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arXiv:cond-mat/0001374 · Physical review. B, Condensed matter

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

A. Zheludev, Takatsugu Masuda, I. Tsukada, Y. Uchiyama, K. Uchinokura, P. Böni, S.-H. Lee

Published Oct 1, 2000• 90 citations
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Abstract

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

DOI
10.1103/physrevb.62.8921

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Two quasi-one-dimensional S=1S=1S=1 quantum antiferromagnetic materials, PbNi2V2O8{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}PbNi2​V2​O8​ and SrNi2V2O8,{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8},SrNi2​V2​O8​, 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 SrNi2V2O8{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrNi2​V2​O8​ and disordered ``spin liquid'' Haldane-gap state in PbNi2V2O8.{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}.PbNi2​V2​O8​.
Effects of interchain couplings and anisotropy on a Haldane chain have been investigated by single-crystal inelastic neutron scattering and density functional theory (DFT) calculations on the model compound SrNi2V2O8{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrNi2​V2​O8​. Significant effects on low-energy excitation spectra are found where the Haldane gap (${\ensuremath{\Delta}}_{0}\ensuremath{\approx}0.41J$, where JJJ is the intrachain exchange interaction) is replaced by three energy minima at different antiferromagnetic zone centers due to the complex interchain couplings. Further, the triplet states are split into two branches by single-ion anisotropy. Quantitative information on the intrachain and interchain interactions as well as on the single-ion anisotropy is obtained from the analyses of the neutron scattering spectra by the random-phase approximation method. The presence of multiple competing interchain interactions is found from the analysis of the experimental spectra and is also confirmed by the DFT calculations. The interchain interactions are two orders of magnitude weaker than the nearest-neighbor intrachain interaction J=8.7J=8.7J=8.7 meV. The DFT calculations reveal that the dominant intrachain nearest-neighbor interaction occurs via nontrivial extended superexchange pathways Ni-O-V-O-Ni involving the empty ddd orbital of V ions. The present single-crystal study also allows us to correctly position SrNi2V2O8{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrNi2​V2​O8​ in the theoretical $D\text{\ensuremath{-}}{J}_{\ensuremath{\perp}}$ phase diagram [T. Sakai and M. Takahashi, Phys. Rev. B 42, 4537 (1990)], showing where it lies within the spin-liquid phase.
We use inelastic neutron scattering to measure magnetic fluctuations as a function of transverse magnetic field and temperature in a single crystal of the coupled Haldane chain compound SrNi2V2O8\mathrm{SrNi}{}_{2}{\text{V}}_{2}{\text{O}}_{8}SrNi2​V2​O8​ with uniaxial anisotropy. At the base temperature (2 K), spin excitations confirm a field-induced quantum phase transition from the disordered Haldane (gapped singlet) state to a gapped long-range ordered state through a quantum critical point (QCP) (${\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}11.5$ T). At elevated temperatures in the vicinity of the QCP, both the energy and linewidth of the lowest triplet mode scale linearly with temperature, in accordance with quantum criticality. We also demonstrate that the experimental field dependence of the triplet excitation modes at the base temperature is in agreement with the bosonic and macroscopic models, but is in contrast to the fermionic and perturbative models.
The effect of spin-vacancy doping on the ground state of the quasi-one-dimensional S=1S=1S=1 quantum antiferromagnet PbNi2V2O8{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}PbNi2​V2​O8​ is studied by X band as well as high-field ESR. A very broad ESR line is observed at low temperatures in powdered ${\mathrm{PbNi}}_{2\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ for 0< x< 0.24.0<~x<~0.24.0< x< 0.24. The frequency dependence of the observed ESR line rules out the possibility that the low-temperature ESR signal comes from the isolated S=12S=\frac{1}{2}S=21​ spins. Instead, it is proposed that a magnetic coupling (most likely of second order) between the chain-end spins on both sides of the Mg2+{\mathrm{Mg}}^{2+}Mg2+ impurity plays an important role in this system. Impurity-induced spin states, due to the strong interchain coupling, also induce a staggered magnetization on the neighboring chains with a characteristic length \ensuremath{\xi}. \ensuremath{\xi} increases with decreasing temperature, as suggested by the additional broadening and the shift of the ESR signal at low temperatures. On the other hand the temperature dependence of the low temperature susceptibility suggests a much more complicated picture in which impurity-induced spins are exposed to coupling to thermal excitations on each chain as well as to three-dimensional antiferromagnetic correlations.
We present a systematic inelastic neutron scattering and neutron diffraction study on the magnetic structure of the quasi-one-dimensional spin-12\frac{1}{2}21​ magnet SrCo2V2O8{\mathrm{SrCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrCo2​V2​O8​, where the interchain coupling in the N\'eel-type antiferromagnetic ground state breaks the static spin lattice into two independent domains. At zero magnetic field, we have observed two new spin excitations with small spectral weights inside the gapped region defined by the spinon bound states. In an external magnetic field along the chain axis, the N\'eel order gets partially destabilized at ${\ensuremath{\mu}}_{0}{H}^{★}=2.0\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ and completely suppressed at ${\ensuremath{\mu}}_{0}{H}_{\mathrm{p}}=3.9\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, above which a quantum disordered Tomonaga--Luttinger liquid (TLL) prevails. The low-energy spin excitations between ${\ensuremath{\mu}}_{0}{H}^{★}$ and ${\ensuremath{\mu}}_{0}{H}_{\mathrm{p}}$ are not homogeneous, containing the dispersionless (or weakly dispersive) spinon bound states excited in the N\'eel phase and the highly dispersive psinon-antipsinon mode characteristic of a TLL. We propose that the two new modes at zero field are spinon excitations inside the domain walls. Since they have a smaller gap than those excited in the N\'eel domains, the underlying spin chains enter the TLL state via a local quantum phase transition at ${\ensuremath{\mu}}_{0}{H}^{★}$, making the N\'eel/TLL coexistence a stable configuration until the excitation gap in the N\'eel domains closes at ${\ensuremath{\mu}}_{0}{H}_{\mathrm{p}}$.
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.
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.