Journal of the Physical Society of Japan

Spin Correlations around Mobile Holes in an Antiferromagnet

Jun-ichiro Inoue, Sadamichi Maekawa

Published Oct 15, 1990• 9 citations

Abstract

Various spin correlation functions around a mobile hole in a two-dimensional antiferromagnetic state are calculated in the t - J model. The correlations show canted and twisted character at k =(0, 0) and (π/2, π/2), respectively, where the latter is the wave vector of the ground state. Possible spin configurations around the hole are discussed.

DOI: 10.1143/jpsj.59.3467

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Journal of the Physical Society of Japan

Spin Correlations around Mobile Holes in an Antiferromagnet

Jun-ichiro Inoue, Sadamichi Maekawa

Published Oct 15, 1990• 9 citations

Publisher

Abstract

DOI: 10.1143/jpsj.59.3467

Related papers

Mobile holes in a two-dimensional Heisenberg antiferromagnet

Toshihiro Itoh, M. Arai, Takeo Fujiwara

Th t-t'-t''-J model is investigated by a rigorous diagonalization in a two-dimensional square lattice as large as \ensuremath{\surd}20 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}20 , which has no additional degeneracy. The ground state of one hole in the t-J model is at a momentum k near (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) with a total spin S=1/2 and that of two holes is at k=(0,0) with S=0. The hole pairing and nonclustering may be preferable for the ground state of the t-t'-t''-J model in the region of t'>0 and t''\ensuremath{\lesssim}0.Th t-t'-t''-J model is investigated by a rigorous diagonalization in a two-dimensional square lattice as large as \ensuremath{\surd}20 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}20 , which has no additional degeneracy. The ground state of one hole in the t-J model is at a momentum k near (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) with a total spin S=1/2 and that of two holes is at k=(0,0) with S=0. The hole pairing and nonclustering may be preferable for the ground state of the t-t'-t''-J model in the region of t'>0 and t''\ensuremath{\lesssim}0.

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Ground state of a mobile vacancy in a quantum antiferromagnet: Small-cluster study

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The ground state of a mobile vacancy in a square-lattice spin-1/2 Heisenberg antiferromagnet described by the t-J Hamiltonian is investigated numerically for an 18-site cluster. The ground state has spin 1/2, and the bottom of the vacancy band is at momentum k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), for t/J4, which is consistent with the spin-wave perturbation theory. The structure of the spin configuration in the vicinity of the vacancy is examined using a number of correlation functions. The latter reveal the existence of a dipolar distortion of the staggered magnetization, as suggested by the semiclassical theory.The ground state of a mobile vacancy in a square-lattice spin-1/2 Heisenberg antiferromagnet described by the t-J Hamiltonian is investigated numerically for an 18-site cluster. The ground state has spin 1/2, and the bottom of the vacancy band is at momentum k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), for t/J4, which is consistent with the spin-wave perturbation theory. The structure of the spin configuration in the vicinity of the vacancy is examined using a number of correlation functions. The latter reveal the existence of a dipolar distortion of the staggered magnetization, as suggested by the semiclassical theory.

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arXiv:cond-mat/9904030Physical review. B, Condensed matterAug 1, 199947 citations

Mobile vacancy in a quantum antiferromagnet: Effective Hamiltonian

Boris I. Shraiman, Eric D. Siggia

A semiclassical analysis, as well as symmetry considerations, are used to explain and extend published quantum-cluster results for the ground state of a hole in a quantum antiferromagnet (AF). For the ground state with a wave vector in the face center of the reduced Brillouin zone, the spins twist into a dipolar configuration around the hole to optimize the hopping term, but remain coplanar. More complicated three-dimensional spin textures with staggered topological charge can be constructed by superimposing dipole states corresponding to distinct points in the Brillouin zone and different planes of spin twist. An effective Hamiltonian for the hole that generalizes the nonlinear sigma model is derived. The essential new term that is responsible for the textures described is a coupling between spin currents for the holes and background spins. The presence of the local antiferromagnetic correlations dictates a spinor representation of the vacancy. This description provides the foundation for the study of the phases of a quantum AF at low vacancy density.A semiclassical analysis, as well as symmetry considerations, are used to explain and extend published quantum-cluster results for the ground state of a hole in a quantum antiferromagnet (AF). For the ground state with a wave vector in the face center of the reduced Brillouin zone, the spins twist into a dipolar configuration around the hole to optimize the hopping term, but remain coplanar. More complicated three-dimensional spin textures with staggered topological charge can be constructed by superimposing dipole states corresponding to distinct points in the Brillouin zone and different planes of spin twist. An effective Hamiltonian for the hole that generalizes the nonlinear sigma model is derived. The essential new term that is responsible for the textures described is a coupling between spin currents for the holes and background spins. The presence of the local antiferromagnetic correlations dictates a spinor representation of the vacancy. This description provides the foundation for the study of the phases of a quantum AF at low vacancy density.

Physical review. B, Condensed matterAug 1, 199090 citations

Spatial distribution of mobile holes in thet-Jmodel

K. J. E. Vos, Robert J Gooding, P. W. Leung +1 more

We have calculated the hole-hole correlation function for two holes doped into a S=1/2 antiferromagnetic insulator described by the t-J model on a 16-site \ensuremath{\surd}8\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}32 lattice and a 24-site \ensuremath{\surd}18\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}32 lattice using an exact diagonalization technique. We predict that the carriers described by this model, in the parameter range relevant to ${\mathrm{CuO}}_{2}$ planes, tend to stay as far apart as possible. This result is in direct contradiction to previously published exact diagonalization data [e.g., D. Poilblanc, Phys. Rev. B 49, 1477 (1994)]. We suggest that if the carriers do tend to stay as far apart from one another as possible, then the electron momentum distribution function shows evidence for hole pockets at k\ensuremath{\rightarrow}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), consistent with many recent studies of these models, including recent photoemission work.We have calculated the hole-hole correlation function for two holes doped into a S=1/2 antiferromagnetic insulator described by the t-J model on a 16-site \ensuremath{\surd}8\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}32 lattice and a 24-site \ensuremath{\surd}18\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}32 lattice using an exact diagonalization technique. We predict that the carriers described by this model, in the parameter range relevant to ${\mathrm{CuO}}_{2}$ planes, tend to stay as far apart as possible. This result is in direct contradiction to previously published exact diagonalization data [e.g., D. Poilblanc, Phys. Rev. B 49, 1477 (1994)]. We suggest that if the carriers do tend to stay as far apart from one another as possible, then the electron momentum distribution function shows evidence for hole pockets at k\ensuremath{\rightarrow}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), consistent with many recent studies of these models, including recent photoemission work.

Physical review. B, Condensed matterMay 1, 19950 citations

The two-dimensional extended $t\ensuremath{-}J$ model is studied computationally in a broad region of parameter space, motivated by recent photoemission experiments for the undoped cuprate

{\mathrm{Ca}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}

[F. Ronning et al., Science 282, 2067 (1998)]. The one-hole ground state is shown to develop robust antiferromagnetic (AF) correlations between spins separated by the mobile hole (i.e., across the hole). This effect tends to decouple charge from spin, and the quasiparticle weight becomes negligible, particularly at momenta $(0,\ensuremath{\pi})\ensuremath{-}(\ensuremath{\pi},0).$ Studies with more holes show precursors of metallic stripe formation, with holes sharing their individual spin arrangements, and AF correlations generated across the stripe.

{\mathrm{CuO}}_{2}

planes, tend to stay as far apart as possible. This result is in direct contradiction to previously published exact diagonalization data [e.g., D. Poilblanc, Phys. Rev. B 49, 1477 (1994)]. We suggest that if the carriers do tend to stay as far apart from one another as possible, then the electron momentum distribution function shows evidence for hole pockets at k\ensuremath{\rightarrow}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), consistent with many recent studies of these models, including recent photoemission work.