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Physical review. B, Condensed matter

Y2 BaNi O5 : A nearly ideal realization of the S=1 Heisenberg chain with antiferromagnetic interactions

Guangyong Xu, J. F. DiTusa, T. Ito, Kunihiko Oka, H. Takagi, C. Broholm, G. Aeppli

Published Sep 1, 1996• 134 citations
Publisher

Abstract

We report an inelastic-neutron-scattering experiment on single crystals of the one-dimensional spin-one antiferromagnet ${\mathrm{Y}}_{2}$BaNi${\mathrm{O}}_{5}$. The data show that this compound is a nearly ideal material for studying the Haldane conjecture in the Heisenberg limit. In particular, the Haldane gap at $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}=\ensuremath{\pi}$ is almost isotropic, taking on the values of 7.5(1), 8.6(1), and 9.6(1) meV for polarizations parallel to the three principal orthorhombic axes respectively. Interchain coupling along the edges of the orthorhombic unit cell is found to be very weak ($\frac{{J}^{\ensuremath{'}}}{J}<~5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$). Finally, we show that defects in our sample at the 1% level cause visible broadening of the excitation at $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}=\ensuremath{\pi}$.

DOI
10.1103/physrevb.54.r6827

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We report an inelastic-neutron-scattering experiment on single crystals of the one-dimensional spin-one antiferromagnet Y2{\mathrm{Y}}_{2}Y2​BaNiO5{\mathrm{O}}_{5}O5​. The data show that this compound is a nearly ideal material for studying the Haldane conjecture in the Heisenberg limit. In particular, the Haldane gap at q\ifmmode~\else˜\fi=\ensuremathπ\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}=\ensuremath{\pi}q\ifmmode~\else˜\fi​=\ensuremathπ is almost isotropic, taking on the values of 7.5(1), 8.6(1), and 9.6(1) meV for polarizations parallel to the three principal orthorhombic axes respectively. Interchain coupling along the edges of the orthorhombic unit cell is found to be very weak (J\ensuremath′J< 5\ifmmode×\else\texttimes\fi10\ensuremath−4\frac{{J}^{\ensuremath{'}}}{J}<~5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}JJ\ensuremath′​< 5\ifmmode×\else\texttimes\fi10\ensuremath−4). Finally, we show that defects in our sample at the 1% level cause visible broadening of the excitation at q\ifmmode~\else˜\fi=\ensuremathπ\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}=\ensuremath{\pi}q\ifmmode~\else˜\fi​=\ensuremathπ.
Magnetic excitations of the ideal one-dimensional, spin S =1, antiferromagnet Y 2 BaNiO 5 are studied by means of inelastic neutron scattering on single crystal sample. Our experimental results at low temperature indicate that Y 2 BaNiO 5 can be regarded as the best isotropic Haldane-system sofar studied with the intrachain exchange energy J / k B =-24.1 meV and the averaged gap Δ( T =7 K)=8.5 meV. Y 2 BaNiO 5 exhibits a good magnetic one-dimensionality with the inter-/intrachain exchange ratio of | J ′ / J |≤10 -4 and has only very small easy-axis and in-plane single ion anisotropy of | D / J |=0.03 and | E / J |∼0.01. In addition the temperature dependence of the Haldane gap Δ( T ) and its damping rate was determined.
Spin fluctuations in the Haldane ground state should exhibit a quantum spin gap observable with Raman scattering. The Raman spectra of single-crystalline Y2{\mathrm{Y}}_{2}Y2​BaNiO5{\mathrm{BaNiO}}_{5}BaNiO5​, 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.
Neutron scattering has shown that the lowest spin excitations in the spin-1 antiferromagnet CsNiCl3{\mathrm{CsNiCl}}_{3}CsNiCl3​ in its one-dimensional phase occur at finite frequency. After allowance for the known weak interchain coupling the gap is found to be in good agreement with recent numerical calculations. The results support the Haldane conjecture that in integral-spin chains with isotropic interactions a gap separates the ground state from the excitations.
A full description of a series of spin-wave measurements in CsNiCl3{\mathrm{CsNiCl}}_{3}CsNiCl3​ in the three-dimensional (3D) and one-dimensional (1D) phases and their analysis to provide the first experimental evidence for the Haldane gap is presented. Neutron scattering experiments were performed on a single crystal of CsNiCl3{\mathrm{CsNiCl}}_{3}CsNiCl3​ with both (h,0,l) and (h,h,l) as the scattering plane. The order parameter in both 3D phases was measured and the spin-wave dispersion determined in the lower phase. The spin-wave spectrum calculated from a dynamic susceptibility method was compared with the experimental response in the lower 3D phase to obtain the following values for the exchange and anisotropy constants: J=0.345\ifmmode\pm\else\textpm\fi{}0.008 THz, J'=0.0060\ifmmode\pm\else\textpm\fi{}0.005 THz, and D=-0.0130\ifmmode\pm\else\textpm\fi{}0.0015 THz. These parameters confirm that CsNiCl3{\mathrm{CsNiCl}}_{3}CsNiCl3​ in its disordered phase is a good approximation to a one-dimensional Heisenberg antiferromagnet. In the 1D phase the gap frequency for an isolated chain of Ni2+{\mathrm{Ni}}^{2+}Ni2+ ions is found to be 0.32 THz close to the gap estimated in finite-chain calculations. The results constitute experimental support for the Haldane conjecture that the excitations of integer-spin chains, unlike half-integer--spin chains, exhibit an apparent anisotropy that arises not from the underlying isotropic Hamiltonian, but from many-body effects.
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 KT=0.1\text{ }\mathrm{K}T=0.1 K]. Continuum contributions to the chain-end spectrum indicate interchain segment interactions. We also observe a finite size blueshift of the Haldane gap.
The spin correlations of the S=1 Heisenberg antiferromagnetic chains in AgVP2{\mathrm{AgVP}}_{2}AgVP2​S6{\mathrm{S}}_{6}S6​ have been studied by neutron scattering at temperatures of the order of T\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}2}$ J/kB{\mathit{k}}_{\mathit{B}}kB​. On the polycrystalline samples, with a careful choice of experimental conditions, we have observed a Haldane gap of Eg{\mathit{E}}_{\mathit{g}}Eg​=26 meV at the antiferromagnetic point at q=\ensuremath{\pi}. The excitation spectra are consistent with a mode that has a spin-wave velocity C=150 meV and a correlation length \ensuremath{\xi}\ensuremath{\approxeq}5.5, close to C/Eg{\mathit{E}}_{\mathit{g}}Eg​. These results are in quantitative agreement with the predictions and numerical results on the Haldane state.