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arXiv:cond-mat/0410487 · Journal of Statistical Mechanics Theory and Experiment

Haldane-gap chains in a magnetic field

Fabian H. L. Eßler, Ian K. Affleck

Published Dec 18, 2004• 23 citations
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Abstract

We consider quasi-one-dimensional spin-1 Heisenberg chains with crystal field anisotropy in a uniform magnetic field. We determine the dynamical structure factor in various limits and obtain a fairly complete qualitative picture of how it changes with the applied field. In particular, we discuss how the width of the higher energy single magnon modes depends on the field. We consider the effects of a weak interchain coupling. We discuss the relevance of our results for recent neutron scattering experiments on the quasi-1D Haldane-gap compound NDMAP.

DOI
10.1088/1742-5468/2004/12/p12006

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We consider quasi-one-dimensional spin-1 Heisenberg chains with crystal field anisotropy in a uniform magnetic field. We determine the dynamical structure factor in various limits and obtain a fairly complete qualitative picture of how it changes with the applied field. In particular, we discuss how the width of the higher energy single magnon modes depends on the field. We consider the effects of a weak interchain coupling. We discuss the relevance of our results for recent neutron scattering experiments on the quasi-1D Haldane-gap compound NDMAP.
We calculate dynamical structure factors of the S=1S=1S=1 bond-alternating Heisenberg chain with a single-ion anisotropy in transverse magnetic fields, using a continued fraction method based on the Lanczos algorithm. In the Haldane-gap phase and the dimer phase, dynamical structure factors show characteristic field dependence. Possible interpretations are discussed in the viewpoint of the field dependence of the excitation continuum. The numerical results are in qualitative agreement with recent results for inelastic neutron-scattering experiments on the S=1S=1S=1 bond-alternating Heisenberg-chain compound Ni(C9D24N4)(NO2)ClO4\mathrm{Ni}({\mathrm{C}}_{9}{\mathrm{D}}_{24}{\mathrm{N}}_{4})(\mathrm{N}{\mathrm{O}}_{2})\mathrm{Cl}{\mathrm{O}}_{4}Ni(C9​D24​N4​)(NO2​)ClO4​ and the S=1S=1S=1 Haldane-gap compound Ni(C5D14N2)2N3(PF6)\mathrm{Ni}{({\mathrm{C}}_{5}{\mathrm{D}}_{14}{\mathrm{N}}_{2})}_{2}{\mathrm{N}}_{3}(\mathrm{P}{\mathrm{F}}_{6})Ni(C5​D14​N2​)2​N3​(PF6​) in transverse magnetic fields.
Inelastic neutron scattering experiments on the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependence of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q(parallel) = pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev, Phys. Rev. B 68, 134438 (2003)].
Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].
The subject of the talk is the dynamics of gapped spin systems in presence of an external magnetic field sufficiently high to close the energy gap. The focus will be on anisotropic S = 1 Haldane chain, although applications to weakly coupled dimer system of the TlCuCl3 type and spin ladders with four-spin (ring) interaction will be briefly considered. Existing effective field-theoretical descriptions [1, 2, 3] of anisotropic S = 1 Haldane chain in applied field are reviewed and their predictions are compared with the results of recent inelastic neu-tron scattering experiments on the Haldane chain material NDMAP [4]. It is shown that none of the known theories can provide a consistent description of the experimental data. A new effective theory, based on the dimer field description for alternated S = 1 2 chain, is proposed. In the isotropic case it coincides with the theory of Affleck [1] but differs from it considerably when a finite anisotropy is present. It is shown that the theory is capable of a quantitative description of the data on NDMAP with a satisfactory accuracy, in the whole range of the applied fields both below and above the critical field [4, 5, 6].
We consider the anisotropic Heisenberg spin-1/2 chain in a transverse magnetic field at zero temperature. We first determine all components of the dynamical structure factor by combining exact results with a mean-field approximation recently proposed by Dmitriev et al. [JETP 95, 538 (2002)]. We then turn to the small anisotropy limit, in which we use field theory methods to obtain exact results. We discuss the relevance of our results to neutron scattering experiments on the one-dimensional Heisenberg chain compound Cs2CoCl4.{\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}.Cs2​CoCl4​.
We investigate the magnetic field behaviour of an antiferromagnetic Heisenberg spin-1 chain with the most general single-ion anisotropy. We discuss the regime in which the magnetic field is below the transition value. The splitting of the Haldane triplet is obtained as a function of a field applied in an arbitrary orientation by means of a Lanczos exact diagonalization of chains of up to 16 spins. Our results are well summarized in terms of a first-order perturbation theory. We explain various level crossings that occur by the existence of discrete symmetries. A discussion is given of the electron-spin-resonance and neutron-scattering experiments on the compound Ni(C 2 H 8 N 2 ) 2 NO 2 ClO 4 (NENP).