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Journal of the Physical Society of Japan

ESR in Antiferromagnetic Chains: a Field-Theory Approach

Masaki Oshikawa

Published Jan 2, 2003• 5 citations
Publisher

Abstract

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.

DOI
10.1143/jpsjs.72sb.36

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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.
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.
Abstract A spin-1/2 Heisenberg antiferromagnetic chain is one of the most important paradigmatic models in quantum magnetism. Its ground state is a spin singlet, while the excitation spectrum is formed by gapless fractional excitations, spinons. The presence of alternating g-tensors and/or the staggered Dzyaloshinskii-Moriya interaction results in opening the energy gap Δ∝H2/3\varDelta \propto H^{2/3}Δ∝H2/3 Δ ∝ H 2 / 3 , once the magnetic field H is applied. A fairly good understanding of this phenomenon was achieved in the framework of the sine-Gordon quantum-field theory, taking into account the effective transverse staggered field induced by the applied uniform field. The theory predicts solitons and antisolitons as elementary excitations, as well as their bound states, breathers. Here, I review recent high-field electron spin resonance spectroscopy studies of such systems, focusing on peculiarities of their spin dynamics in the sine-Gordon regime and beyond.
This article is a review of the recent achievements in experimental studies of magnetic excitations in the copper pyrimidine dinitrate [PM–Cu(NO3)2(H2O)2]n (PM = pyrimidine), an S = 1/2 antiferromagnetic chain material with an alternating g-tensor and the Dzyaloshinskii–Moriya interaction, by means of high-field electron spin resonance (ESR). Due to this alternation, in the 1D critical regime this material exhibits a field-induced gap. The excitation spectrum is formed by solitons and their bound states, breathers, and can be effectively described using the sine-Gordon model. With increasing temperature, the soliton-breather regime can be suppressed, resulting in a substantial evolution of ESR parameters. These changes can be described using a new theoretical concept recently proposed for S = 1/2 AF chains with a staggered transverse field. High magnetic field induces a transition into the spin-polarized state with the excitation spectrum formed by magnons. Nonmonotonous behavior of the field-induced gap is observed in vicinity of the saturation field. Experimental data are compared with results of existing theoretical approaches, revealing excellent agreement with predictions.
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​).