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arXiv:cond-mat/0510487 · Physical Review Letters

Quantum Statistics of Interacting Dimer Spin Systems

Christian Rüegg, Bruce Normand, M. Matsumoto, Ch. Niedermayer, A. Fürrer, Karl W. Krämer, H. U. Güdel, P. Bourges, Y. Sidis, H. Mutka

Published Dec 19, 2005• 50 citations
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Abstract

The compound TlCuCl(3) represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Würtz [Phys. Rev. B 50, 13 515 (1994)10.1103/Phys. Rev. B 50, 13515] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important.

DOI
10.1103/physrevlett.95.267201

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The compound TlCuCl(3) represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Würtz [Phys. Rev. B 50, 13 515 (1994)10.1103/Phys. Rev. B 50, 13515] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important.
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 .
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.
Dimerized magnets forming alternating Heisenberg chains exhibit quantum coherence and entanglement and thus can find potential applications in quantum information and computation. However, magnetic systems typically undergo thermal decoherence at finite temperatures. Here, we show inelastic neutron scattering results on an alternating antiferromagnetic-ferromagnetic chain compound Na2Cu2TeO6{\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}Na2​Cu2​TeO6​ that the excited quasiparticles can counter thermal decoherence and maintain strong correlations at elevated temperatures. At low temperatures, we observe clear dispersive singlet-triplet excitations arising from the dimers formed along the crystalline bbb axis. The excitation gap is of $\ensuremath{\sim}18\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ and the bandwidth is about half of the gap. The band top energy has a weak modulation along the [100] direction, indicative of a small interchain coupling. The gap increases while the bandwidth decreases with increasing temperature, leading to a strong reduction in the available phase space for the triplons. As a result, the Lorentzian-type energy broadening becomes highly asymmetric as the temperature is raised. These results are associated with a strongly correlated state resulting from hard-core constraint and quasiparticle interactions. We consider these results to be not only evidence for strong correlations at finite temperatures in Na2Cu2TeO6{\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}Na2​Cu2​TeO6​, but also for the universality of the strongly correlated state in a broad range of quantum magnetic systems.
Quasi-one-dimensional magnetic materials provide important test beds for rigorous models of interacting many-body systems. Nevertheless, there have been few studies of finite temperature effects on spin correlations in low-spin systems, though these are most likely to exhibit quantum effects. Copper benzoate, Cu(C6D5COO)2⋅3D2O, is a good realization of the S=1/2 Heisenberg antiferromagnetic chain (HAFC). We have performed ac susceptibility and inelastic neutron scattering experiments on this material which establish the Hamiltonian and an excitation spectrum which is consistent with the spinon continuum ansatz of Müller et al. We present inelastic neutron scattering measurements of the temperature evolution of the dynamic spin–spin correlation function Szz(π,ω). Comparison will be made to the classical prediction and to a finite temperature field theory of Schulz as applied to this S=1/2 HAFC.
The authors study spin-triplet excitations in the strongly correlated spin-1/2 dimer system Sr3{}_{3}3​Cr2{}_{2}2​O8{}_{8}8​ via inelastic neutron scattering. They find that the thermal broadening of the excitations can be accurately described by going beyond RPA via diagrammatic high-density 1/z1/z1/z expansion.