We investigate the elementary excitations of quasi-one-dimensional S = ½ systems built up from zigzag chains with general isotropic exchange constants, using exact (Lanczos) diagonalization for 24 spins and series expansions starting from the decoupled dimer limit. For the ideal one-dimensional zigzag chain we discuss the systematic variation of the basic (magnon) triplet excitation with general exchange parameters and in particular the presence of practically flat dispersions in certain regions of phase space. We extend the dimer expansion in order to include the effects of three-dimensional interactions on the spectra of weakly interacting zigzag chains. In an application to KCuCl 3 we show that this approach allows us to determine the exchange interactions between individual pairs of spins from the spectra as determined in recent neutron scattering experiments.
We investigate the elementary excitations of quasi-one-dimensional S = ½ systems built up from zigzag chains with general isotropic exchange constants, using exact (Lanczos) diagonalization for 24 spins and series expansions starting from the decoupled dimer limit. For the ideal one-dimensional zigzag chain we discuss the systematic variation of the basic (magnon) triplet excitation with general exchange parameters and in particular the presence of practically flat dispersions in certain regions of phase space. We extend the dimer expansion in order to include the effects of three-dimensional interactions on the spectra of weakly interacting zigzag chains. In an application to KCuCl 3 we show that this approach allows us to determine the exchange interactions between individual pairs of spins from the spectra as determined in recent neutron scattering experiments.
The subject of the present work are dimerized spin 1/2 systems in one, two and three dimensions.The models are investigated perturbatively by means of cluster expansion.This method makes it possible to study systems even in two and three dimension up to high orders.Starting with a generic HAMILTON-Operator which includes both bilinear and biquadratic interaction terms, the groundstate energies and the low lying excitations of the alternating spin chain und the spin ladder are calculated.Well-known results from BETHE ansatz and bosonization are used to verify the series.Based on this model, two speci£c one-dimensional problems are investigated in more detail: the £rst one is the incommensurate regime of the generalized spin ladder, which was previously analyzed by other approximation techniques.This regime is characterized by a minimum of the dispersion between 0 and π.The second problem deals with a quantum phase transition in the spin ladder with additional cyclic four-spin interaction (ring exchange).The excitation gap which is always present in the regular spin ladder can be reduced by taking the ring exchange into account.Within the region which is accessible by perturbation theory a transition line is presented on which the gap vanishes.For further characterization of the phase transition critical exponents are calculated which give a connection between exchange strength and gap size.Within the range of the higher-dimensional spin dimer systems the compounds KCuCl 3 , TlCuCl 3 (3d) and (C 4 H 12 N 2 )Cu 2 Cl 6 (2d) are studied.To clarify the microscopic interactions, dispersion relations which take all reasonable (i.e.evident from the chemical structure) interactions into account are computed.In the case of KCuCl 3 and TlCuCl 3 there are nine and in the case of (C 4 H 12 N 2 )Cu 2 Cl 6 there are ten spin spin interactions considered.The strength of the exchange parameters is determined by comparison with inelastic neutron scattering data.For the above-mentioned substances the interaction constants are evaluated to match the dispersion relation with the experimental data to a high accuracy.Finally, the dynamical structure factor which is limited to the singlet-triplet transition is calculated perturbatively for the compounds KCuCl 3 and TlCuCl 3 .Since it is proportional to the differential cross section, one is able to establish a relationship to inelastic neutron scattering experiments.
We discuss the transition strength between the disordered ground state and the basic low-lying triplet excitation for interacting dimer materials by presenting theoretical calculations and series expansions as well as inelastic neutron scattering results for the material KCuCl 3 . We describe in detail the features resulting from the presence of two differently oriented dimers per unit cell and show how energies and spectral weights of the resulting two modes are related to each other. We present results from the perturbation expansion in the interdimer interaction strength and thus demonstrate that the wavevector dependence of the simple dimer approximation is modified in higher orders. Explicit results are given in tenth order for dimers coupled in 1D, and in second order for dimers coupled in 3D with application to KCuCl 3 and TlCuCl 3 .
Various static spin-correlation functions and the weights of the spin excitations, or collective normal modes, in the van Hove response function, observed in neutron scattering experiments, are calculated as a function of temperature for a model quantum-spin chain. The spins interact through an isotropic Heisenberg exchange that extends to nearest-neighbour spins. In our model, spins of magnitude 1/2 form a dimerized chain with alternating exchange interactions. We explore the static and dynamic properties for ferromagnetic and antiferromagnetic exchange interactions. Results for the various properties are shown to be exact in the limit of a high temperature, and we argue that the results are very good at low temperatures. Unlike the case for linear spin-wave theory, the results are also exact in the limit of strong dimerization, i.e. non-interacting coupled pairs of spins.
In this work diverse results obtained from a number of low-dimensional quantum spin systems using Raman spectroscopy have been presented. The main motivation of this thesis is to hunt for new types of elementary excitations which may be present in low-dimensional spin systems with exotic spin topology. The studied systems can be on the one hand characterized by the formation of spin dimers which originate from a special spin topology like ACuCl3 (A=Tl, K), LiCu2O2, and SrCu(BO3)2. On the other hand, the system such as K2V3O8 and Cu2Te2O5X2 (X=Br,Cl) is dominated by quantum fluctuations due to reduced dimensionalilty. A powerful tool for studying low-dimensional spin systems is Raman spectroscopy which is sensitive to nearly all possible types of collective excitations as well as the interplay among them. In particular, magnetic light scattering can provide information about exchange paths and coupling constants, spinon excitations, spin gaps, and triplet-triplet interactions. The main results are summarized as follows; (i) the observation of a coherent coexistence of long-rang order and dimerized state in the frustrated spin chain system LiCu2O2, (ii) the presence of three-magnon scattering and dynamic spin-phonon coupling in the three-dimensional coupled spin dimer systems ACuCl3 (A=Tl, K), (iii) anomalous low-energy excitations including two-magnon scattering and electronic/orbital excitations in the two-dimensional Heisenberg antiferromagnetic system K2V3O8, (iv) the observation of inter-plane soft mode and a coupling of spin to soft mode in the quasi two-dimensional orthogonal dimer system SrCu(BO3)2, and (v) the existence of longitudinal magnons in the spin tetrahedra system Cu2Te2O5X2 (X=Br,Cl).
A full description of a series of spin-wave measurements in CsNiCl3 in the three-dimensional (3D) and one-dimensional (1D) phases and their analysis to provide the first experimental evidence for the Haldane gap is presented. Neutron scattering experiments were performed on a single crystal of CsNiCl3 with both (h,0,l) and (h,h,l) as the scattering plane. The order parameter in both 3D phases was measured and the spin-wave dispersion determined in the lower phase. The spin-wave spectrum calculated from a dynamic susceptibility method was compared with the experimental response in the lower 3D phase to obtain the following values for the exchange and anisotropy constants: J=0.345\ifmmode\pm\else\textpm\fi{}0.008 THz, J'=0.0060\ifmmode\pm\else\textpm\fi{}0.005 THz, and D=-0.0130\ifmmode\pm\else\textpm\fi{}0.0015 THz. These parameters confirm that CsNiCl3 in its disordered phase is a good approximation to a one-dimensional Heisenberg antiferromagnet. In the 1D phase the gap frequency for an isolated chain of Ni2+ ions is found to be 0.32 THz close to the gap estimated in finite-chain calculations. The results constitute experimental support for the Haldane conjecture that the excitations of integer-spin chains, unlike half-integer--spin chains, exhibit an apparent anisotropy that arises not from the underlying isotropic Hamiltonian, but from many-body effects.
We study the spin-1/2 Heisenberg chain with alternating nearest neighbor interactions ${J}_{1}(1+\ensuremath{\delta})$ and ${J}_{1}(1\ensuremath{-}\ensuremath{\delta})$ and a uniform second neighbor interaction ${J}_{2}=y(1\ensuremath{-}\ensuremath{\delta})$ by series expansions around the limit of decoupled dimers $(\ensuremath{\delta}=1).$ By extrapolating to $\ensuremath{\delta}=0$ and tuning y, we study the critical point separating the power-law and spontaneously dimerized phases of the spin-1/2 antiferromagnet. We then focus on the disorder line y=0.5, $0<~\ensuremath{\delta}<~1,$ where the ground states are known exactly. We calculate the triplet excitation spectrum, their spectral weights, and wave vector dependent static susceptibility along this line. It is well known that as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\delta}}0,$ the spin gap is still nonzero but the triplets are replaced by spinons as the elementary excitations. We study this dynamical transition by analyzing the series for the spectral weight and the static susceptibility. In particular, we show that the spectral weight for the triplets vanishes and the static spin susceptibility changes from a simple pole at imaginary wave vectors to a branch cut at the transition.