Physical Review B

NMR study of lineshifts and relaxation rates of the one-dimensional antiferromagnet LiCuVO4

C. Kegler, Norbert Büttgen, H.‐A. Krug von Nidda, Alois Loidl, R. Nath, A. V. Mahajan, Andrey Prokofiev, W. Aßmus

Published Mar 15, 2006• 21 citations

Abstract

NMR measurements were performed on single-crystalline samples of the one-dimensional Heisenberg antiferromagnet (1D HAF) ${\mathrm{LiCuVO}}_{4}$. We investigated $^{7}\mathrm{Li}$ and $^{51}\mathrm{V}$ NMR spectra, deduced the respective lineshifts $K(T)$, spin-lattice relaxation rates $1∕{T}_{1}$, and spin-spin relaxation rates $1∕{T}_{2}$ and $1∕{T}_{2G}$. The results are compared to theoretical predictions for the relaxation rates $1∕{T}_{1}(T)$ and $1∕{T}_{2G}(T)$ deduced from the dynamic susceptibility $\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega})$ of a 1D HAF spin chain as proposed by Sachdev [Phys. Rev. B 50, 13006 (1994)]. We document a correspondence between the anisotropic relaxation rates derived from electron paramagnetic resonance linewidth $\mathrm{\ensuremath{\Delta}}H(T)$ and nuclear magnetic resonance $1∕{T}_{1}(T)$, respectively, the former being well described in the framework of symmetric anisotropic exchange interactions for ${\mathrm{LiCuVO}}_{4}$ by Krug von Nidda et al. [Phys. Rev. B 65, 134445 (2002)].

DOI: 10.1103/physrevb.73.104418

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Physical Review B

NMR study of lineshifts and relaxation rates of the one-dimensional antiferromagnet LiCuVO4

C. Kegler, Norbert Büttgen, H.‐A. Krug von Nidda, Alois Loidl, R. Nath, A. V. Mahajan, Andrey Prokofiev, W. Aßmus

Published Mar 15, 2006• 21 citations

Publisher

Abstract

NMR measurements were performed on single-crystalline samples of the one-dimensional Heisenberg antiferromagnet (1D HAF)

{\mathrm{LiCuVO}}_{4}

. We investigated

^{7}\mathrm{Li}

and

^{51}\mathrm{V}

NMR spectra, deduced the respective lineshifts

K(T)

, spin-lattice relaxation rates

1∕{T}_{1}

, and spin-spin relaxation rates

1∕{T}_{2}

and

1∕{T}_{2G}

. The results are compared to theoretical predictions for the relaxation rates

1∕{T}_{1}(T)

and

1∕{T}_{2G}(T)

deduced from the dynamic susceptibility

\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega})

of a 1D HAF spin chain as proposed by Sachdev [Phys. Rev. B 50, 13006 (1994)]. We document a correspondence between the anisotropic relaxation rates derived from electron paramagnetic resonance linewidth

\mathrm{\ensuremath{\Delta}}H(T)

and nuclear magnetic resonance

1∕{T}_{1}(T)

, respectively, the former being well described in the framework of symmetric anisotropic exchange interactions for

{\mathrm{LiCuVO}}_{4}

by Krug von Nidda et al. [Phys. Rev. B 65, 134445 (2002)].

DOI: 10.1103/physrevb.73.104418

Related papers

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The spin-lattice relaxation rate 1/ ${\mathit{T}}_{1}$ and the spin-echo decay rate 1/ ${\mathit{T}}_{2\mathit{G}}$ 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 ${\mathit{A}}_{\mathit{q}}$ is strongly peaked around q=\ensuremath{\pi}, the predicted low-temperature behavior [1/ ${\mathit{T}}_{1}$ \ensuremath{\sim} ${\mathrm{ln}}^{1/2}$ (1/T), 1/ ${\mathit{T}}_{2\mathit{G}}$ \ensuremath{\sim} ${\mathrm{ln}}^{1/2}$ (1/T)/\ensuremath{\surd}T] extends up to temperatures as high as T/J\ensuremath{\approxeq}0.5. If ${\mathit{A}}_{\mathit{q}}$ 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.The spin-lattice relaxation rate 1/${\mathit{T}}_{1}$ and the spin-echo decay rate 1/${\mathit{T}}_{2\mathit{G}}$ 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 ${\mathit{A}}_{\mathit{q}}$ is strongly peaked around q=\ensuremath{\pi}, the predicted low-temperature behavior [1/${\mathit{T}}_{1}$\ensuremath{\sim}${\mathrm{ln}}^{1/2}$(1/T), 1/${\mathit{T}}_{2\mathit{G}}$\ensuremath{\sim}${\mathrm{ln}}^{1/2}$(1/T)/\ensuremath{\surd}T] extends up to temperatures as high as T/J\ensuremath{\approxeq}0.5. If ${\mathit{A}}_{\mathit{q}}$ 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.

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We consider the low-temperature behavior of NMR relaxation rates ${T}_{1}$ and ${T}_{2G}$ in the spin- $1/2$ antiferromagnetic chain. We find that ${T}_{1}\ensuremath{\propto}\mathrm{const}$ and ${T}_{2G}\ensuremath{\propto}\sqrt{T},$ with logarithmic corrections. We determine both constants and logarithmic terms by matching perturbative renormalization-group with exact results, so that the final expressions for the relaxation rates do not contain any free parameters. Our theoretical results are in excellent agreement with NMR experiments in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.$ We consider the low-temperature behavior of NMR relaxation rates ${T}_{1}$ and ${T}_{2G}$ in the spin-$1/2$ antiferromagnetic chain. We find that ${T}_{1}\ensuremath{\propto}\mathrm{const}$ and ${T}_{2G}\ensuremath{\propto}\sqrt{T},$ with logarithmic corrections. We determine both constants and logarithmic terms by matching perturbative renormalization-group with exact results, so that the final expressions for the relaxation rates do not contain any free parameters. Our theoretical results are in excellent agreement with NMR experiments in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.$

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NMR relaxation in the spin-1 Heisenberg chain

Sylvain Capponi, Maxime Dupont, Anders W. Sandvik +1 more

We consider the isotropic $S=1$ 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 $1/{T}_{1}$ 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 $\mathrm{\ensuremath{\Delta}}$.We consider the isotropic $S=1$ 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 $1/{T}_{1}$ 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 $\mathrm{\ensuremath{\Delta}}$.

arXiv:1905.12697Physical review. B./Physical review. BSep 9, 201918 citations

NMR measurements were performed on single-crystalline samples of the one-dimensional Heisenberg antiferromagnet (1D HAF)

{\mathrm{LiCuVO}}_{4}

. We investigated

^{7}\mathrm{Li}

and

^{51}\mathrm{V}

NMR spectra, deduced the respective lineshifts

K(T)

, spin-lattice relaxation rates

1∕{T}_{1}

, and spin-spin relaxation rates

1∕{T}_{2}

and

1∕{T}_{2G}

. The results are compared to theoretical predictions for the relaxation rates

1∕{T}_{1}(T)

and

1∕{T}_{2G}(T)

deduced from the dynamic susceptibility

\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega})

\mathrm{\ensuremath{\Delta}}H(T)

and nuclear magnetic resonance

1∕{T}_{1}(T)

, respectively, the former being well described in the framework of symmetric anisotropic exchange interactions for

{\mathrm{LiCuVO}}_{4}

by Krug von Nidda et al. [Phys. Rev. B 65, 134445 (2002)].

The spin-lattice relaxation rate 1/

{\mathit{T}}_{1}

and the spin-echo decay rate 1/

{\mathit{T}}_{2\mathit{G}}

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

{\mathit{A}}_{\mathit{q}}

is strongly peaked around q=\ensuremath{\pi}, the predicted low-temperature behavior [1/

{\mathit{T}}_{1}

\ensuremath{\sim}

{\mathrm{ln}}^{1/2}

(1/T), 1/

{\mathit{T}}_{2\mathit{G}}

\ensuremath{\sim}

{\mathrm{ln}}^{1/2}

(1/T)/\ensuremath{\surd}T] extends up to temperatures as high as T/J\ensuremath{\approxeq}0.5. If

{\mathit{A}}_{\mathit{q}}

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.

The NMR relaxation data on

{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}

[Phys. Rev. Lett. 76, 4612 (1996)] are reexamined and compared with the analytic theory of the dynamic susceptibility in the

S=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/T}_{1}

and

{1/T}_{2G}

) 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

{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}

is well described by an

S=1/2

one-dimensional Heisenberg model with a nearest-neighbor exchange.

1/{T}_{1}

of probe nuclei in the QC phase of 1D HAFs is obtained by considering Raman scattering processes which induce nuclear spin flips. The relaxation rate expression, which involves the temperature and the chemical potential, predicts scaling behavior of

1/{T}_{1}

consistent with recent experimental findings for quasi-1D HAF systems. A simple relationship between

1/{T}_{1}

and the deviation of the magnetization from saturation (${M}_{S}\ensuremath{-}M$) is predicted for the QC region.

Measurements of the spin-lattice relaxation rate

1∕{T}_{1}

by nuclear magnetic resonance for the one-dimensional Heisenberg antiferromagnet

{\mathrm{Sr}}_{2}\mathrm{Cu}{\mathrm{O}}_{3}

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>J

, where

J

is the coupling constant, but that it becomes exponentially suppressed for

T⪡J

. I present evidence that the frequency dependence of

1∕{T}_{1}

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.

We consider the low-temperature behavior of NMR relaxation rates

{T}_{1}

and

{T}_{2G}

in the spin-

1/2

antiferromagnetic chain. We find that ${T}_{1}\ensuremath{\propto}\mathrm{const}$ and ${T}_{2G}\ensuremath{\propto}\sqrt{T},$ with logarithmic corrections. We determine both constants and logarithmic terms by matching perturbative renormalization-group with exact results, so that the final expressions for the relaxation rates do not contain any free parameters. Our theoretical results are in excellent agreement with NMR experiments in

{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.

We consider the isotropic

S=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/{T}_{1}

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 $\mathrm{\ensuremath{\Delta}}$.