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Physical Review B

Critical properties of coupled anisotropic Haldane spin chains in a magnetic field

Anup Kumar Bera, B. Lake, A. T. M. N. Islam, A. Schneidewind

Published Aug 25, 2015• 9 citations
Publisher

Abstract

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 $\mathrm{SrNi}{}_{2}{\text{V}}_{2}{\text{O}}_{8}$ 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.

DOI
10.1103/physrevb.92.060412

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The thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies are investigated via the integrable $su(3)$ model in terms of the quantum transfer matrix method and the recently developed high temperature expansion method for exactly solved models. It is shown that large single-ion anisotropy may result in a singlet gapped phase in the spin-$1$ chain which is significantly different from the standard Haldane phase. A large in-plane anisotropy may destroy the gapped phase. On the other hand, in the vicinity of the critical point a weak in-plane anisotropy leads to a different phase transition than the Pokrovsky-Talapov transition. The magnetic susceptibility, specific heat, and magnetization evaluated from the free energy are in excellent agreement with the experimental data for the compounds ${\mathrm{Ni}(\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}$ and ${\mathrm{Ni}(\mathrm{C}}_{10}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$.

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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) (\ensuremathμ0Hc\ensuremath≈11.5{\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}11.5\ensuremathμ0​Hc​\ensuremath≈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.
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.
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​.
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)].
The magnetization process of a single crystal of the spin (S) one linear-chain Heisenberg antiferromagnet, Ni(C2H8N2)2NO2(ClO4), under very high magnetic field has been measured. The magnetization is very small in the low-field region and begins to increase sharply at a finite field for all three of the principal axes. The transition field (HT) above which the system becomes magnetic depends on the direction of the applied field. These experimental results are consistent with the picture that (i) the ground state of S=1 linear chain Heisenberg antiferromagnet is a singlet and (ii) the system becomes magnetic above HT due to closing of the quantum energy gap. The experimental results are analyzed based on a simple energy level scheme. The anisotropy in HT is successfully explained by the theory using the following parameters; the Haldane gap energy EG=17K and the single ion anisotropy constant |D|=16K. These values of EG and D are close to those obtained from other experiments. Using the theory developed in analyzing the magnetization data, we can also explain the behavior of the excitation spectrum of this compound in external magnetic fields determined from the neutron inelastic scattering experiment.
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)].
The thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies are investigated via the integrable su(3)su(3)su(3) model in terms of the quantum transfer matrix method and the recently developed high temperature expansion method for exactly solved models. It is shown that large single-ion anisotropy may result in a singlet gapped phase in the spin-111 chain which is significantly different from the standard Haldane phase. A large in-plane anisotropy may destroy the gapped phase. On the other hand, in the vicinity of the critical point a weak in-plane anisotropy leads to a different phase transition than the Pokrovsky-Talapov transition. The magnetic susceptibility, specific heat, and magnetization evaluated from the free energy are in excellent agreement with the experimental data for the compounds Ni(C2H8N2)2Ni(CN)4{\mathrm{Ni}(\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}Ni(C2​H8​N2​)2​Ni(CN)4​ and ${\mathrm{Ni}(\mathrm{C}}_{10}{\mathrm{H}}_{8}{\mathrm{N}}_{2}{)}_{2}\mathrm{Ni}{(\mathrm{CN})}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$.