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arXiv:2206.06249 · Physical review. B./Physical review. B

High-pressure inelastic neutron scattering study of the anisotropic S=1 spin chain [Ni(HF2)(3−Clpyradine)4]BF4

Daniel M. Pajerowski, Andrey A. Podlesnyak, J. Herbrych, Jamie L. Manson

Published Apr 18, 2022• 10 citations
arXivHTMLPDF

Abstract

$[\mathrm{Ni}({\mathrm{HF}}_{2}){(3\text{\ensuremath{-}}\mathrm{Clpyradine})}_{4}]\mathrm{B}{\mathrm{F}}_{4}$ (NBCT) is a one-dimensional, $S=1$ 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-$D$ quantum paramagnetic phase of the $D/J$ phase diagram, where $D$ is the axial single-ion anisotropy and $J$ 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 $D/J$ 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-$D$ phase.

DOI
10.1103/physrevb.105.134420

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$[\mathrm{Ni}({\mathrm{HF}}_{2})(3\ensuremath{-}\text{Clpyridine}){}_{4}]{\mathrm{BF}}_{4}$ (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.

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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)].

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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)].

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A Quantum Spin Chain in High Magnetic Fields

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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.

Progress of Theoretical Physics Supplement•May 16, 2013•0 citations
[Ni(HF2)(3\ensuremath-Clpyradine)4]BF4[\mathrm{Ni}({\mathrm{HF}}_{2}){(3\text{\ensuremath{-}}\mathrm{Clpyradine})}_{4}]\mathrm{B}{\mathrm{F}}_{4}[Ni(HF2​)(3\ensuremath-Clpyradine)4​]BF4​ (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.
$[\mathrm{Ni}({\mathrm{HF}}_{2})(3\ensuremath{-}\text{Clpyridine}){}_{4}]{\mathrm{BF}}_{4}$ (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 ($E/D\ensuremath{\approx}0.03, E/J\ensuremath{\approx}0.05$). 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.
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.
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)].
Exact diagonalization calculations of finite antiferromagnetic spin-1 Heisenberg chains at finite temperatures are presented and compared to a recent inelastic neutron scattering experiment for temperatures T up to 7.57.57.5 times the intrachain exchange constant J. The calculations show that the excitations at the antiferromagnetic point q=1q=1q=1 and at q=0.5q=0.5q=0.5 remain resonant up to at least T=2J,T=2J,T=2J, confirming the recent experimental observation of resonant high-temperature domain wall excitations. The predicted first and second moments are in good agreement with experiment, except at temperatures where three-dimensional spin correlations are most important. The ratio of the structure factors at q=1q=1q=1 and 0.5 is well predicted for the paramagnetic infinite-temperature limit. For T< 2J,T<~2J,T< 2J, however, we found that the experimentally observed intensity is considerably less than predicted. This suggests that domain wall excitations on different chains interact up to temperatures of the order of the spin band width.
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 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.