Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0310741 · Physical Review B

Distribution of exchange energy in a bond-alternating S=1 quantum spin chain

A. Zheludev, Takatsugu Masuda, B. C. Sales, David Mandrus, T. Papenbrock, Ted Barnes, S. Park

Published Apr 16, 2004• 21 citations
arXivHTMLPDF

Abstract

The quasi-one-dimensional bond-alternating $S=1$ quantum antiferromagnet [Ni${(N,N}^{\ensuremath{'}}$$\ensuremath{-}\mathrm{b}\mathrm{i}\mathrm{s}(3\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l})\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{e}\ensuremath{-}1,3\ensuremath{-}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}(\ensuremath{\mu}\ensuremath{-}{\mathrm{NO}}_{2})]{\mathrm{ClO}}_{4}$ (NTENP) is studied by single-crystal inelastic neutron scattering. Parameters of the measured dispersion relation for magnetic excitations are compared to existing numerical results and used to determine the magnitude of bond-strength alternation. The measured neutron-scattering intensities are also analyzed, using the first-moment sum rules for the magnetic dynamic structure factor, to directly determine the modulation of ground-state exchange energies. These independently determined modulation parameters characterize the level of spin dimerization in NTENP. First-principles density-matrix renormalization-group calculations are used to study the relation between these two quantities.

DOI
10.1103/physrevb.69.144417

Related papers

Field theory analysis of S=1 antiferromagnetic bond-alternating chains in the dimer phase

Junya Tamaki, Masaki Oshikawa

Dynamics of $S=1$ antiferromagnetic bond-alternating chains in the dimer phase, in the vicinity of the critical point with the Haldane phase, is studied by a field theoretical method. This model is considered to represent the compound Ni(C${}_{9}$H${}_{24}$N${}_{4}$)(NO${}_{2}$)ClO${}_{4}$ (abbreviated as NTENP). We derive a sine-Gordon (SG) field theory as a low-energy effective model of this system, starting from a Tomonaga-Luttinger liquid at the critical point. Using the exact solution of the SG theory, we give a field theoretical picture of the low-energy excitation spectrum of NTENP. Results derived from our picture are in a good agreement with results of inelastic neutron scattering experiments on NTENP and numerical calculation of the dynamical structure factor. Furthermore, on the basis of the obtained theoretical picture, we predict that the sharp peaks corresponding to a single elementary excitation are absent in the Raman scattering spectrum of NTENP in contrast to the inelastic neutron scattering spectrum.

arXiv:1201.5170•Physical Review B•Apr 19, 2012•3 citations

Spin Excitations in an Anisotropic Bond-Alternating Quantum S=1 Chain in a Magnetic Field: Contrast to Haldane Spin Chains

Masayuki Hagiwara, L. P. Régnault, A. Zheludev +8 more

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)].

Physical Review Letters•May 4, 2005•45 citations

Spin excitations under fields in an anisotropic bond-alternating quantum S=1 chain: contrast with Haldane spin chains

Masayuki Hagiwara, L. P. Régnault, A. Zheludev +8 more

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)].

arXiv:cond-mat/0501207•Jan 10, 2005•0 citations

AnS=1/2 Impurity Spin in the AntiferromagneticS=1 Bond-Alternating Chain

Nobuyuki Ogawa, Toshiya Hikihara, Makoto Kaburagi +1 more

We explore low-lying excited states as well as the ground state of the antiferromagnetic S=1 bond-alternating chain with an S=1/2 impurity spin. For the case where the ground-state phase of the host system is the Haldane phase, we review a numerical analysis of the electron-spin-resonance experimental results on the NENP:Cu2+ system. For the case where the ground-state phase of the host system is the dimer phase, on the other hand, we calculate, using the exact-diagonalization method, the dependences of the energy differences between the ground and low-lying excited states upon both the impurity-host exchange constant and the single-ion-type anisotropy constant, and also calculate, using the density-matrix renormalization-group method, the external-magnetic-field dependence of the impurity-spin magnetizaion in the ground state. In these calculations, we keep the NTENP:Cu2+ system in mind to choose the value of the bond-alternation parameter. We find that a few low-lying excited states which are expected from the valence-bond-solid picture appear as the impurity states in the energy gap between the singlet ground and triplet first-excited states (the dimer gap). Furthermore, for certain values of the above constants, we find that the impurity-spin magnetizaion shows a clear jump at a magnetic field which is in the dimer-gap region or in the magnetization-plateau region of the host system, and also that the impurity-spin magnetizaion has a magnetic-field region where it decreases as a function of the magnetic field.

Progress of Theoretical Physics Supplement•Jan 1, 2002•0 citations

Dynamical structure factors of S=1 bond-alternating Heisenberg chains

Takahumi Suzuki, Sei-ichiro Suga

We calculate the dynamical structural factor of the $S=1$ bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~{q}_{c}$ and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in $0<~q<~{q}_{c}.$ As the bond-alternation becomes strong, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is $93%,$ which is slightly smaller than that in the $S=1$ Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.

arXiv:cond-mat/0309178•Physical review. B, Condensed matter•Oct 17, 2003•5 citations

Dominance of long-lived excitations in the antiferromagnetic spin-1 chain NENP

Shaolong Ma, C. Broholm, Daniel H. Reich +2 more

We have measured the dynamic spin correlation function for the quasi-one-dimensional S=1 antiferromagnet NENP by inelastic magnetic neutron scattering. Long-lived excitations (\ensuremath{\omega}\ensuremath{\tau}>10) exist for 0.3\ensuremath{\pi}\ensuremath{\le}q\ifmmode \tilde{}\else \~{}\fi{}\ensuremath{\le}\ensuremath{\pi}, and within error exhuast the total moment sum rule. The dispersion relation retains the fundamental periodicity of the spin chain, explicitly demonstrating the absence of broken translational symmetry in the ground state. The instantaneous spin correlation function follows a square-root Lorentzian for q\ifmmode \tilde{}\else \~{}\fi{}\ensuremath{\simeq}\ensuremath{\pi} but deviates substantially from this form for q\ifmmode \tilde{}\else \~{}\fi{}0.8\ensuremath{\pi}.

Physical Review Letters•Dec 14, 1992•169 citations
The quasi-one-dimensional bond-alternating S=1S=1S=1 quantum antiferromagnet [Ni{(N,N}^{\ensuremath{'}}$$\ensuremath{-}\mathrm{b}\mathrm{i}\mathrm{s}(3\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{l})\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{e}\ensuremath{-}1,3\ensuremath{-}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}(\ensuremath{\mu}\ensuremath{-}{\mathrm{NO}}_{2})]{\mathrm{ClO}}_{4} (NTENP) is studied by single-crystal inelastic neutron scattering. Parameters of the measured dispersion relation for magnetic excitations are compared to existing numerical results and used to determine the magnitude of bond-strength alternation. The measured neutron-scattering intensities are also analyzed, using the first-moment sum rules for the magnetic dynamic structure factor, to directly determine the modulation of ground-state exchange energies. These independently determined modulation parameters characterize the level of spin dimerization in NTENP. First-principles density-matrix renormalization-group calculations are used to study the relation between these two quantities.
Dynamics of S=1S=1S=1 antiferromagnetic bond-alternating chains in the dimer phase, in the vicinity of the critical point with the Haldane phase, is studied by a field theoretical method. This model is considered to represent the compound Ni(C9{}_{9}9​H24{}_{24}24​N4{}_{4}4​)(NO2{}_{2}2​)ClO4{}_{4}4​ (abbreviated as NTENP). We derive a sine-Gordon (SG) field theory as a low-energy effective model of this system, starting from a Tomonaga-Luttinger liquid at the critical point. Using the exact solution of the SG theory, we give a field theoretical picture of the low-energy excitation spectrum of NTENP. Results derived from our picture are in a good agreement with results of inelastic neutron scattering experiments on NTENP and numerical calculation of the dynamical structure factor. Furthermore, on the basis of the obtained theoretical picture, we predict that the sharp peaks corresponding to a single elementary excitation are absent in the Raman scattering spectrum of NTENP in contrast to the inelastic neutron scattering spectrum.
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)].
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)].
We explore low-lying excited states as well as the ground state of the antiferromagnetic S=1 bond-alternating chain with an S=1/2 impurity spin. For the case where the ground-state phase of the host system is the Haldane phase, we review a numerical analysis of the electron-spin-resonance experimental results on the NENP:Cu2+ system. For the case where the ground-state phase of the host system is the dimer phase, on the other hand, we calculate, using the exact-diagonalization method, the dependences of the energy differences between the ground and low-lying excited states upon both the impurity-host exchange constant and the single-ion-type anisotropy constant, and also calculate, using the density-matrix renormalization-group method, the external-magnetic-field dependence of the impurity-spin magnetizaion in the ground state. In these calculations, we keep the NTENP:Cu2+ system in mind to choose the value of the bond-alternation parameter. We find that a few low-lying excited states which are expected from the valence-bond-solid picture appear as the impurity states in the energy gap between the singlet ground and triplet first-excited states (the dimer gap). Furthermore, for certain values of the above constants, we find that the impurity-spin magnetizaion shows a clear jump at a magnetic field which is in the dimer-gap region or in the magnetization-plateau region of the host system, and also that the impurity-spin magnetizaion has a magnetic-field region where it decreases as a function of the magnetic field.
We calculate the dynamical structural factor of the S=1S=1S=1 bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in 0< q< qc0<~q<~{q}_{c}0< q< qc​ and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point, qc{q}_{c}qc​ shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in 0< q< qc.0<~q<~{q}_{c}.0< q< qc​. As the bond-alternation becomes strong, qc{q}_{c}qc​ shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is 9393%,93 which is slightly smaller than that in the S=1S=1S=1 Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.
We have measured the dynamic spin correlation function for the quasi-one-dimensional S=1 antiferromagnet NENP by inelastic magnetic neutron scattering. Long-lived excitations (\ensuremath{\omega}\ensuremath{\tau}>10) exist for 0.3\ensuremath{\pi}\ensuremath{\le}q\ifmmode \tilde{}\else \~{}\fi{}\ensuremath{\le}\ensuremath{\pi}, and within error exhuast the total moment sum rule. The dispersion relation retains the fundamental periodicity of the spin chain, explicitly demonstrating the absence of broken translational symmetry in the ground state. The instantaneous spin correlation function follows a square-root Lorentzian for q\ifmmode \tilde{}\else \~{}\fi{}\ensuremath{\simeq}\ensuremath{\pi} but deviates substantially from this form for q\ifmmode \tilde{}\else \~{}\fi{}0.8\ensuremath{\pi}.