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Progress of Theoretical Physics Supplement

Weakly CoupledS=1/2 Quantum Heisenberg Antiferromagnetic Chains in an Effective Staggered Field

Masahiro Sato, Masaki Oshikawa

Published Jan 1, 2002• 0 citations
Publisher

Abstract

We study weakly coupled S = 1/2 quantum Heisenberg antiferromagnetic chains in an effective staggered field. Applying mean-field (MF) theory, spin-wave theory and chain MF (CMF) theory, we can see analytically some effects of the staggered field in this higher dimensional spin system. In particular, when the staggered field and the inter-chain interaction compete with each other, we conjecture from the MF theory that a nontrivial phase is present. The spin wave theory predicts that the behavior of the gaps induced by a staggered field is different between the competitive case and the non-competitive case. When the inter-chain interactions are weak enough, we can improve the MF phase diagram by using CMF theory and the analytical results of field theories. The ordered phase region predicted by the CMF theory is fairly smaller than one of the MF theory. Cu-benzoate, CuCl2·2DMSO (dimethylsulphoxide), BaCu2(Si1-xGex)2O7, etc., could be described by our model in enough low temperature.

DOI
10.1143/ptps.145.212

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We study weakly coupled S = 1/2 quantum Heisenberg antiferromagnetic chains in an effective staggered field. Applying mean-field (MF) theory, spin-wave theory and chain MF (CMF) theory, we can see analytically some effects of the staggered field in this higher dimensional spin system. In particular, when the staggered field and the inter-chain interaction compete with each other, we conjecture from the MF theory that a nontrivial phase is present. The spin wave theory predicts that the behavior of the gaps induced by a staggered field is different between the competitive case and the non-competitive case. When the inter-chain interactions are weak enough, we can improve the MF phase diagram by using CMF theory and the analytical results of field theories. The ordered phase region predicted by the CMF theory is fairly smaller than one of the MF theory. Cu-benzoate, CuCl2·2DMSO (dimethylsulphoxide), BaCu2(Si1-xGex)2O7, etc., could be described by our model in enough low temperature.
We present a systematic study of the anisotropic spin-1/2 Heisenberg model in staggered magnetic fields in two dimensions. To mimic real materials, we consider a system of coupled, antiferromagnetic chains, whose interchain interaction can be either ferro- or antiferromagnetic. When the staggered field is commensurate with the magnetic interactions, an energy gap opens immediately and follows a power law as a function of the applied field, similar to the situation in one dimension. When the field competes with the interactions, a quantum phase transition (QPT) occurs from a gapless, magnetically ordered phase at low fields to a gapped, disordered regime. We use a continuous-time Monte Carlo method to compute the staggered moment of the ordered phases and the spin gap of the disordered phases. We deduce the phase diagrams as functions of the anisotropy ratio and the applied field, and calculate the scaling behavior of the models in both quantities. We show that in the competitive case, the staggered field acts to maintain a regime of quasi-1D behavior around the QPT, and we discuss as a consequence the nature of the crossover from one-dimensional (1D) to 2D physics.
We study the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain in both uniform and (perpendicular) staggered magnetic fields using the density-matrix renormalization-group method. This model has been shown earlier to describe the physics of the copper benzoate materials in magnetic field. In the present work, we extend the study to more general case for a systematic investigation of the field-induced gap and related properties of the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg chain. In particular, we explore the high magnetic field regime where interesting behaviors in the field-induced gap, magnetization, and spin correlation functions are found. Careful examination of the low energy properties and magnetization reveals interesting competing effects of the staggered and uniform fields. The incommensurate behavior in the spin correlation functions is demonstrated and discussed in detail. The present work reproduces earlier results in good agreement with experimental data on copper benzoate and predicts new interesting field-induced features at very high magnetic field.
Heisenberg spin-1/21/21/2 chain materials are known to substantially alter their static and dynamic properties when experiencing an effective transverse staggered field originating from the varying local environment of the individual spins. We present a temperature-, angular- and field-dependent 29{}^{29}29Si NMR study of the model compound BaCu2{}_{2}2​Si2{}_{2}2​O7{}_{7}7​. The experimental data are interpreted in terms of the divergent low-temperature transverse susceptibility, predicted by theory for spin chains in coexisting longitudinal and transverse staggered fields. First, our analysis employs a finite-temperature density matrix renormalization group (DMRG) study of the relevant one-dimensional Hamiltonian. Next, we compare our numerical with the presently known analytical results. With an analysis based on crystal symmetries, we show how the anisotropic contribution to the sample magnetization is experimentally accessible even below the ordering temperature, in spite of its competition with the collinear order parameter of the antiferromagnetic phase. The modification of static and dynamic properties of the system due to the presence of a local transverse staggered field (LTSF) acting on the one-dimensional spin array are argued to cause the unusual spin reorientation transitions observed in BaCu2{}_{2}2​Si2{}_{2}2​O7{}_{7}7​. On the basis of a Ginzburg-Landau type analysis, we discuss aspects of competing spin structures in the presence of magnetic order and of the enhanced transverse susceptibility.
Static and dynamical properties of weakly coupled antiferromagnetic spin chains are treated using a mean-field approximation for the interchain coupling and exact results for the resulting effective one-dimensional problem. Results for staggered magnetization, N\'eel temperature, and spin wave excitations are in agreement with experiments on KCuF3{\mathrm{KCuF}}_{3}KCuF3​. The existence of a narrow longitudinal mode is predicted. The results are in agreement with general scaling arguments, contrary to spin wave theory.
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.
A multichain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 Heisenberg chains. The environment of a chain C0{C}_{0}C0​ is modeled by a number of neighboring chains ${C}_{\ensuremath{\delta}}$, $\ensuremath{\delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}1,\dots{},\ifmmode\pm\else\textpm\fi{}n$, with the edge chains ${C}_{\ifmmode\pm\else\textpm\fi{}n}$ coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1)(2n+1)(2n+1)-chain Hamiltonian is solved self-consistently for nnn up to 444. The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization MMM for small interchain couplings $\ensuremath{\alpha}$ behaves as $M\ensuremath{\sim}\sqrt{\ensuremath{\alpha}}$ enhanced by a multiplicative logarithmic correction.