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arXiv:2001.08555 · Physical review. B./Physical review. B

Inelastic neutron scattering study of the anisotropic S=1 spin chain [Ni(HF2)(3−Clpyridine)4]BF4

Daniel M. Pajerowski, Jamie L. Manson, J. Herbrych, Jesper Bendix, Andrey A. Podlesnyak, John M. Cain, Mark W. Meisel

Published Mar 27, 2020• 6 citations
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Abstract

$[\mathrm{Ni}({\mathrm{HF}}_{2})(3\ensuremath{-}\text{Clpyridine}){}_{4}]{\mathrm{BF}}_{4}$ (NBCT) is a one-dimensional, $S=1$ spin chain material that shows no magnetic neutron Bragg peaks down to temperatures of 0.1 K. Previous work identified NBCT as being in the Haldane phase and near a quantum phase transition as a function of $D/J$ to the large-$D$ quantum paramagnet phase (QPM), where $D$ is the axial single-ion anisotropy and $J$ is the intrachain superexchange. Herein, inelastic neutron scattering results are presented on partially deuterated, $^{11}\mathrm{B}$-enriched NBCT polycrystalline samples in zero magnetic field and down to temperatures of 0.3 K. Comparison to density matrix renormalization group calculations yields $D/J=1.51$ and a significant rhombic single-ion anisotropy $E$ ($E/D\ensuremath{\approx}0.03, E/J\ensuremath{\approx}0.05$). These $D, J$, and $E$ values place NBCT in the large-$D$ QPM phase but precipitously near a quantum phase transition to a long-range ordered phase.

DOI
10.1103/physrevb.101.094431

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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.

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[Ni(HF2)(3\ensuremath−Clpyridine)4]BF4[\mathrm{Ni}({\mathrm{HF}}_{2})(3\ensuremath{-}\text{Clpyridine}){}_{4}]{\mathrm{BF}}_{4}[Ni(HF2​)(3\ensuremath−Clpyridine)4​]BF4​ (NBCT) is a one-dimensional, S=1S=1S=1 spin chain material that shows no magnetic neutron Bragg peaks down to temperatures of 0.1 K. Previous work identified NBCT as being in the Haldane phase and near a quantum phase transition as a function of D/JD/JD/J to the large-DDD quantum paramagnet phase (QPM), where DDD is the axial single-ion anisotropy and JJJ is the intrachain superexchange. Herein, inelastic neutron scattering results are presented on partially deuterated, 11B^{11}\mathrm{B}11B-enriched NBCT polycrystalline samples in zero magnetic field and down to temperatures of 0.3 K. Comparison to density matrix renormalization group calculations yields D/J=1.51D/J=1.51D/J=1.51 and a significant rhombic single-ion anisotropy EEE (E/D\ensuremath≈0.03,E/J\ensuremath≈0.05E/D\ensuremath{\approx}0.03, E/J\ensuremath{\approx}0.05E/D\ensuremath≈0.03,E/J\ensuremath≈0.05). These D,JD, JD,J, and EEE values place NBCT in the large-DDD QPM phase but precipitously near a quantum phase transition to a long-range ordered phase.
$[\mathrm{Ni}({\mathrm{HF}}_{2}){(3\text{\ensuremath{-}}\mathrm{Clpyradine})}_{4}]\mathrm{B}{\mathrm{F}}_{4}$ (NBCT) is a one-dimensional, S=1S=1S=1 spin-chain material that shows no long-range magnetic order down to thermometer temperatures of 0.1 K. Previous ambient pressure inelastic neutron scattering experiments identified NBCT to be in the large-DDD quantum paramagnetic phase of the D/JD/JD/J phase diagram, where DDD is the axial single-ion anisotropy and JJJ is the intrachain superexchange. Here, we extend the previous experiments to a hydrostatic pressure of 0.9 GPa. By comparing to density matrix renormalization group calculations, we find D/JD/JD/J increases from 1.5 to 3.2 as pressure increases from 0 GPa to 0.9 GPa, which pushes the system further into the large-DDD phase.
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.
We study a Heisenberg antiferromagnetic chain of spin S=1 with nearest-neighbor exchange interaction J and easy-plane single-ion anisotropy D. We follow the splitting of the Haldane gap into two components as a function of the anisotropy. Chains of length up to 16 sites are studied by a Lancz\"os method and longer chains up to 32 sites have been investigated by a quantum Monte Carlo simulation for D/J=0.10, 0.15, 0.20, and 0.25. A careful finite-size scaling treatment of our data leads to values that are directly relevant to the interpretation of experiments on Ni(C2{\mathrm{C}}_{2}C2​H8{\mathrm{H}}_{8}H8​N2{\mathrm{N}}_{2}N2​)2{)}_{2})2​NO2{\mathrm{NO}}_{2}NO2​ClO4{\mathrm{ClO}}_{4}ClO4​ (NENP). We discuss the relationship between our results and the magnetic-susceptibility measurements as well as the inelastic-neutron-scattering data and on the Haldane conjecture. Values are proposed for the parameters D and J in the case of NENP.
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)].
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.