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arXiv:1208.6017 · Physical Review B

Electron spin resonance shifts in S=1 antiferromagnetic chains

Shunsuke C. Furuya, Yoshitaka Maeda, Masaki Oshikawa

Published Mar 15, 2013• 1 citation
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Abstract

We discuss electron spin resonance (ESR) shifts in spin-1 Heisenberg antiferromagnetic chains with a weak single-ion anisotropy, based on several effective field theories: the O(3) nonlinear sigma model (NLSM) in the Haldane phase, free-fermion theories around the lower and the upper critical fields. In the O(3) NLSM, the single-ion anisotropy corresponds to a composite operator which creates two magnons at the same time and position. Therefore, even inside a parameter range where free magnon approximation is valid for thermodynamics, we have to take interactions among magnons into account in order to include the single-ion anisotropy as a perturbation. Although the O(3) NLSM is only valid in the Haldane phase, an appropriate translation of Faddeev-Zamolodchikov operators of the O(3) NLSM to fermion operators enables one to treat ESR shifts near the lower critical field in a similar manner to discussions in the Haldane phase. Our theory gives quantitative agreements with a numerical evaluation using quantum Monte Carlo simulation, and also with recent ESR experimental results on a spin-1 chain compound $\mathrm{Ni}{({\mathrm{C}}_{5}{\mathrm{H}}_{14}{\mathrm{N}}_{2})}_{2}{\mathrm{N}}_{3}({\mathrm{PF}}_{6})$.

DOI
10.1103/physrevb.87.125122

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We discuss electron spin resonance (ESR) shifts in spin-1 Heisenberg antiferromagnetic chains with a weak single-ion anisotropy, based on several effective field theories: the O(3) nonlinear sigma model (NLSM) in the Haldane phase, free-fermion theories around the lower and the upper critical fields. In the O(3) NLSM, the single-ion anisotropy corresponds to a composite operator which creates two magnons at the same time and position. Therefore, even inside a parameter range where free magnon approximation is valid for thermodynamics, we have to take interactions among magnons into account in order to include the single-ion anisotropy as a perturbation. Although the O(3) NLSM is only valid in the Haldane phase, an appropriate translation of Faddeev-Zamolodchikov operators of the O(3) NLSM to fermion operators enables one to treat ESR shifts near the lower critical field in a similar manner to discussions in the Haldane phase. Our theory gives quantitative agreements with a numerical evaluation using quantum Monte Carlo simulation, and also with recent ESR experimental results on a spin-1 chain compound Ni(C5H14N2)2N3(PF6)\mathrm{Ni}{({\mathrm{C}}_{5}{\mathrm{H}}_{14}{\mathrm{N}}_{2})}_{2}{\mathrm{N}}_{3}({\mathrm{PF}}_{6})Ni(C5​H14​N2​)2​N3​(PF6​).
We consider spin-1 Haldane chains with single-ion anisotropy, which exists in known Haldane chain materials. We develop a perturbation theory in terms of anisotropy, where the magnon-magnon interaction is important even in the low-temperature limit. The exact two-particle form factor in the O(3)O(3)O(3) nonlinear sigma model leads to quantitative predictions on several dynamical properties, including the dynamical structure factor and electron-spin-resonance frequency shift. These agree very well with numerical results, and with experimental data on the Haldane chain material Ni(C5{}_{5}5​H14{}_{14}14​N2{}_{2}2​)2{}_{2}2​N3{}_{3}3​(PF6{}_{6}6​).
We use a quantum O(N) nonlinear \ensuremath{\sigma} model to describe one-dimensional quantum Heisenberg antiferromagnets with integer spin S. A large-N analytical treatment of this effective theory leads to definite predictions for thermodynamic quantities in the low-temperature regime. We obtain the Haldane gap as a function of the temperature and note a trend similar to that found in the compound NENP. The specific heat and magnetic susceptibility are also obtained and comparison with exact numerical results for the S=1 spin chain allows us to determine the domain of validity of our approximation. By a calculation at subleading 1/N order we compute the quasiparticle lifetime. Results are given on-shell, for the width observed at the quasiparticle pole as seen in neutron-scattering experiments, and also off-shell, for the NMR relaxation rate ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$. The phenomenological interacting boson model is compared with our approach. We discuss the effects of anisotropy and compare our results with present experiments on NENP.
This thesis is devoted to the study of a class of antifferomagnetic spin–1 chains with astrong easy plane anisotropy in the presence of magnetic field H. At zero temperature thesystem undergoes two quantum phase transitions at critical fields H1 and H2. Reliableand detailed theoretical analysis is provided on the Electron Spin Resonance (ESR)spectrum, thermodynamics and the thermal transport of the model. The tools at handrange from exact analytical solutions and to numerical simulation techniques. The S = 1antiferromagnet in a magnetic field can be systematically mapped onto an S = 1/2XXZ chain in a longitudinal magnetic field. This effective S = 1/2 description has beenextensively used in order to gain a better physical understanding of the original S = 1chain.For the Electron Spin Resonance spectrum, apart from the theoretical analysis, high-field ESR experimental studies of the compound N iCl2 − 4SC(NH2)2 (abbreviatedas DTN) are presented and found consistent with theoretical predictions. The mostinteresting feature is the experimental signature of the single–ion two–magnon boundstate.Part of this thesis is devoted to the magnetic–field and temperature dependence ofmagnetization and specific heat for the whole field–region and a wide range of temperatures,with special emphasis at the critical behaviour of these quantities at the criticalfields. Finally, the calculation of dynamic correlation functions pertinent to the studyof thermal transport is addressed for the S = 1 model with easy plane anisotropy andthe S = 1/2 XXZ model in the presence of finite magnetic field.
Electron spin resonance (ESR) is an important experimental technique. A comprehensive theory of ESR has been di cult to establish, and as such several di erent approximations are used to predict and explain experimental results. This thesis applies the bond-mean- eld theory to the problem of ESR frequency shift for the one-dimensional antiferromagnetic Heisenberg spin chain with uniaxial exchange anisotropy. We use this theory to calculate the ESR resonance frequency shift as a function of temperature and magnetic eld. We perform numerical calculations using the expression obtained. These results are compared to existing results in the literature; they are in broad agreement with theoretical results such as those of Oshikawa and A eck obtained via bosonisation, but they show discrepancies with experimental results. We agree with the theoretical authors that the discrepancy is due to our use of the simplest-case interaction model.
A systematic field-theory approach to electron spin resonance (ESR) in the S=1/2S=1/2S=1/2 quantum antiferromagnetic chain at low temperature T (compared to the exchange coupling J) is developed. In particular, effects of a transverse staggered field h and an exchange anisotropy (including a dipolar interaction) \ensuremath{\delta} on the ESR line shape are discussed. In the lowest order perturbation theory, the linewidth is given as $\ensuremath{\propto}{\mathrm{Jh}}^{2}{/T}^{2}$ and $\ensuremath{\propto}(\ensuremath{\delta}{/J)}^{2}T,$ respectively. In the case of a transverse staggered field, the perturbative expansion diverges at lower temperature; nonperturbative effects at very low temperature are discussed using exact results on the sine-Gordon field theory. We also compare our field-theory results with the predictions of Kubo-Tomita theory for the high-temperature regime, and discuss the crossover between the two regimes. It is argued that a naive application of the standard Kubo-Tomita theory to the Dzyaloshinskii-Moriya interaction gives an incorrect result. A rigorous and exact identity on the polarization dependence is derived for certain class of anisotropy, and compared with the field-theory results.
Motivated by recent experiments on Ni(C2H8N2)2Ni(CN)4\mathrm{Ni}({\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}(\mathrm{CN}{)}_{4}Ni(C2​H8​N2​)2​Ni(CN)4​ (commonly known as NENC), we study the electron spin resonance in the critical high-field phase of the antiferromagnetic S=1S=1S=1 chain with strong planar anisotropy and show that the ESR spectra exhibit several peculiarities in the critical phase. Possible relevance of those results for other gapped spin systems is discussed.