arXiv:cond-mat/0211703 · Physical Review Letters

Structure of End States for a Haldane Spin Chain

M. Kenzelmann, Guangyong Xu, Igor A. Zaliznyak, C. Broholm, J. F. DiTusa, G. Aeppli, T. Ito, Kunihiko Oka, H. Takagi

Published Feb 26, 2003• 50 citations

Abstract

Inelastic neutron scattering was used to probe edge states in a quantum spin liquid. The experiment was performed on finite length antiferromagnetic spin-1 chains in ${\mathrm{Y}}_{2}{\mathrm{B}\mathrm{a}\mathrm{N}\mathrm{i}}_{1\ensuremath{-}x}{\mathrm{M}\mathrm{g}}_{x}{\mathrm{O}}_{5}$. At finite fields, there is a Zeeman resonance below the Haldane gap. The wave-vector dependence of its intensity provides direct evidence for staggered magnetization at chain ends, which decays exponentially towards the bulk [$\ensuremath{\xi}=8(1)$ at $T=0.1\text{ }\mathrm{K}$]. Continuum contributions to the chain-end spectrum indicate interchain segment interactions. We also observe a finite size blueshift of the Haldane gap.

DOI: 10.1103/physrevlett.90.087202

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Raman study of one-dimensional spin fluctuations in the spin-1 Heisenberg-chain compound Y2 BaNiO5 : Contrast with simple expectations

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Spin excitations under fields in an anisotropic bond-alternating quantum S=1 chain: contrast with Haldane spin chains

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Effects of edges inS=1 Heisenberg antiferromagnetic chains

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Physical review. B, Condensed matterJul 1, 1993123 citations

arXiv:cond-mat/0211703 · Physical Review Letters

Structure of End States for a Haldane Spin Chain

M. Kenzelmann, Guangyong Xu, Igor A. Zaliznyak, C. Broholm, J. F. DiTusa, G. Aeppli, T. Ito, Kunihiko Oka, H. Takagi

Published Feb 26, 2003• 50 citations

arXiv HTML PDF

Abstract

Inelastic neutron scattering was used to probe edge states in a quantum spin liquid. The experiment was performed on finite length antiferromagnetic spin-1 chains in

{\mathrm{Y}}_{2}{\mathrm{B}\mathrm{a}\mathrm{N}\mathrm{i}}_{1\ensuremath{-}x}{\mathrm{M}\mathrm{g}}_{x}{\mathrm{O}}_{5}

. At finite fields, there is a Zeeman resonance below the Haldane gap. The wave-vector dependence of its intensity provides direct evidence for staggered magnetization at chain ends, which decays exponentially towards the bulk [

\ensuremath{\xi}=8(1)

T=0.1\text{ }\mathrm{K}

]. Continuum contributions to the chain-end spectrum indicate interchain segment interactions. We also observe a finite size blueshift of the Haldane gap.

DOI: 10.1103/physrevlett.90.087202

Related papers

Raman study of one-dimensional spin fluctuations in the spin-1 Heisenberg-chain compound Y2 BaNiO5 : Contrast with simple expectations

P. E. Sulewski, S‐W. Cheong

Spin fluctuations in the Haldane ground state should exhibit a quantum spin gap observable with Raman scattering. The Raman spectra of single-crystalline ${\mathrm{Y}}_{2}$ ${\mathrm{BaNiO}}_{5}$ , a linear spin-1 Heisenberg antiferromagnet, exhibit broad continuum scattering between \ensuremath{\sim}200 and \ensuremath{\sim}800 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in the energy range expected for magnetic excitations (\ensuremath{\sim}J=224 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Numerous weak and broad features superimposed on this continuum scattering possibly result from quantization of the magnon continuum by local molecular fields from nearby chains. A strong and relatively narrow mode at \ensuremath{\sim}680 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, near 3J, unrelated to lattice vibrations, may also be of magnetic origin. All of these features are strongly resonant in the red (${\ensuremath{\lambda}}_{\mathit{L}}$=6328 \AA{}), disappearing for shorter excitation wavelengths. These spectra provide a view of the Haldane spin system excitations complementary to that given by inelastic neutron scattering. Modeling the excitations with Schwinger bosons or spin waves predicts a highly asymmetric scattering feature with a sharp onset near 2\ensuremath{\Delta}(\ensuremath{\sim}0.8J), gradually diminishing toward higher energies. The observed spectra disagree with this theoretical expectation, perhaps due to spin-phonon coupling which may provide an efficient decay channel for the magnon pairs.Spin fluctuations in the Haldane ground state should exhibit a quantum spin gap observable with Raman scattering. The Raman spectra of single-crystalline ${\mathrm{Y}}_{2}$${\mathrm{BaNiO}}_{5}$, a linear spin-1 Heisenberg antiferromagnet, exhibit broad continuum scattering between \ensuremath{\sim}200 and \ensuremath{\sim}800 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in the energy range expected for magnetic excitations (\ensuremath{\sim}J=224 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Numerous weak and broad features superimposed on this continuum scattering possibly result from quantization of the magnon continuum by local molecular fields from nearby chains. A strong and relatively narrow mode at \ensuremath{\sim}680 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, near 3J, unrelated to lattice vibrations, may also be of magnetic origin. All of these features are strongly resonant in the red (${\ensuremath{\lambda}}_{\mathit{L}}$=6328 \AA{}), disappearing for shorter excitation wavelengths. These spectra provide a view of the Haldane spin system excitations complementary to that given by inelastic neutron scattering. Modeling the excitations with Schwinger bosons or spin waves predicts a highly asymmetric scattering feature with a sharp onset near 2\ensuremath{\Delta}(\ensuremath{\sim}0.8J), gradually diminishing toward higher energies. The observed spectra disagree with this theoretical expectation, perhaps due to spin-phonon coupling which may provide an efficient decay channel for the magnon pairs.

Physical review. B, Condensed matterFeb 1, 199510 citations

Spin excitations under fields in an anisotropic bond-alternating quantum S=1 chain: contrast with Haldane spin chains

Masayuki Hagiwara, L. P. Régnault, A. Zheludev +8 more

Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].

arXiv:cond-mat/0501207Jan 10, 20050 citations

Spin Excitations in an Anisotropic Bond-Alternating Quantum S=1 Chain in a Magnetic Field: Contrast to Haldane Spin Chains

Masayuki Hagiwara, L. P. Régnault, A. Zheludev +8 more

Inelastic neutron scattering experiments on the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependence of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q(parallel) = pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev, Phys. Rev. B 68, 134438 (2003)].Inelastic neutron scattering experiments on the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependence of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q(parallel) = pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev, Phys. Rev. B 68, 134438 (2003)].

Physical Review LettersMay 4, 200545 citations

Magnetic excitations in coupled Haldane spin chains near the quantum critical point

A. Zheludev, Takatsugu Masuda, I. Tsukada +4 more

Two quasi-one-dimensional $S=1$ quantum antiferromagnetic materials, ${\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ and ${\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8},$ are studied by inelastic neutron scattering on powder samples. A simple model Hamiltonian is proposed for the two systems and used to analyze the data. Quantitative information on in-chain and interchain interactions obtained from this analysis is discussed in the context of qualitatively different ground-state properties: magnetic long-range order in ${\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ and disordered ``spin liquid'' Haldane-gap state in ${\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}.$ Two quasi-one-dimensional $S=1$ quantum antiferromagnetic materials, ${\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ and ${\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8},$ are studied by inelastic neutron scattering on powder samples. A simple model Hamiltonian is proposed for the two systems and used to analyze the data. Quantitative information on in-chain and interchain interactions obtained from this analysis is discussed in the context of qualitatively different ground-state properties: magnetic long-range order in ${\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ and disordered ``spin liquid'' Haldane-gap state in ${\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}.$

arXiv:cond-mat/0001374Physical review. B, Condensed matterOct 1, 200090 citations

Y89 NMR Imaging of the Staggered Magnetization in the Doped Haldane Chain Y2BaNi1−xMgxO5

Fabio Tedoldi, Raoul Santachiara, M. Horvatić

We present a static, model-independent, experimental determination of the spin-spin correlation length $\ensuremath{\xi}$ in a quantum spin system. This is achieved in the doped Haldane (i.e., $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ Heisenberg antiferromagnetic) chain ${\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{O}}_{5}$ by ${}^{89}\mathrm{Y}$ NMR imaging of the staggered magnetization induced around the Mg impurities (i.e., chain boundaries) by a magnetic field. The magnitude of this magnetization is found to decay exponentially, with $\ensuremath{\xi}$ equal to the theoretical prediction for an infinite $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ chain and the staggered magnetic moment at the edge site showing the Curie behavior of an effective $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ spin.We present a static, model-independent, experimental determination of the spin-spin correlation length $\ensuremath{\xi}$ in a quantum spin system. This is achieved in the doped Haldane (i.e., $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ Heisenberg antiferromagnetic) chain ${\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{O}}_{5}$ by ${}^{89}\mathrm{Y}$ NMR imaging of the staggered magnetization induced around the Mg impurities (i.e., chain boundaries) by a magnetic field. The magnitude of this magnetization is found to decay exponentially, with $\ensuremath{\xi}$ equal to the theoretical prediction for an infinite $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ chain and the staggered magnetic moment at the edge site showing the Curie behavior of an effective $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ spin.

arXiv:cond-mat/9902084Physical Review LettersJul 12, 199968 citations

Effects of edges inS=1 Heisenberg antiferromagnetic chains

Seiji Miyashita, Shoji Yamamoto

Properties of the ground state of open chains of the S=1 Heisenberg antiferromagnet are studied by a quantum Monte Carlo method. Size (length) dependences of the ground-state energy, the energy gap, the staggered magnetization 〈 ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ 〉 and the spin-correlation function 〈 ${\mathit{S}}_{1}^{\mathit{z}}$ ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ 〉 are investigated under free, fixed, and periodic boundary conditions. The size dependences are significant in chains with less than 25 spins, where the magnitude of the staggered magnetization is rather large. However, the fourfold degeneracy of the ground state and the exponential decay of correlations that are inherent to the Haldane system are recovered when the chain length becomes long enough. Both the staggered magnetization and the spin-correlation function decay exponentially. The correlation length is about six in lattice spacing, which agrees with the value obtained in the bulk.Properties of the ground state of open chains of the S=1 Heisenberg antiferromagnet are studied by a quantum Monte Carlo method. Size (length) dependences of the ground-state energy, the energy gap, the staggered magnetization 〈${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$〉 and the spin-correlation function 〈${\mathit{S}}_{1}^{\mathit{z}}$${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$〉 are investigated under free, fixed, and periodic boundary conditions. The size dependences are significant in chains with less than 25 spins, where the magnitude of the staggered magnetization is rather large. However, the fourfold degeneracy of the ground state and the exponential decay of correlations that are inherent to the Haldane system are recovered when the chain length becomes long enough. Both the staggered magnetization and the spin-correlation function decay exponentially. The correlation length is about six in lattice spacing, which agrees with the value obtained in the bulk.

Physical review. B, Condensed matterJul 1, 1993123 citations

Inelastic neutron scattering was used to probe edge states in a quantum spin liquid. The experiment was performed on finite length antiferromagnetic spin-1 chains in

{\mathrm{Y}}_{2}{\mathrm{B}\mathrm{a}\mathrm{N}\mathrm{i}}_{1\ensuremath{-}x}{\mathrm{M}\mathrm{g}}_{x}{\mathrm{O}}_{5}

\ensuremath{\xi}=8(1)

T=0.1\text{ }\mathrm{K}

]. Continuum contributions to the chain-end spectrum indicate interchain segment interactions. We also observe a finite size blueshift of the Haldane gap.

Spin fluctuations in the Haldane ground state should exhibit a quantum spin gap observable with Raman scattering. The Raman spectra of single-crystalline

{\mathrm{Y}}_{2}

{\mathrm{BaNiO}}_{5}

, a linear spin-1 Heisenberg antiferromagnet, exhibit broad continuum scattering between \ensuremath{\sim}200 and \ensuremath{\sim}800 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in the energy range expected for magnetic excitations (\ensuremath{\sim}J=224 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Numerous weak and broad features superimposed on this continuum scattering possibly result from quantization of the magnon continuum by local molecular fields from nearby chains. A strong and relatively narrow mode at \ensuremath{\sim}680 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, near 3J, unrelated to lattice vibrations, may also be of magnetic origin. All of these features are strongly resonant in the red (${\ensuremath{\lambda}}_{\mathit{L}}$=6328 \AA{}), disappearing for shorter excitation wavelengths. These spectra provide a view of the Haldane spin system excitations complementary to that given by inelastic neutron scattering. Modeling the excitations with Schwinger bosons or spin waves predicts a highly asymmetric scattering feature with a sharp onset near 2\ensuremath{\Delta}(\ensuremath{\sim}0.8J), gradually diminishing toward higher energies. The observed spectra disagree with this theoretical expectation, perhaps due to spin-phonon coupling which may provide an efficient decay channel for the magnon pairs.

Two quasi-one-dimensional

S=1

quantum antiferromagnetic materials,

{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}

and

{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8},

are studied by inelastic neutron scattering on powder samples. A simple model Hamiltonian is proposed for the two systems and used to analyze the data. Quantitative information on in-chain and interchain interactions obtained from this analysis is discussed in the context of qualitatively different ground-state properties: magnetic long-range order in

{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}

and disordered ``spin liquid'' Haldane-gap state in

{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}.

We present a static, model-independent, experimental determination of the spin-spin correlation length $\ensuremath{\xi}$ in a quantum spin system. This is achieved in the doped Haldane (i.e.,

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

Heisenberg antiferromagnetic) chain ${\mathrm{Y}}_{2}{\mathrm{BaNi}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{O}}_{5}$ by

{}^{89}\mathrm{Y}

NMR imaging of the staggered magnetization induced around the Mg impurities (i.e., chain boundaries) by a magnetic field. The magnitude of this magnetization is found to decay exponentially, with $\ensuremath{\xi}$ equal to the theoretical prediction for an infinite

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

chain and the staggered magnetic moment at the edge site showing the Curie behavior of an effective

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

spin.

{\mathit{S}}_{\mathit{i}}^{\mathit{z}}

〉 and the spin-correlation function 〈

{\mathit{S}}_{1}^{\mathit{z}}

{\mathit{S}}_{\mathit{i}}^{\mathit{z}}

〉 are investigated under free, fixed, and periodic boundary conditions. The size dependences are significant in chains with less than 25 spins, where the magnitude of the staggered magnetization is rather large. However, the fourfold degeneracy of the ground state and the exponential decay of correlations that are inherent to the Haldane system are recovered when the chain length becomes long enough. Both the staggered magnetization and the spin-correlation function decay exponentially. The correlation length is about six in lattice spacing, which agrees with the value obtained in the bulk.