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arXiv:cond-mat/0108272 · Physical Review Letters

O17 NMR Study of q=0 Spin Excitations in a Nearly Ideal S=12 1D Heisenberg Antiferromagnet, Sr2CuO3 , up to 800 K

Kent R. Thurber, A. W. Hunt, Takashi Imai, F. C. Chou

Published Nov 26, 2001• 98 citations
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Abstract

We used ${}^{17}\mathrm{O}$ NMR to probe the uniform (wave vector $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) electron spin excitations up to 800 K in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ and separate the $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ from the $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}\frac{\ensuremath{\pi}}{a}$ staggered components. Our results support the logarithmic decrease of the uniform spin susceptibility below $T\ensuremath{\sim}0.015J$, where $J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2200\mathrm{K}$. From measurement of the dynamical spin susceptibility for $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ by the spin-lattice relaxation rate ${1/T}_{1}$, we demonstrate that the $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ mode of spin transport is ballistic at the $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ limit, but has a diffusion-like contribution at finite temperatures even for $T\ensuremath{\ll}J$.

DOI
10.1103/physrevlett.87.247202

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We used 17O{}^{17}\mathrm{O}17O NMR to probe the uniform (wave vector q=0q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0q=0) electron spin excitations up to 800 K in Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ and separate the q=0q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0q=0 from the q=\ifmmode±\else\textpm\fi\ensuremathπaq\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}\frac{\ensuremath{\pi}}{a}q=\ifmmode±\else\textpm\fia\ensuremathπ​ staggered components. Our results support the logarithmic decrease of the uniform spin susceptibility below T\ensuremath∼0.015JT\ensuremath{\sim}0.015JT\ensuremath∼0.015J, where J=2200KJ\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2200\mathrm{K}J=2200K. From measurement of the dynamical spin susceptibility for q=0q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0q=0 by the spin-lattice relaxation rate 1/T1{1/T}_{1}1/T1​, we demonstrate that the q=0q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0q=0 mode of spin transport is ballistic at the T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 limit, but has a diffusion-like contribution at finite temperatures even for T\ensuremath≪JT\ensuremath{\ll}JT\ensuremath≪J.
The NMR relaxation data on Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ [Phys. Rev. Lett. 76, 4612 (1996)] are reexamined and compared with the analytic theory of the dynamic susceptibility in the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg chain including multiplicative logarithmic corrections [Phys. Rev. Lett. 78, 539 (1997)]. Comparisons of the spin-lattice and the Gaussian spin-echo decay rates (1/T1{1/T}_{1}1/T1​ and 1/T2G{1/T}_{2G}1/T2G​) and their ratio all show good quantitative agreement. Our results demonstrate the importance of the logarithmic corrections in the analysis of experimental data for quasi-one-dimensional systems and indicate that the dynamics of Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ is well described by an S=1/2S=1/2S=1/2 one-dimensional Heisenberg model with a nearest-neighbor exchange.
Measurements of the spin-lattice relaxation rate 1∕T11∕{T}_{1}1∕T1​ by nuclear magnetic resonance for the one-dimensional Heisenberg antiferromagnet Sr2CuO3{\mathrm{Sr}}_{2}\mathrm{Cu}{\mathrm{O}}_{3}Sr2​CuO3​ have provided evidence for a diffusionlike contribution at finite temperature and small wave vector. By analyzing real-time data for the auto- and nearest-neighbor spin-spin correlation functions obtained by the density-matrix renormalization group I show that such a contribution indeed exists for temperatures T>JT>JT>J, where JJJ is the coupling constant, but that it becomes exponentially suppressed for T⪡JT⪡JT⪡J. I present evidence that the frequency dependence of 1∕T11∕{T}_{1}1∕T1​ in the Heisenberg case is smoothly connected to that in the free fermion case where the exponential suppression of the diffusionlike contribution is easily understood.
Proton spin-lattice relaxation times have been measured in the quasi-one-dimensional s=12s=\frac{1}{2}s=21​ Heisenberg antiferromagnetic compounds CuSeO4{\mathrm{O}}_{4}O4​\ifmmode\cdot\else\textperiodcentered\fi{}5H2{\mathrm{H}}_{2}H2​O and CuSO4{\mathrm{O}}_{4}O4​\ifmmode\cdot\else\textperiodcentered\fi{}5H2{\mathrm{H}}_{2}H2​O, in order to study the magnetic field dependence of the 1D quantum spin dynamics at various temperatures. Information is obtained on the low-frequency behavior of the spin autocorrelation functions for the linear chains. The transverse component shows at high TTT a marked decrease with magnetic field above the saturation field Bc{B}_{c}Bc​. Towards lower temperatures a pronounced maximum just below Bc{B}_{c}Bc​ develops and the decrease above Bc{B}_{c}Bc​ becomes more abrupt. The longitudinal component behaves more smoothly near and above Bc{B}_{c}Bc​. The field dependence of the relaxation rates is well explained at all nonzero temperatures by finite-chain calculations. For T=0T=0T=0 we present analytical calculations of autocorrelation functions based on the predominance of a two-parameter spin-wave continuum for the quantum spin dynamics yielding a nondivergent behavior at $\ensuremath{\omega}=0$ and B=0B=0B=0. Exact results are obtained for fields above Bc{B}_{c}Bc​. Further, an effective XY\mathrm{XY}XY approach is used for low but finite TTT. Here, good agreement is found with the proton relaxation data for very low temperatures.
The spin-lattice relaxation rate 1/T1{\mathit{T}}_{1}T1​ and the spin-echo decay rate 1/T2G{\mathit{T}}_{2\mathit{G}}T2G​ for the spin-1/2 antiferromagnetic Heisenberg chain are calculated using quantum Monte Carlo and maximum-entropy analytic continuation. The results are compared with recent analytical calculations by Sachdev. If the nuclear hyperfine form factor Aq{\mathit{A}}_{\mathit{q}}Aq​ is strongly peaked around q=\ensuremath{\pi}, the predicted low-temperature behavior [1/T1{\mathit{T}}_{1}T1​\ensuremath{\sim}ln1/2{\mathrm{ln}}^{1/2}ln1/2(1/T), 1/T2G{\mathit{T}}_{2\mathit{G}}T2G​\ensuremath{\sim}ln1/2{\mathrm{ln}}^{1/2}ln1/2(1/T)/\ensuremath{\surd}T] extends up to temperatures as high as T/J\ensuremath{\approxeq}0.5. If Aq{\mathit{A}}_{\mathit{q}}Aq​ has significant weight for q\ensuremath{\approxeq}0 there are large contributions from diffusive long-wavelength processes not taken into account in the theory, and very low temperatures are needed in order to observe the asymptotic T\ensuremath{\rightarrow}0 forms.
Magnetic susceptibility is measured on the one-dimensional spin 1/2 antiferromagnets Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ and SrCuO2\mathrm{Sr}{\mathrm{CuO}}_{2}SrCuO2​ using single crystals. Large, nearly contamination-free single crystals enable us to measure the intrinsic spin susceptibility over a wide temperature range between 5 and 800 K. The results are in excellent agreement with the recent calculation by Eggert, Affleck, and Takahashi, and the exchange interaction energy JJJ is estimated to be $2200\ifmmode\pm\else\textpm\fi{}200$ and $2100\ifmmode\pm\else\textpm\fi{}200\mathrm{K}$, respectively. In Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​, an isotropic susceptibility drop is observed below about 20 K, which is also consistent with the result of this rigorous calculation.
We consider the isotropic S=1S=1S=1 Heisenberg chain with a finite Haldane gap $\mathrm{\ensuremath{\Delta}}$ and use state-of-the-art numerical techniques to investigate its dynamical properties at finite temperature, focusing on the nuclear spin-lattice relaxation rate 1/T11/{T}_{1}1/T1​ measured in nuclear magnetic resonance (NMR) experiments, for instance. In particular, we analyze the contributions from modes with momenta close to $q\ensuremath{\approx}0$ and $q\ensuremath{\approx}\ensuremath{\pi}$ as a function of temperature. At high-temperature we observe spin diffusion, while at low-temperature we argue that a simple activated behavior $1/{T}_{1}\ensuremath{\propto}exp(\ensuremath{-}\mathrm{\ensuremath{\Delta}}/T)$ can be observed only at temperatures much smaller than the gap $\mathrm{\ensuremath{\Delta}}$.