are calculated. Si doping effectively segments the CuO_2-chains leading to $J_{nn}(Si)\simeq0$ or even slightly ferromagnetic. Strong sensitivity of the exchange constants to Cu-O-Cu and (Cu-O-Cu)-Ge angles may be responsible for the spin-Peierls transition itself (``bond-bending mechanism'' of the transition). The nature of excitations in the isolated and coupled spin-Peierls chains is studied and it is shown that topological excitations (solitons) play crucial role. Such solitons appear in particular in doped systems (Cu_{1-x}Zn_xGeO_3, CuGe_{1-x}Si_xO_3) which can explain the $T_{SP}(x)$ phase diagram.Comment: 7 pages, revtex, 7 Postscript figure

Triplet Dispersion in CuGeO_3: Perturbative Analysis

We reconsider the 2d model for CuGeO_3 introduced previously (Phys. Rev. Lett. 79, 163 (1997)). Using a computer aided perturbation method based on flow equations we expand the 1-triplet dispersion up to 10th order. The expansion is provided as a polynom in the model parameters. The latter are fixed by fitting the theoretical result to experimental data obtained by INS. For a dimerization delta = 0.08(1) we find an excellent agreement with experiment. This value is at least 2 to 3 times higher than values deduced previously from 1d chain approaches. For the intrachain frustration alpha_0 we find a smaller value of 0.25(3). The existence of interchain frustration conjectured previously is confirmed by the analysis of temperature dependent susceptibility.Comment: 8 pages, 10 figures, submitted to Phys. Rev.

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

Anisotropic Superexchange for nearest and next nearest coppers in chain, ladder and lamellar cuprates

We present a detailed calculation of the magnetic couplings between nearest-neighbor and next-nearest-neighbor coppers in the edge-sharing geometry, ubiquitous in many cuprates. In this geometry, the interaction between nearest neighbor coppers is mediated via two oxygens, and the Cu-O-Cu angle is close to 90 degrees. The derivation is based on a perturbation expansion of a general Hubbard Hamiltonian, and produces numerical estimates for the various magnetic energies. In particular we find the dependence of the anisotropy energies on the angular deviation away from the 90 degrees geometry of the Cu-O-Cu bonds. Our results are required for the correct analysis of the magnetic structure of various chain, ladder and lamellar cuprates.Comment: 13 pages, Latex, 7 figure

The microscopic spin-phonon coupling constants in CuGeO_3

Using RPA results, mean field theory, and refined data for the polarization vectors we determine the coupling constants of the four Peierls-active phonon modes to the spin chains of CuGeO_3. We then derive the values of the coupling of the spin system to the linear ionic displacements, the bond lengths and the angles between bonds. Our values are consistent with microscopic theories and various experimental results. We discuss the applicability of static approaches to the spin-phonon coupling. The c-axis anomaly of the thermal expansion is explained. We give the values of the coupling constants in an effective one-dimensional Hamiltonian.Comment: 11 pages, two figures, 13 tables, PRB 59 (in press

Magnetic Excitations in quasi two-dimensional Spin-Peierls Systems

A study is presented of a two-dimensional frustrated and dimerized quantum spin-system which models the effect of inter-chain coupling in a spin-Peierls compound. Employing a bond-boson method to account for quantum disorder in the ground state the elementary excitations are evaluated in terms of gapful triplet modes. Results for the ground state energy and the spin gap are discussed. The triplet dispersion is found to be in excellent agreement with inelastic neutron scattering data in the dimerized phase of the spin-Peierls compound CuGeO_3. Moreover, consistent with these neutron scattering experiments, the low-temperature dynamic structure factor exhibits a high-energy continuum split off from the elementary triplet mode.Comment: 8 pages, Revtex, 8 eps-figure

Field-induced structural evolution in the spin-Peierls compound CuGeO3_3: high-field ESR study

The dimerized-incommensurate phase transition in the spin-Peierls compound CuGeO$_3$ is probed using multifrequency high-resolution electron spin resonance (ESR) technique, in magnetic fields up to 17 T. A field-induced development of the soliton-like incommensurate superstructure is clearly indicated as a pronounced increase of the ESR linewidth $\Delta B$ (magnon excitations), with a $\Delta B_{max}$ at $B_{c}\sim$ 13.8 T. The anomaly is explained in terms of the magnon-soliton scattering, and suggests that the soliton-like phase exists close to the boundary of the dimerized-incommensurate phase transition. In addition, magnetic excitation spectra in 0.8% Si-doped CuGeO$_3$ are studied. Suppression of the $\Delta B$ anomaly observed in the doped samples suggests a collapse of the long-range-ordered soliton states upon doping, that is consistent with high-field neutron scattering experiments.Comment: Accepted to Phys. Rev.