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arXiv:cond-mat/0108424 · Physical review. B, Condensed matter

Electron spin resonance in S=12 antiferromagnetic chains

Masaki Oshikawa, Ian K. Affleck

Published Mar 19, 2002• 197 citations
arXivHTMLPDF

Abstract

A systematic field-theory approach to electron spin resonance (ESR) in the $S=1/2$ 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.

DOI
10.1103/physrevb.65.134410

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The dynamical mean-field-like theory of the electron spin resonance (ESR) in spin-1/2 chains with nearest and next-nearest neighbor interactions (or zigzag spin ladders) and alternation is developed. It is explained that either the magnetic anisotropy of spin-spin couplings or the Dzyaloshinskii-Moriya interaction causes shifts of the resonance position in spin chains, comparing to only magnetically isotropic interactions. The power of the ac ESR field, absorbed by the spin chain, is calculated. It is shown that the temperature dependence of the shift of the resonance position is related to the temperature dependence of the ESR absorption. Depending on the strength of next-nearest neighbor interactions, the shift of the ESR position can become either exponentially small or can be increased near quantum critical points. The absorbed by the alternating spin chain power of the ac magnetic field is calculated, manifesting two resonances. The influence of mentioned spin-spin interactions on the linewidth of the ESR is analyzed.
This paper presents numerical results of the ESR absorption spectrum for S=12S=\frac{1}{2}S=21​ XY\mathrm{XY}XY model in one dimension. We obtain detailed numerical results for a wide range of temperature and magnetic field for a large system of 400 sites, using the method developed by Derzhko et al. In the high-temperature regime, a similar behavior is observed for both the ferromagnet and the antiferromagnet; these line shapes have only one peak. On the other hand, in the low-temperature regime, line shapes show very different behaviors depending on the sign of the exchange coupling. While the line shape for the ferromagnet has only one peak as in the high-temperature regime, the line shape for antiferromagnet has two peaks and shows very strong magnetic-field dependence. We also discuss the physical meaning by comparing our numerical results with several theoretical results: the exact result in the high-temperature limit, Kubo-Tomita theory, field theory, mean-field theory, and elementary excitations.
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.