arXiv:cond-mat/0109065 · Journal of Applied Physics

Continuum spin excitations in S=1 one-dimensional antiferromagnet

Igor A. Zaliznyak

Published May 15, 2002• 6 citations

Abstract

We present detailed measurement of the nonhydrodynamic part of the spin excitation spectrum in the model quasi-one-dimensional S=1 antiferromagnet CsNiCl3 by inelastic magnetic neutron scattering. In the better part of the Brillouin zone the effect of interchain coupling is negligible, and the spin dynamics reflects that of a single Haldane chain. We find that at q≲0.6π this quantum spin system ceases to support coherent propagating excitation, which gradually turns into a continuum band of states, whose width grows with decreasing q. This finding is consistently verified under different resolution conditions, obtained with two different high-luminosity experimental setups.

DOI: 10.1063/1.1456440

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arXiv:cond-mat/0109065 · Journal of Applied Physics

Continuum spin excitations in S=1 one-dimensional antiferromagnet

Igor A. Zaliznyak

Published May 15, 2002• 6 citations

arXiv HTML PDF

Abstract

DOI: 10.1063/1.1456440

Related papers

Continuum in the Spin-Excitation Spectrum of a Haldane Chain Observed by Neutron Scattering in CsNiCl3

Igor A. Zaliznyak, S.-H. Lee, S. V. Petrov

The spin-excitation continuum, expected to dominate the low-energy fluctuation spectrum in the Haldane spin chain around the Brillouin zone center, $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ , is directly observed by inelastic magnetic neutron scattering in the $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ quasi-1D antiferromagnet ${\mathrm{CsNiCl}}_{3}$ . We find that the single mode approximation fails, and that a finite energy width appears in the dynamic correlation function $S(q,\ensuremath{\omega})$ for $q\ensuremath{\lesssim}0.5\ensuremath{\pi}$. The width increases with decreasing $q$ , while $S(q,\ensuremath{\omega})$ acquires an asymmetric shape qualitatively similar to that predicted for the two-magnon continuum in the nonlinear $\ensuremath{\sigma}$-model.The spin-excitation continuum, expected to dominate the low-energy fluctuation spectrum in the Haldane spin chain around the Brillouin zone center, $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$, is directly observed by inelastic magnetic neutron scattering in the $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ quasi-1D antiferromagnet ${\mathrm{CsNiCl}}_{3}$. We find that the single mode approximation fails, and that a finite energy width appears in the dynamic correlation function $S(q,\ensuremath{\omega})$ for $q\ensuremath{\lesssim}0.5\ensuremath{\pi}$. The width increases with decreasing $q$, while $S(q,\ensuremath{\omega})$ acquires an asymmetric shape qualitatively similar to that predicted for the two-magnon continuum in the nonlinear $\ensuremath{\sigma}$-model.

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A full description of a series of spin-wave measurements in ${\mathrm{CsNiCl}}_{3}$ in the three-dimensional (3D) and one-dimensional (1D) phases and their analysis to provide the first experimental evidence for the Haldane gap is presented. Neutron scattering experiments were performed on a single crystal of ${\mathrm{CsNiCl}}_{3}$ with both (h,0,l) and (h,h,l) as the scattering plane. The order parameter in both 3D phases was measured and the spin-wave dispersion determined in the lower phase. The spin-wave spectrum calculated from a dynamic susceptibility method was compared with the experimental response in the lower 3D phase to obtain the following values for the exchange and anisotropy constants: J=0.345\ifmmode\pm\else\textpm\fi{}0.008 THz, J'=0.0060\ifmmode\pm\else\textpm\fi{}0.005 THz, and D=-0.0130\ifmmode\pm\else\textpm\fi{}0.0015 THz. These parameters confirm that ${\mathrm{CsNiCl}}_{3}$ in its disordered phase is a good approximation to a one-dimensional Heisenberg antiferromagnet. In the 1D phase the gap frequency for an isolated chain of ${\mathrm{Ni}}^{2+}$ ions is found to be 0.32 THz close to the gap estimated in finite-chain calculations. The results constitute experimental support for the Haldane conjecture that the excitations of integer-spin chains, unlike half-integer--spin chains, exhibit an apparent anisotropy that arises not from the underlying isotropic Hamiltonian, but from many-body effects.A full description of a series of spin-wave measurements in ${\mathrm{CsNiCl}}_{3}$ in the three-dimensional (3D) and one-dimensional (1D) phases and their analysis to provide the first experimental evidence for the Haldane gap is presented. Neutron scattering experiments were performed on a single crystal of ${\mathrm{CsNiCl}}_{3}$ with both (h,0,l) and (h,h,l) as the scattering plane. The order parameter in both 3D phases was measured and the spin-wave dispersion determined in the lower phase. The spin-wave spectrum calculated from a dynamic susceptibility method was compared with the experimental response in the lower 3D phase to obtain the following values for the exchange and anisotropy constants: J=0.345\ifmmode\pm\else\textpm\fi{}0.008 THz, J'=0.0060\ifmmode\pm\else\textpm\fi{}0.005 THz, and D=-0.0130\ifmmode\pm\else\textpm\fi{}0.0015 THz. These parameters confirm that ${\mathrm{CsNiCl}}_{3}$ in its disordered phase is a good approximation to a one-dimensional Heisenberg antiferromagnet. In the 1D phase the gap frequency for an isolated chain of ${\mathrm{Ni}}^{2+}$ ions is found to be 0.32 THz close to the gap estimated in finite-chain calculations. The results constitute experimental support for the Haldane conjecture that the excitations of integer-spin chains, unlike half-integer--spin chains, exhibit an apparent anisotropy that arises not from the underlying isotropic Hamiltonian, but from many-body effects.

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Measurement of the spin-excitation continuum in one-dimensional KCuF3 using neutron scattering

D. M. Tennant, Roger Arthur Cowley, S. E. Nagler +1 more

In this, and the following paper, we present the results of a detailed experimental investigation into the spin dynamics of the quasi-one-dimensional S=1/2 Heisenberg antiferromagnet ${\mathrm{KCuF}}_{3}$ . In this paper we report results of inelastic neutron-scattering measurements made using the MARI time-of-flight spectrometer at the Rutherford Appleton Laboratory. Measurement of the magnetic excitation spectrum was made in both the low-temperature phase, where the chains are ordered together, and in the high-temperature phase, where the correlations between chains become unimportant. We compare our measurements with the M\"uller ansatz, which is identified with a two-spinon cross section, and find excellent agreement with this. The effect of temperature on the excitation continuum was also investigated. A series of measurements were made at temperatures ranging from 20 to 200 K. These results are compared to the predictions of field theory for the one-dimensional Heisenberg chain. Again good agreement is found with the theoretical predictions. In the following paper measurements of the low-energy scattering in the ordered phase, made on a triple-axis spectrometer, are presented.In this, and the following paper, we present the results of a detailed experimental investigation into the spin dynamics of the quasi-one-dimensional S=1/2 Heisenberg antiferromagnet ${\mathrm{KCuF}}_{3}$. In this paper we report results of inelastic neutron-scattering measurements made using the MARI time-of-flight spectrometer at the Rutherford Appleton Laboratory. Measurement of the magnetic excitation spectrum was made in both the low-temperature phase, where the chains are ordered together, and in the high-temperature phase, where the correlations between chains become unimportant. We compare our measurements with the M\"uller ansatz, which is identified with a two-spinon cross section, and find excellent agreement with this. The effect of temperature on the excitation continuum was also investigated. A series of measurements were made at temperatures ranging from 20 to 200 K. These results are compared to the predictions of field theory for the one-dimensional Heisenberg chain. Again good agreement is found with the theoretical predictions. In the following paper measurements of the low-energy scattering in the ordered phase, made on a triple-axis spectrometer, are presented.

Physical review. B, Condensed matterNov 1, 1995157 citations

Energy Separation of Single-Particle and Continuum States in an S=1/2 Weakly Coupled Chains Antiferromagnet

A. Zheludev, M. Kenzelmann, S. Raymond +7 more

Inelastic neutron scattering is used to study transverse-polarized magnetic excitations in the quasi-one-dimensional $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ antiferromagnet ${\mathrm{BaCu}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}$ , where the saturation value for the N\'eel order parameter is ${m}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.12{\ensuremath{\mu}}_{\mathrm{B}}$ per spin. At low energies the spectrum is totally dominated by resolution-limited spin-wave-like excitations. An excitation continuum sets in above a well-defined threshold frequency. Experimental results are discussed in the context of current theories for weakly interacting quantum half-integer-spin chains.Inelastic neutron scattering is used to study transverse-polarized magnetic excitations in the quasi-one-dimensional $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ antiferromagnet ${\mathrm{BaCu}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}$, where the saturation value for the N\'eel order parameter is ${m}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.12{\ensuremath{\mu}}_{\mathrm{B}}$ per spin. At low energies the spectrum is totally dominated by resolution-limited spin-wave-like excitations. An excitation continuum sets in above a well-defined threshold frequency. Experimental results are discussed in the context of current theories for weakly interacting quantum half-integer-spin chains.

arXiv:cond-mat/0006426Physical Review LettersNov 27, 200054 citations

The spin-excitation continuum, expected to dominate the low-energy fluctuation spectrum in the Haldane spin chain around the Brillouin zone center,

q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

, is directly observed by inelastic magnetic neutron scattering in the

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

quasi-1D antiferromagnet

{\mathrm{CsNiCl}}_{3}

. We find that the single mode approximation fails, and that a finite energy width appears in the dynamic correlation function $S(q,\ensuremath{\omega})$ for $q\ensuremath{\lesssim}0.5\ensuremath{\pi}$. The width increases with decreasing

q

, while $S(q,\ensuremath{\omega})$ acquires an asymmetric shape qualitatively similar to that predicted for the two-magnon continuum in the nonlinear $\ensuremath{\sigma}$-model.

We report inelastic time-of-flight and triple-axis neutron scattering measurements of the excitation spectrum of the coupled antiferromagnetic spin-1 Heisenberg chain system

{\mathrm{CsNiCl}}_{3}.

Measurements over a wide range of wave-vector transfers along the chain confirm that above

{T}_{N} {\mathrm{CsNiCl}}_{3}

is in a quantum-disordered phase with an energy gap in the excitation spectrum. The spin correlations fall off exponentially with increasing distance with a correlation length $\ensuremath{\xi}=4.0(2)$ sites at

T=6.2\mathrm{K}.

This is shorter than the correlation length for an antiferromagnetic spin-1 Heisenberg chain at this temperature, suggesting that the correlations perpendicular to the chain direction and associated with the interchain coupling lower the single-chain correlation length. A multiparticle continuum is observed in the quantum-disordered phase in the region in reciprocal space where antiferromagnetic fluctuations are strongest, extending in energy up to twice the maximum of the dispersion of the well-defined triplet excitations. We show that the continuum satisfies the Hohenberg-Brinkman sum rule. The dependence of the multiparticle continuum on the chain wave vector resembles that of the two-spinon continuum in antiferromagnetic spin-1/2 Heisenberg chains. This suggests the presence of spin-1/2 degrees of freedom in

{\mathrm{CsNiCl}}_{3}

for

T<~12 \mathrm{K},

possibly caused by multiply frustrated interchain interactions.

A full description of a series of spin-wave measurements in

{\mathrm{CsNiCl}}_{3}

in the three-dimensional (3D) and one-dimensional (1D) phases and their analysis to provide the first experimental evidence for the Haldane gap is presented. Neutron scattering experiments were performed on a single crystal of

{\mathrm{CsNiCl}}_{3}

with both (h,0,l) and (h,h,l) as the scattering plane. The order parameter in both 3D phases was measured and the spin-wave dispersion determined in the lower phase. The spin-wave spectrum calculated from a dynamic susceptibility method was compared with the experimental response in the lower 3D phase to obtain the following values for the exchange and anisotropy constants: J=0.345\ifmmode\pm\else\textpm\fi{}0.008 THz, J'=0.0060\ifmmode\pm\else\textpm\fi{}0.005 THz, and D=-0.0130\ifmmode\pm\else\textpm\fi{}0.0015 THz. These parameters confirm that

{\mathrm{CsNiCl}}_{3}

in its disordered phase is a good approximation to a one-dimensional Heisenberg antiferromagnet. In the 1D phase the gap frequency for an isolated chain of

{\mathrm{Ni}}^{2+}

ions is found to be 0.32 THz close to the gap estimated in finite-chain calculations. The results constitute experimental support for the Haldane conjecture that the excitations of integer-spin chains, unlike half-integer--spin chains, exhibit an apparent anisotropy that arises not from the underlying isotropic Hamiltonian, but from many-body effects.

In this, and the following paper, we present the results of a detailed experimental investigation into the spin dynamics of the quasi-one-dimensional S=1/2 Heisenberg antiferromagnet

{\mathrm{KCuF}}_{3}

. In this paper we report results of inelastic neutron-scattering measurements made using the MARI time-of-flight spectrometer at the Rutherford Appleton Laboratory. Measurement of the magnetic excitation spectrum was made in both the low-temperature phase, where the chains are ordered together, and in the high-temperature phase, where the correlations between chains become unimportant. We compare our measurements with the M\"uller ansatz, which is identified with a two-spinon cross section, and find excellent agreement with this. The effect of temperature on the excitation continuum was also investigated. A series of measurements were made at temperatures ranging from 20 to 200 K. These results are compared to the predictions of field theory for the one-dimensional Heisenberg chain. Again good agreement is found with the theoretical predictions. In the following paper measurements of the low-energy scattering in the ordered phase, made on a triple-axis spectrometer, are presented.

Inelastic neutron scattering is used to study transverse-polarized magnetic excitations in the quasi-one-dimensional

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

antiferromagnet

{\mathrm{BaCu}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}

, where the saturation value for the N\'eel order parameter is ${m}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.12{\ensuremath{\mu}}_{\mathrm{B}}$ per spin. At low energies the spectrum is totally dominated by resolution-limited spin-wave-like excitations. An excitation continuum sets in above a well-defined threshold frequency. Experimental results are discussed in the context of current theories for weakly interacting quantum half-integer-spin chains.