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arXiv:cond-mat/0105515 · Physical review. B, Condensed matter

Electron spin resonance in high-field critical phase of gapped spin chains

Alexei K. Kolezhuk, H.-J. Mikeska

Published Nov 30, 2001• 18 citations
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Abstract

Motivated by recent experiments on $\mathrm{Ni}({\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}(\mathrm{CN}{)}_{4}$ (commonly known as NENC), we study the electron spin resonance in the critical high-field phase of the antiferromagnetic $S=1$ 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.

DOI
10.1103/physrevb.65.014413

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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.
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 present electron spin resonance experiments in the one-dimensional antiferromagnetic S=1S=1S=1 spin chains NENP and NINO in pulsed magnetic fields up to 50 T. The measured field dependence of the quantum energy gap for B∣∣bB||bB∣∣b is analyzed using the exact diagonalization method and the density matrix renormalization group method. A staggered anisotropy term $(\ensuremath{-}{1)}^{i}{d(S}_{i}^{x}{S}_{i}^{z}{+S}_{i}^{z}{S}_{i}^{x})$ was considered in addition to a staggered field term $(\ensuremath{-}{1)}^{i}{S}_{i}^{x}{B}_{\mathrm{st}}.$ We show that the spin dynamics in high magnetic fields strongly depends on the orthorhombic anisotropy E.
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.
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.
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.