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arXiv:cond-mat/0305476 · Physical Review Letters

Bound Spinons in an Antiferromagnetic S=1/2 Chain with a Staggered Field

M. Kenzelmann, Yinghao Chen, C. Broholm, Daniel H. Reich, Yunfeng Qiu

Published Jul 2, 2004• 71 citations
arXivHTMLPDF

Abstract

Inelastic neutron scattering was used to measure the magnetic field dependence of spin excitations in the antiferromagnetic $S=1/2$ chain ${\mathrm{C}\mathrm{u}\mathrm{C}\mathrm{l}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2(\mathrm{\text{dimethylsulfoxide}})$ in the presence of uniform and staggered fields. Dispersive bound states emerge from a zero-field two-spinon continuum with different finite energy minima at wave numbers $q=\ensuremath{\pi}$ and ${q}_{i}\ensuremath{\approx}\ensuremath{\pi}(1\ensuremath{-}2\ensuremath{\langle}{S}_{z}\ensuremath{\rangle})$. The ratios of the field dependent excitation energies are in excellent agreement with predictions for breather and soliton solutions to the quantum sine-Gordon model, the proposed low-energy theory for $S=1/2$ chains in a staggered field. The data are also consistent with the predicted soliton and $n=1,2$ breather polarizations and scattering cross sections.

DOI
10.1103/physrevlett.93.017204

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Inelastic neutron scattering was used to measure the magnetic field dependence of spin excitations in the antiferromagnetic S=1/2S=1/2S=1/2 chain CuCl2\ifmmode⋅\else\textperiodcentered\fi2(dimethylsulfoxide){\mathrm{C}\mathrm{u}\mathrm{C}\mathrm{l}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2(\mathrm{\text{dimethylsulfoxide}})CuCl2​\ifmmode⋅\else\textperiodcentered\fi2(dimethylsulfoxide) in the presence of uniform and staggered fields. Dispersive bound states emerge from a zero-field two-spinon continuum with different finite energy minima at wave numbers q=\ensuremathπq=\ensuremath{\pi}q=\ensuremathπ and qi\ensuremath≈\ensuremathπ(1\ensuremath−2\ensuremath⟨Sz\ensuremath⟩){q}_{i}\ensuremath{\approx}\ensuremath{\pi}(1\ensuremath{-}2\ensuremath{\langle}{S}_{z}\ensuremath{\rangle})qi​\ensuremath≈\ensuremathπ(1\ensuremath−2\ensuremath⟨Sz​\ensuremath⟩). The ratios of the field dependent excitation energies are in excellent agreement with predictions for breather and soliton solutions to the quantum sine-Gordon model, the proposed low-energy theory for S=1/2S=1/2S=1/2 chains in a staggered field. The data are also consistent with the predicted soliton and n=1,2n=1,2n=1,2 breather polarizations and scattering cross sections.
Spinon, soliton and breather in the spin-1/2 antiferromagnetic chain KCuGaF6_66​
Elementary excitations of the S=1/2 one-dimensional antiferromagnet KCuGaF_6 were investigated by inelastic neutron scattering in zero and finite magnetic fields perpendicular to the (1, 1, 0) plane combined with specific heat measurements. KCuGaF6_66​ exhibits no long-range magnetic ordering down to 50 mK despite the large exchange interaction J/k_B=103 K. At zero magnetic field, well-defined spinon excitations were observed. The energy of the des Cloizeaux and Pearson mode of the spinon excitations is somewhat larger than that calculated with the above exchange constant. This discrepancy is mostly ascribed to the effective XY anisotropy arising from the large Dzyaloshinsky-Moriya interaction with an alternating D vector. KCuGaF_6 in a magnetic field is represented by the quantum sine-Gordon model, for which low-energy elementary excitations are composed of solitons, antisolitons and their bound states called breathers. Unlike the theoretical prediction, it was found that the energy of a soliton is smaller than that of the first breather, although the energy of the first breather coincides with that observed in a previous ESR measurement.
We report an experimental and theoretical study of the antiferromagnetic S=12S=\frac{1}{2}S=21​ chain subject to uniform and staggered fields. Using inelastic neutron scattering, we observe a bound-spinon state at high energies in the linear chain compound ${\mathrm{CuCl}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2({({\mathrm{CD}}_{3})}_{2}\mathrm{SO})$. The excitation is explained with a mean-field theory of interacting S=12S=\frac{1}{2}S=21​ fermions and arises from the opening of a gap at the Fermi surface due to confining spinon interactions. The mean-field model also describes the wave-vector dependence of the bound-spinon states, particularly in regions where effects of the discrete lattice are important. We calculate the dynamic structure factor using exact diagonalization of finite length chains, obtaining excellent agreement with the experiments.
Elementary excitations of the S=12S=\frac{1}{2}S=21​ one-dimensional antiferromagnet KCuGaF6{\mathrm{KCuGaF}}_{6}KCuGaF6​ were investigated by inelastic neutron scattering in zero and finite magnetic fields perpendicular to the (1,1,0)(1,1,0)(1,1,0) plane combined with specific heat measurements. KCuGaF6{\mathrm{KCuGaF}}_{6}KCuGaF6​ exhibits no long-range magnetic ordering down to 50 mK despite the large exchange interaction J/kB=103J/{k}_{\mathrm{B}}=103J/kB​=103 K. At zero magnetic field, well-defined spinon excitations were observed. The energy of the des Cloizeaux and Pearson [J. des Cloizeaux and J. J. Pearson, Phys. Rev. 128, 2131 (1962)] mode of the spinon excitations is somewhat larger than that calculated with the above exchange constant. This discrepancy is mostly ascribed to the effective XYXYXY anisotropy arising from the large Dzyaloshinsky-Moriya [T. Moriya, Phys. Rev. 120, 91 (1960)] interaction with an alternating $\mathbit{D}$ vector. KCuGaF6{\mathrm{KCuGaF}}_{6}KCuGaF6​ in a magnetic field is represented by the quantum sine-Gordon model, for which low-energy elementary excitations are composed of solitons and antisolitons and their bound states called breathers. Unlike the theoretical prediction, it was found that the energy of a soliton is smaller than that of the first breather, although the energy of the first breather coincides with that observed in a previous electron spin resonance measurement.
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.
Recent experiments on the S=12S=\frac{1}{2}S=21​ antiferromagnetic chain compound, Cu benzoate, discovered an unexpected gap scaling as approximately the 23\frac{2}{3}32​ power of an applied magnetic field. A theory of this gap, based on an effective staggered field, orthogonal to the applied uniform field, resulting from a staggered gyromagnetic tensor and a Dzyaloshinskii-Moriya interaction, leading to a sine-Gordon quantum field theory, has been developed. Here we discuss many aspects of this subject in considerable detail, including a review of the S=12S=\frac{1}{2}S=21​ chain in a uniform field, a spin-wave theory analysis of the uniform plus staggered field problem, exact amplitudes for the scaling of gap, staggered susceptibility and staggered magnetization with field or temperature, intensities of soliton and breather peaks in the structure function, and field and temperature dependence of the total susceptibility.