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arXiv:cond-mat/9905002 · Physical review. B, Condensed matter

Field-induced gap in Cu benzoate and other S=12 antiferromagnetic chains

Ian K. Affleck, Masaki Oshikawa

Published Jul 1, 1999• 309 citations
arXivHTMLPDF

Abstract

Recent experiments on the $S=\frac{1}{2}$ antiferromagnetic chain compound, Cu benzoate, discovered an unexpected gap scaling as approximately the $\frac{2}{3}$ 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 $S=\frac{1}{2}$ 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.

DOI
10.1103/physrevb.60.1038

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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.
We measured the magnetization processes of the S = 1/2 antiferromagnetic chain compound, Cu benzoate. From the inelastic neutron scattering and the specific heat measurements it was recently discovered that the substance exhibits an unexpected gap which varies approximately as the 2/3 power of an applied magnetic field. The primary mechanism of the gap formation is produced by an effective staggered field due to both the alternating g-tensor and the Dzyaloshinskii-Moriya interaction. We observed the effect of the effective staggered field on the magnetization process of Cu benzoate as a rounding behavior near the saturation field as well as an initial nonlinear increment near zero field. The experimental results are well reproduced by the numerical calculation on the Hamiltonian which includes the appropriate term of the staggered field, using the finite temperature density matrix renormalization group method.
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.
Magnetic excitations in copper pyrimidine dinitrate, a spin-1/2 antiferromagnetic chain with alternating ggg-tensor and Dzyaloshinskii-Moriya interactions that exhibits a field-induced spin gap, are probed by means of pulsed-field electron-spin-resonance spectroscopy. In particular, we report on a minimum of the gap in the vicinity of the saturation field Hsat=48.5{H}_{\mathrm{sat}}=48.5Hsat​=48.5 T associated with a transition from the sine-Gordon region (with soliton-breather elementary excitations) to a spin-polarized state (with magnon excitations). This interpretation is fully confirmed by the quantitative agreement over the entire field range of the experimental data with the density matrix renormalization group calculations for a spin-1/2 Heisenberg chain with a staggered transverse field.
We investigated the thermodynamic properties of the spin-1/2 one-dimensional Heisenberg antiferromagnet KCuGaF6{}_{6}6​ by measuring the specific heat in magnetic fields. When this compound is subjected to a uniform magnetic field $\mathbit{H}$, a transverse staggered magnetic field $\mathbit{h}$ is induced in this compound owing to the staggered component of the $\mathbit{g}$ tensor and the Dzyaloshinskii-Moriya interaction with an alternating $\mathbit{D}$ vector. Consequently, the quantum sine-Gordon (SG) model is an effective model of this compound in a uniform magnetic field. In three different field directions, we observed a magnetic-field-induced gap, which increases with HHH. We analyzed experimental results using specific heat theory based on quantum SG theory. The thermodynamic property for $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}c$ is very well described in terms of the elementary excitations characteristic of the quantum SG model, while for the other field directions significant contributions from other excitation modes beyond the framework of the quantum SG model were observed. For $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}b$, a quantum phase transition between gapless and gapped ground states was observed.
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.
The magnetic-excitation spectrum of copper pyrimidine dinitrate, a material containing S = 1/2 antiferromagnetic chains with alternating g -tensor and the Dzyaloshinskii-Moriya interaction, and exhibiting a field-induced spin gap, is probed using tunable-frequency electron spin resonance spectroscopy in magnetic fields up to 25 T. The data are interpreted in frame of the sine-Gordon quantum-field theoretical concept proposed recently by Oshikawa and Affleck. The field-induced gap is measured directly ; signatures of soliton and three breather branches are identified.