arXiv:cond-mat/0309178 · Physical review. B, Condensed matter

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

Takahumi Suzuki, Sei-ichiro Suga

Published Oct 17, 2003• 5 citations

Abstract

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.

DOI: 10.1103/physrevb.68.134429

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arXiv:cond-mat/0309178 · Physical review. B, Condensed matter

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

Takahumi Suzuki, Sei-ichiro Suga

Published Oct 17, 2003• 5 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physrevb.68.134429

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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.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:1201.5170Physical Review BApr 19, 20123 citations

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.

We calculate dynamical structure factors of the

S=1

bond-alternating Heisenberg chain with a single-ion anisotropy in transverse magnetic fields, using a continued fraction method based on the Lanczos algorithm. In the Haldane-gap phase and the dimer phase, dynamical structure factors show characteristic field dependence. Possible interpretations are discussed in the viewpoint of the field dependence of the excitation continuum. The numerical results are in qualitative agreement with recent results for inelastic neutron-scattering experiments on the

S=1

bond-alternating Heisenberg-chain compound

\mathrm{Ni}({\mathrm{C}}_{9}{\mathrm{D}}_{24}{\mathrm{N}}_{4})(\mathrm{N}{\mathrm{O}}_{2})\mathrm{Cl}{\mathrm{O}}_{4}

and the

S=1

Haldane-gap compound

\mathrm{Ni}{({\mathrm{C}}_{5}{\mathrm{D}}_{14}{\mathrm{N}}_{2})}_{2}{\mathrm{N}}_{3}(\mathrm{P}{\mathrm{F}}_{6})

in transverse magnetic fields.

We calculate the dynamical structure factors of the magnetization plateau state in the

S=\frac{1}{2}

bond-alternating spin chain with a next-nearest-neighbor interaction. The results show characteristic behaviors depending on the next-nearest-neighbor interaction $\ensuremath{\alpha}$ and the bond alternation \ensuremath{\delta}. We discuss the lower excited states in comparison with the exact excitation spectrums of an effective Hamiltonian. From the finite size effects, characteristics of the lowest excited states are investigated. The dispersionless mode of the lowest excitation appears in adequate sets of $\ensuremath{\alpha}$ and \ensuremath{\delta}, indicating that the lowest excitation is localized spatially and forms an isolated mode below the excitation continuum. We further calculate the static structure factors. The largest intensity is located at $q=\ensuremath{\pi}$ for small $\ensuremath{\delta}$ in fixed \ensuremath{\alpha}. With increasing \ensuremath{\delta}, the wave number of the largest intensity shifts towards $q=\ensuremath{\pi}/2,$ taking the incommensurate value.

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}

{}_{24}

{}_{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.