Thermodynamic properties of the Haldane spin chain: a statistical model for the elementary excitations

Regnault, L.P.; Zaliznyak, Igor; Meshkov, S. V.

doi:10.1088/0953-8984/5/50/004

Cited by 34 publications

(33 citation statements)

References 14 publications

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“…19,73 Equation ͑13a͒ predicts a critical field of H c Ϸ⌬/g B . Obviously, nonlinear effects should take place near H c , in particular to account for the fact that g B H c is about 16% smaller than ⌬.…”

Section: Neutron Scattering Under Fieldmentioning

confidence: 99%

Inelastic-neutron-scattering investigation of the spin-Peierls system CuGeO3

Regnault¹,

et al. 1996

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We have investigated the spin dynamics of the spin-Peierls system CuGeO 3 by inelastic neutron scattering. The measurements have been performed as a function of wave vector, temperature, and magnetic field, for fields perpendicular to the chain axis ͑up to 10 T͒. Our neutron results confirm the occurrence of a crystalline distortion below T SP Ϸ14.2 K, corroborated by the appearance of superlattice peaks indexed with a commensurate wave vector k SP ϭ͑ 1 2 ,0, 1 2 ͒. At low temperature, the spin-excitation spectrum exhibits a well defined energy gap ⌬Ϸ2 meVϷ1.66 kT SP at the antiferromagnetic point k AF ϭ͑0,1, 1 2 ͒, distinct from k SP . The experimental results for TӶT SP are quantitatively understood from an alternating-exchange Hamiltonian with an exchange parameter ͑2J 1 ͒Ϸ10.6 meV and an alternation parameter ␣ϭJ 2 /J 1 Ϸ0.92, despite the existence of sizable interchain couplings both along the a and b axes ͑J a Ј/J 1 Ϸ0.011 and J b Ј/J 1 Ϸ0.11, respectively͒. We present the temperature dependence of the spin dynamics on both sides of T SP . Our results confirm the persistence of a pseudogap in the excitation spectrum for qϭk AF , but only in the immediate vicinity of the spin-Peierls transition temperature. The pseudogap vanishes rapidly with T, following decreasing size of dimerized segments. The stronger inelasticity observed above T SP at qϭk SP has been attributed to an effect of the dispersion of magnetic excitations due to interchain couplings J a Ј and J b Ј . Under a magnetic field applied perpendicular to the chain axis, the excited triplet is split into three components, with gap values depending linearly on the field. The spin-Peierls transition temperature T SP decreases with increasing field, following a quadratic dependence on H, in agreement with theoretical as well as other experimental results. We have determined the field dependence of the dimerization peak intensities up to 10 T, which show very small changes. In particular, no trace of pretransitional incommensurability could be detected, at least up to 0.77H c .where J is the average exchange value [Jϭ(J 1 ϩJ 2 )/2]. In the most general case, ␦ should be a function of displacement vectors ␦ i associated with the various atomic entities involved in the intrachain exchange paths. Moreover, in the SP problem J, ␣, and ␦ must depend on temperature to account for the inherent lattice effects. The simple expression ␦ϭ͑1 Ϫ␣͒/͑1ϩ␣͒ relates the alternation ␣ and distortion ␦.As for the magnetic excitation spectrum of an alternating chain, it is expected for a SP system that a gap ⌬ ͑function of J 1 and ␣ or, equivalently, J and ␦͒ opens at the antiferromagnetic point k AF between a nonmagnetic singlet ͑Sϭ0͒ ground state and the ''continuum'' of lowest-excited triplet ͑Sϭ1͒ states. 9-11 k AF is frequently defined as the point ''qϭ'' in the literature. The reduced gap ⌬/2J 1 has been calculated numerically 9-13 for an alternating chain as a function of the alternation parameter ␣. For not too large values of 1Ϫ␣, this ratio is given by the simple p...

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Section: Neutron Scattering Under Fieldmentioning

confidence: 99%

Inelastic-neutron-scattering investigation of the spin-Peierls system CuGeO3

Regnault¹,

et al. 1996

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“…In Heisenberg exchange approximation the critical field value H c and the energy gap ∆ are related by a simple relation gµ B µ 0 H c = ∆. The influence of the single-ion anisotropy on the Haldane spin chains was analysed theoretically by the exact diagonalization for finite chains, 4 by a perturbative approach, 4,5 as well as by macroscopic field theory methods. 6 In the magnetic field range far below H c all models result in the same energy levels, parametrized by the main gap, one or two anisotropy constants and g-factor.…”

Section: Introductionmentioning

confidence: 99%

Triplet spin resonance of the Haldane magnetPbNi2V2O8with interchain coupling

et al. 2008

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Spin resonance absorption of the triplet excitations is studied experimentally in the Haldane magnet PbNi2V2O8. The spectrum has features of spin S = 1 resonance in a crystal field, with all three components, corresponding to transitions | ± 1 ⇆ |0 and | − 1 ⇆ |1 , being observable. The resonance field is temperature dependent, indicating the renormalization of excitation spectrum in interaction between the triplets. Magnetic resonance frequencies and critical fields of the magnetization curve are consistent with a boson version of the macroscopic field theory, 6,10 implying the field induced ordering at the critical field, while contradict the previously used approach of noninteracting spin chains.

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“…As the alternation parameter δ = (J 1 − J 2 )/(J 1 + J 2 ) deviates from zero (uniform chain), the energy gap ∆ decreases and closes at some critical value |δ| = δ c ≈ 0. 26,5,6,7,8,9,10,11 as illustrated in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Distribution of exchange energy in a bond-alternatingS=1quantum spin chain

et al. 2004

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The quasi-one-dimensional bond-alternating S = 1 quantum antiferromagnet [Ni(N, N ′ -bis(3-aminopropyl)propane-1,3-diamine(µ-NO2)]ClO4 (NTENP) is studied by single crystal inelastic neutron scattering. Parameters of the measured dispersion relation for magnetic excitations are compared to existing numerical results and used to determine the magnitude of bond-strength alternation. The measured neutron scattering intensities are also analyzed using the 1st-moment sum rules for the magnetic dynamic structure factor, to directly determine the modulation of ground state exchange energies. These independently determined modulation parameters characterize the level of spin dimerization in NTENP. First-principle DMRG calculations are used to study the relation between these two quantities.

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Thermodynamic properties of the Haldane spin chain: a statistical model for the elementary excitations

Cited by 34 publications

References 14 publications

Inelastic-neutron-scattering investigation of the spin-Peierls system CuGeO3

Inelastic-neutron-scattering investigation of the spin-Peierls system CuGeO3

Triplet spin resonance of the Haldane magnetPbNi2V2O8with interchain coupling

Distribution of exchange energy in a bond-alternatingS=1quantum spin chain

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