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Physical Review Letters

Extended Universal Finite- T Renormalization of Excitations in a Class of One-Dimensional Quantum Magnets

A. Zheludev, Vasile Ovidiu Garlea, L. P. Régnault, Hirotaka Manaka, Alexei M. Tsvelik, Jae-Ho Chung

Published Apr 16, 2008• 43 citations
Publisher

Abstract

Temperature dependencies of gap energies and magnon lifetimes are measured in the quasi-one-dimensional $S=1/2$ gapped quantum magnets $({\mathrm{CH}}_{3}{)}_{2}{\mathrm{CHNH}}_{3}{\mathrm{CuCL}}_{3}$ ($\mathrm{IPA}\mathrm{\text{\ensuremath{-}}}{\mathrm{CuCl}}_{3}$, where IPA denotes isopropyl ammonium) and ${\mathrm{Cu}}_{2}{\mathrm{Cl}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{8}{\mathrm{C}}_{4}{\mathrm{SO}}_{2}$ ($\mathrm{Sul}\mathrm{\text{\ensuremath{-}}}{\mathrm{Cu}}_{2}{\mathrm{Cl}}_{4}$) using inelastic neutron scattering. The results are compared to those found in literature for $S=1$ Haldane spin chain materials and to theoretical calculations for the $O(3)$- and $O(N)$- quantum nonlinear $\ensuremath{\sigma}$-models. It is found that when the $T=0$ energy gap $\ensuremath{\Delta}$ is used as the temperature scale, all experimental and theoretical curves are identical to within system-dependent but temperature-independent scaling factors of the order of unity. This quasi-universality extends over a surprising broad $T$ range, at least up to $\ensuremath{\kappa}T\ensuremath{\sim}1.5\ensuremath{\Delta}$.

DOI
10.1103/physrevlett.100.157204

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Quasi-universal finite-TTT scaling in gapped one-dimensional quantum magnets
Temperature dependencies of gap energies and magnon lifetimes are measured in the quasi-1-dimensional S=1/2 gapped quantum magnets IPA-CuCl3 and Sul-Cu2Cl4 using inelastic neutron scattering. The results are compared to those found in literature for S=1 Haldane spin chain materials and to theoretical calculations for the O(3)- and O(N)- quantum non-linear sigma-models. It is found that when the T=0 energy gap Delta is used as the temperature scale, all experimental and theoretical curves are identical to within system-dependent but temperature-independent scaling factors of the order of unity. This quasi-universality extends over a surprising broad T range, at least up to kappa T ~ 1.5 Delta.
We have used a combination of neutron resonant spin-echo and triple-axis spectroscopies to determine the energy, fine structure, and linewidth of the magnon resonance in the model spin-1/2 ladder antiferromagnet IPA-CuCl(3) at temperatures T≪Δ(0)/k(B), where Δ(0) is the spin gap at T=0. In this low-temperature regime we find that the results deviate substantially from the predictions of the nonlinear sigma model proposed as a description of magnon excitations in one-dimensional quantum magnets and attribute these deviations to real-space and spin-space anisotropies in the spin Hamiltonian as well as scattering of magnon excitations from a dilute density of impurities. These effects are generic to experimental realizations of one-dimensional quantum magnets.
Neutron-scattering measurements on the one-dimensional gapped S=1S=1S=1 antiferromagnet, CsNiCl3,{\mathrm{CsNiCl}}_{3},CsNiCl3​, have shown that excitation corresponding to the Haldane mass gap $\ensuremath{\Delta}$ at low temperatures persists as a resonant feature to high temperatures. We find that the strong upward renormalization of the gap excitation, by a factor of three between 5 and 70 K, is more than enough to overcome its decreasing lifetime. We find that the gap lifetime is substantially shorter than that predicted by the scaling theory of Damle and Sachdev based on a classical dispersion for the Haldane excitations, but when we include their expected relativistic dispersion, the theory, in its low-temperature range of validity, gives a good account of experiment. The upward gap renormalization agrees with the nonlinear sigma model at low temperatures and even up to T of order $2\ensuremath{\Delta}$ provided an upper momentum cutoff is included.
The effect of thermal fluctuations on the dynamics of a gapped quantum magnet is studied using inelastic neutron scattering on copper nitrate, a model material for the spin-1/2, one-dimensional (1D) bond alternating Heisenberg chain. A large, highly deuterated, single-crystal sample of copper nitrate is produced using a solution growth method and measurements are made using the high-resolution backscattering spectrometer OSIRIS at the ISIS Facility. Theoretical calculations and numerical analysis are combined to interpret the physical origin of the thermal effects observed in the magnetic spectra. The primary observations are (1) a thermally induced central peak due to intraband scattering, which is similar to Villain scattering familiar from soliton systems in 1D, and (2) the one-magnon quasiparticle pole is seen to develop with temperature into an asymmetric continuum of scattering. We relate this asymmetric line broadening to a thermal strongly correlated state caused by hard-core constraints and quasiparticle interactions. These findings are a counter example to recent assertions of the universality of line broadening in 1D systems and are applicable to a broad range of quantum systems.
Two quasi-one-dimensional S=1S=1S=1 quantum antiferromagnetic materials, PbNi2V2O8{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}PbNi2​V2​O8​ and SrNi2V2O8,{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8},SrNi2​V2​O8​, are studied by inelastic neutron scattering on powder samples. A simple model Hamiltonian is proposed for the two systems and used to analyze the data. Quantitative information on in-chain and interchain interactions obtained from this analysis is discussed in the context of qualitatively different ground-state properties: magnetic long-range order in SrNi2V2O8{\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrNi2​V2​O8​ and disordered ``spin liquid'' Haldane-gap state in PbNi2V2O8.{\mathrm{PbNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}.PbNi2​V2​O8​.
The effect of thermal fluctuations on the dynamics of a gapped quantum magnet is studied using inelastic neutron scattering on copper nitrate, a model material for the one-dimensional (1D) bond alternating Heisenberg chain, combined with theoretical and numerical analysis. We observe and interpret the thermally induced central peak due to intraband scattering as well as the thermal development of an asymmetric continuum of scattering. We relate this asymmetric line broadening to hard core constraints and quasi-particle interactions. Our findings are a counter example to recent assertions of universality of line broadening in 1D systems and are to be considered as a new paradigm of behaviour, applicable to a broad range of quantum systems.