The magnetic susceptibility and specific heat of the one-dimensional S = 1 bilinear-biquadratic Heisenberg model are calculated using the transfer matrix renormalization group. By comparing the results with the experimental data of LiVGe2O6 measured by Millet et al. [Phys. Rev. Lett. 83, 4176 (1999)], we find that the susceptibility data of this material, after subtracting the impurity contribution, can be quantitatively explained with this model. The biquadratic exchange interaction in this material is found to be ferromagnetic, i.e., with a positive coupling constant.
The spin-Peierls transition at
TSP of spin-
21 chains with isotropic exchange interactions has previously been modeled as correlated for
T>TSP and mean field for
T<TSP. We use correlated states throughout in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model with antiferromagnetic exchange
J1 and ${J}_{2}=\ensuremath{\alpha}{J}_{1}$ between first and second neighbors, respectively, and variable frustration $0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}0.50$. The thermodynamic limit is reached at high
T by exact diagonalization of short chains and at low
T by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter
TSP yields both the stiffness and the lattice dimerization $\ensuremath{\delta}(T)$. The relation between
TSP and $\mathrm{\ensuremath{\Delta}}(\ensuremath{\delta},\ensuremath{\alpha})$, the
T=0 gap induced by dimerization, depends strongly on $\ensuremath{\alpha}$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-
CuS4C4(CF3)4 crystals (
J1=79K, $\ensuremath{\alpha}=0$,
TSP=12K) and
CuGeO3 crystals (
J1=160K, $\ensuremath{\alpha}=0.35$,
TSP=14K). The same parameters describe the specific heat anomaly of
CuGeO3 and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $\ensuremath{\delta}(0)$ limits the range of spin correlations at
T=0 while
T>0 limits the range at $\ensuremath{\delta}=0$.
Magnetic susceptibility is measured on the one-dimensional spin 1/2 antiferromagnets
Sr2CuO3 and
SrCuO2 using single crystals. Large, nearly contamination-free single crystals enable us to measure the intrinsic spin susceptibility over a wide temperature range between 5 and 800 K. The results are in excellent agreement with the recent calculation by Eggert, Affleck, and Takahashi, and the exchange interaction energy
J is estimated to be $2200\ifmmode\pm\else\textpm\fi{}200$ and $2100\ifmmode\pm\else\textpm\fi{}200\mathrm{K}$, respectively. In
Sr2CuO3, an isotropic susceptibility drop is observed below about 20 K, which is also consistent with the result of this rigorous calculation.
Various forms of antiferromagnetic exchange interaction among quantized spins in one-dimensional and quasi-one-dimensional lattices are examined. Primary results are reported in two real compounds, the sodium vanadate NaV2O5 and the copper germanate CuGeO3, and in a class of compounds of real materials modeled as dimerized antiferromagnetically coupled spin-1/2 chains susceptible to spin-1 impurity doping and that include such examples as the strontium cuprate Sr14Cu24O41 and vanadium pyrophosphate (VO)2P2O7. Sodium vanadate, NaV2O5, a quarter-filled two-leg ladder compound that was originally thought to be composed of magnetic legs and nonmagnetic legs was subsequently shown to be a charge ordered system below room temperature. Initial models of the material as isolated antiferromagnetically coupled spin-1/2 chains can be mapped to the subsequently resolved magnetic system of the charge ordered state with the spins on molecular orbitals of V-O-V rungs antiferromagentically coupled between neighboring rungs either on the same ladder or on neighboring ladders. Comparing the model's dynamic structure factor to inelastic neutron scattering data could distinguish between the proposed spin coupling schemes and consequently reveal the details of the interaction between the lattice and the "zig-zag" charge density as well as the magnetic stabilization of the low temperature phase. Copper germanate, the first and only known inorganic spin-Peierls compound, exhibits a strong temperature dependent exchange coupling pattern among the spin-1/2 Cu2+ chains. Above the spin-Peierls transition temperature an unmodulated antiferromagnetic nearest neighbor exchange interaction J1 competes with an antiferromagnetic next nearest neighbor interaction J2. The next nearest neighbor exchange represents an effective coupling equivalent to the net effect of all longer range exchange interactions. This frustration to the nearest neighbor spin exchange produces a distinctive magnetic susceptibility χ (T) much different from the Bonner-Fisher susceptibility of the spin-1/2 Heisenberg chain with nearest neighbor antiferromagnetic exchange only. The ratio of the second to first nearest neighbor couplings α = J2/J1 ≈ 0.36 is sufficient to open a spontaneous gap in the spin-wave excitation spectrum at low temperatures. Below TSP = 14K, the dynamical structure factor is used to fit the dimerization δ and the exchange interactions J1 and J2 to the inelastic neutron scattering data of CuGeO3 at T = 10K. It is found that both δ and α increase significantly at lower temperatures, relative to the values obtained in the high temperature phase and at the onset of dimeration at 14 K. Static structure factor calculations how Scattering inconsistent with the δâJ1âJ2 model and can be attributed primarily to the phonon degrees of freedom but possibly also to the couplings between chains in the b and a directions of the crystal lattice. Structurally dimerized compounds of antiferromagnetic spin-1/2 chains possess dynamic structure factor and magnetic susceptibility features that are very sensitive to doping with magnetic and nonmagnetic impurities. It is shown that the effects of spin-1 impurities are very similar to those of nonmagnetic (S = 0) impurities if the coupling between impurity and native spin is about the same magnitude as or larger than between native S = 1/2 spins. The microscopic origins of the similarity can be appreciated with the consideration that neighboring spins to the impurity find it more energetically favorable to couple to the impurity than the other spins of the lattice. Thus the spin-1 impurity and its neighboring S = 1/2 spins decouple from the lattice, creating a nonmagnetic break in the chain. The spins that now observe a nonmagnetic cluster on one side can couple to the S = 1/2 spins on the other side with a higher AF correlation than in the pure compound since they do not have to have a ï¬uctuating dimer resonating between two neighbors. Such enhancements to the local correlations can stabilize the global AF order in one dimensional compounds as shown in theoretical and experimental studies of CuGeO3. ED calculations of the dynamic structure factor show that S(q, ω) developes states with ω = 0 in the gap at q = π. Magnetic susceptibilites in the presense of spin-1 impurities were obtained for 80 site chains by QMC simulations and for 16 site chains by ED calculations. An impurity concentration-dependent second peak in the low temperature region reveals an increasing second maximum with T as observed in doped copper germanates and suggests that the results of the study are applicable even to phonon mediated dimerization. This is not immediately apparent because spin-phonon coupling could distort the dimerization patterns. However, experimental and theoretical results show that elastic coupling between chains can stabilize the dimerization pattern due to the impurities and the results will still apply.
In the present work we aim to characterize the lattice configurations and the magnetic behavior in the incommensurate phase of spin-Peierls systems. This phase emerges when the magnetic exchange interaction is coupled to the distortions of an underlying triangular lattice and has its experimental realization in the quasi-one-dimensional compound family TiO
X (
X=Cl, Br). With a simple model of spin-
1/2 chains inserted in a planar triangular geometry which couples them elastically, we are able to obtain the uniform-incommensurate and incommensurate-dimerized phase transitions seen in these compounds. Moreover, we follow the evolution of the wave vector of the distortions with temperature inside the incommensurate phase. Finally, we predict gapless spin excitations for the intermediate phase of TiO
X compounds along with incommensurate spin-spin correlations, offering to experimentalists a candidate to observe an exotic Luttinger liquidlike behavior.
We study the spin-Peierls (SP) transition of one-dimensional chain polymeric complexes coupled to lattice by means of many-body Green's function theory. The chain effective elastic constant is an intrinsic factor that determines the order of SP transition. It is found that the SP transition temperature T(SP) and the susceptibility-maximum temperature T(max) are in agreement with the experimental results. When an external magnetic field is applied to the chain, it makes T(SP) and T(max) decrease, and drives the SP transition from the second order to the first order. Besides, we show that the two-site thermal entanglement entropy is a good indicator of SP transition. Further considering the effect of interchain coupling on SP transition, with weak coupling of double-chain, the theoretical values are closer to the experimental results. We also calculate the density of states and spectral functions, which show that the energy gap vanishes at a critical temperature lower than T(SP), indicating a gapless SP phase lies in the gapped dimerized phase. The interchain coupling can drive the SP transition from the second order to the first order, while the SP dimerization may collapse for large interchain couplings.