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Progress of Theoretical Physics Supplement

New Approach to Electron Spin Resonance in Quantum Spin Chains

Masaki Oshikawa

Published Jan 1, 2002• 3 citations
Publisher

Abstract

A field theory approach to ESR in S = 1/2 Heisenberg antiferromagnetic chains is developed. For an exchange anisotropy perturbation, the lineshape is shown to be Lorentzian and the width is proportional to the temperature in the low temperature regime.
DOI
10.1143/ptps.145.243

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We review our recent field-theory approach to ESR in quantum spin chains at low temperature. The perturbative expansion in an anisotropy is formulated systematically, avoiding previously made assumptions. The linewidth is calculated in the lowest order of the perturbation theory for a transverse staggered field and an exhange anisotropy. In the case of the transverse staggered field, the perturbative expansion become divergent at lower temperature. The spectrum in the zero energy limit is discussed using non-perturbative exact results on the sine-Gordon field theory. These theoretical results are compared to experimental data, particularly those on Cu benzoate.
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​).
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.
We analyze the effects of different coupling anisotropies in a spin-1/2 ladder on the electron spin resonance (ESR) shift. Combining a perturbative expression in the anisotropies with density matrix renormalization group computation of the short range correlations at finite temperature, we provide the full temperature and magnetic field evolution of the ESR paramagnetic shift. We show that for well chosen parameters the ESR shift can be in principle used to extract quantitatively the anisotropies and, as an example, discuss the material BPCB.