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Physical review. B, Condensed matter

Spin dynamics of the spin-Peierls transition in a quantum Heisenberg antiferromagnetic chain

Atsuko Kouzuki, 和子 川崎, Katsuhiro Nakamura

Published Nov 1, 1999• 10 citations
Publisher

Abstract

We investigate full dynamical behaviors of the spin-Peierls transition in $S=1/2$ Heisenberg antiferromagnetic chains by means of two-time Green's functions. The effect of temperature-dependent lattice displacements is incorporated self-consistently. Depending on temperature T and transfer wave number k, the imaginary part of the dynamical susceptibility ${\ensuremath{\chi}}_{\mathrm{zz}}^{\ensuremath{''}}(k,\ensuremath{\omega})$ shows rich structures: At $T=0,$ it is nonvanishing in the frequency region ${\ensuremath{\Omega}}_{M}(k)<\ensuremath{\Omega} (\ensuremath{\equiv}\ensuremath{\Elzxh}\ensuremath{\omega}/J)<{\ensuremath{\Omega}}_{H}(k).$ ${\ensuremath{\Omega}}_{M}(k)$ denotes a lower edge of a triplet magnetic excitation continuum, and is finite at $k=0$ due to lattice distortion. The upper edge ${\ensuremath{\Omega}}_{H}(k)$ increases as $k=0$ is approached, which is completely different from the feature without lattice distortion. An asymmetric line shape of ${\ensuremath{\chi}}_{\mathrm{zz}}^{\ensuremath{''}}(k,\ensuremath{\omega})$ is found with a peak at the frequency slightly higher than ${\ensuremath{\Omega}}_{M}(k).$ At $0<T<{T}_{\mathrm{SP}}$ (spin-Peierls transition point) there appears another structure due to thermal fluctuations in the lower-frequency region, $0<\ensuremath{\Omega}<{\ensuremath{\Omega}}_{L}(k).$ Since ${\ensuremath{\Omega}}_{L}(k)<{\ensuremath{\Omega}}_{M}(k),$ the forbidden band always exists at $T<{T}_{\mathrm{SP}}.$ Above ${T}_{\mathrm{SP}},$ ${\ensuremath{\chi}}_{\mathrm{zz}}^{\ensuremath{''}}(k,\ensuremath{\omega})$ reduces to a smooth curve characterized by a single broad maximum. These features in dynamics are systematically explained in terms of different quasiparticle scattering processes proper to the spin-Peierls phase. The results are compared with recent experimental data of neutron scattering for the inorganic compound ${\mathrm{CuGeO}}_{3}.$

DOI
10.1103/physrevb.60.12874

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We investigate full dynamical behaviors of the spin-Peierls transition in S=1/2S=1/2S=1/2 Heisenberg antiferromagnetic chains by means of two-time Green's functions. The effect of temperature-dependent lattice displacements is incorporated self-consistently. Depending on temperature T and transfer wave number k, the imaginary part of the dynamical susceptibility \ensuremathχzz\ensuremath′′(k,\ensuremathω){\ensuremath{\chi}}_{\mathrm{zz}}^{\ensuremath{''}}(k,\ensuremath{\omega})\ensuremathχzz\ensuremath′′​(k,\ensuremathω) shows rich structures: At T=0,T=0,T=0, it is nonvanishing in the frequency region \ensuremathΩM(k)<\ensuremathΩ(\ensuremath≡\ensuremath\Elzxh\ensuremathω/J)<\ensuremathΩH(k).{\ensuremath{\Omega}}_{M}(k)<\ensuremath{\Omega} (\ensuremath{\equiv}\ensuremath{\Elzxh}\ensuremath{\omega}/J)<{\ensuremath{\Omega}}_{H}(k).\ensuremathΩM​(k)<\ensuremathΩ(\ensuremath≡\ensuremath\Elzxh\ensuremathω/J)<\ensuremathΩH​(k). \ensuremathΩM(k){\ensuremath{\Omega}}_{M}(k)\ensuremathΩM​(k) denotes a lower edge of a triplet magnetic excitation continuum, and is finite at k=0k=0k=0 due to lattice distortion. The upper edge \ensuremathΩH(k){\ensuremath{\Omega}}_{H}(k)\ensuremathΩH​(k) increases as k=0k=0k=0 is approached, which is completely different from the feature without lattice distortion. An asymmetric line shape of \ensuremathχzz\ensuremath′′(k,\ensuremathω){\ensuremath{\chi}}_{\mathrm{zz}}^{\ensuremath{''}}(k,\ensuremath{\omega})\ensuremathχzz\ensuremath′′​(k,\ensuremathω) is found with a peak at the frequency slightly higher than \ensuremathΩM(k).{\ensuremath{\Omega}}_{M}(k).\ensuremathΩM​(k). At 0<T<TSP0<T<{T}_{\mathrm{SP}}0<T<TSP​ (spin-Peierls transition point) there appears another structure due to thermal fluctuations in the lower-frequency region, 0<\ensuremathΩ<\ensuremathΩL(k).0<\ensuremath{\Omega}<{\ensuremath{\Omega}}_{L}(k).0<\ensuremathΩ<\ensuremathΩL​(k). Since \ensuremathΩL(k)<\ensuremathΩM(k),{\ensuremath{\Omega}}_{L}(k)<{\ensuremath{\Omega}}_{M}(k),\ensuremathΩL​(k)<\ensuremathΩM​(k), the forbidden band always exists at T<TSP.T<{T}_{\mathrm{SP}}.T<TSP​. Above TSP,{T}_{\mathrm{SP}},TSP​, \ensuremathχzz\ensuremath′′(k,\ensuremathω){\ensuremath{\chi}}_{\mathrm{zz}}^{\ensuremath{''}}(k,\ensuremath{\omega})\ensuremathχzz\ensuremath′′​(k,\ensuremathω) reduces to a smooth curve characterized by a single broad maximum. These features in dynamics are systematically explained in terms of different quasiparticle scattering processes proper to the spin-Peierls phase. The results are compared with recent experimental data of neutron scattering for the inorganic compound CuGeO3.{\mathrm{CuGeO}}_{3}.CuGeO3​.
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