arXiv:cond-mat/0612008 · Physical Review B

NMR relaxation of quantum spin chains in magnetic fields

Takahumi Suzuki, Sei-ichiro Suga

Published Nov 17, 2006• 8 citations

Abstract

We investigate NMR relaxation rates $1∕{T}_{1}$ of quantum spin chains in magnetic fields. Universal properties for the divergence behavior of $1∕{T}_{1}$ are obtained in the Tomonaga-Luttinger-liquid state. The results are discussed in comparison with experimental results.

DOI: 10.1103/physrevb.74.172410

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arXiv:cond-mat/0612008 · Physical Review B

NMR relaxation of quantum spin chains in magnetic fields

Takahumi Suzuki, Sei-ichiro Suga

Published Nov 17, 2006• 8 citations

arXiv HTML PDF

Abstract

We investigate NMR relaxation rates

1∕{T}_{1}

of quantum spin chains in magnetic fields. Universal properties for the divergence behavior of

1∕{T}_{1}

are obtained in the Tomonaga-Luttinger-liquid state. The results are discussed in comparison with experimental results.

DOI: 10.1103/physrevb.74.172410

Related papers

NMR relaxation rate and dynamical structure factors in nematic and multipolar liquids of frustrated spin chains under magnetic fields

Masahiro Sato, Tsutomu Momoi, Akira Furusaki

Recently, it has been shown that spin nematic (quadrupolar) or higher multipolar correlation functions exhibit a quasi-long-range order in the wide region of the field-induced Tomonaga-Luttinger-liquid (TLL) phase in spin- $\frac{1}{2}$ zigzag chains. In this Rapid Communication, we point out that the temperature dependence of the NMR relaxation rate $1/{T}_{1}$ in these multipolar TLLs is qualitatively different from that in more conventional TLLs of one-dimensional quantum magnets (e.g., the spin- $\frac{1}{2}$ Heisenberg chain); $1/{T}_{1}$ decreases with lowering temperature in multipolar TLL. We also discuss low-energy features in spin dynamical structure factors which are characteristic of the multipolar TLL phases.Recently, it has been shown that spin nematic (quadrupolar) or higher multipolar correlation functions exhibit a quasi-long-range order in the wide region of the field-induced Tomonaga-Luttinger-liquid (TLL) phase in spin-$\frac{1}{2}$ zigzag chains. In this Rapid Communication, we point out that the temperature dependence of the NMR relaxation rate $1/{T}_{1}$ in these multipolar TLLs is qualitatively different from that in more conventional TLLs of one-dimensional quantum magnets (e.g., the spin-$\frac{1}{2}$ Heisenberg chain); $1/{T}_{1}$ decreases with lowering temperature in multipolar TLL. We also discuss low-energy features in spin dynamical structure factors which are characteristic of the multipolar TLL phases.

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Quasi-one-dimensional (1D) antiferromagnets are good candidates to realize a Tomonaga-Luttinger liquid (TLL), describing 1D interacting quantum systems, provided 3D coupling remains small as compared to temperature. In systems such as NiCl ${}_{2}$ -4SC(NH ${}_{2}$ ) ${}_{2}$ (DTN), made of weakly coupled spin $S=1$ chains, interchain coupling plays an important role at low temperature as it leads to antiferromagnetic long-range order below $1$ K, corresponding to a Bose-Einstein condensate of magnons. Using time-dependent numerical simulations at finite temperature, the authors compute here the nuclear magnetic resonance (NMR) relaxation rate $1/{T}_{1}$ , a key experimental quantity, and address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime in purely $1$ D quantum spins chains. They also comment on the experimental observation of the TLL regime, possibly masked by $3$ D long-range order in materials such as DTN.Quasi-one-dimensional (1D) antiferromagnets are good candidates to realize a Tomonaga-Luttinger liquid (TLL), describing 1D interacting quantum systems, provided 3D coupling remains small as compared to temperature. In systems such as NiCl${}_{2}$-4SC(NH${}_{2}$)${}_{2}$ (DTN), made of weakly coupled spin $S=1$ chains, interchain coupling plays an important role at low temperature as it leads to antiferromagnetic long-range order below $1$ K, corresponding to a Bose-Einstein condensate of magnons. Using time-dependent numerical simulations at finite temperature, the authors compute here the nuclear magnetic resonance (NMR) relaxation rate $1/{T}_{1}$, a key experimental quantity, and address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime in purely $1$D quantum spins chains. They also comment on the experimental observation of the TLL regime, possibly masked by $3$D long-range order in materials such as DTN.

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It is generally difficult experimentally to distinguish magnetic multipolar orders in spin systems. Recently, it was proposed that the temperature dependence of the nuclear magnetic resonance relaxation rate $1/{T}_{1}$ can involve an indirect but clear signature of the field-induced spin nematic or multipolar Tomonaga-Luttinger (TL) liquid phase [M. Sato, T. Momoi, and A. Furusaki, Phys. Rev. B 79, 060406(R) (2009)]. In this paper, we evaluate accurately the field and temperature dependence of $1/{T}_{1}$ in spin- $\frac{1}{2}$ frustrated ${J}_{1}$ - ${J}_{2}$ chains combining field-theoretical techniques with numerical data. Our results demonstrate that isotherms of $1/{T}_{1}$ as a function of magnetic field also exhibit distinctive nonmonotonic behavior in spin nematic TL liquid, in contrast with the standard TL liquid in the spin- $\frac{1}{2}$ Heisenberg chain. The relevance of our results to quasi-one-dimensional edge-sharing cuprate magnets, such as ${\mathrm{LiCuVO}}_{4}$ , is discussed.It is generally difficult experimentally to distinguish magnetic multipolar orders in spin systems. Recently, it was proposed that the temperature dependence of the nuclear magnetic resonance relaxation rate $1/{T}_{1}$ can involve an indirect but clear signature of the field-induced spin nematic or multipolar Tomonaga-Luttinger (TL) liquid phase [M. Sato, T. Momoi, and A. Furusaki, Phys. Rev. B 79, 060406(R) (2009)]. In this paper, we evaluate accurately the field and temperature dependence of $1/{T}_{1}$ in spin-$\frac{1}{2}$ frustrated ${J}_{1}$-${J}_{2}$ chains combining field-theoretical techniques with numerical data. Our results demonstrate that isotherms of $1/{T}_{1}$ as a function of magnetic field also exhibit distinctive nonmonotonic behavior in spin nematic TL liquid, in contrast with the standard TL liquid in the spin-$\frac{1}{2}$ Heisenberg chain. The relevance of our results to quasi-one-dimensional edge-sharing cuprate magnets, such as ${\mathrm{LiCuVO}}_{4}$, is discussed.

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By means of nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system $({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}$ . In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.By means of nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system $({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}$. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

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Maxime Dupont

We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate $1/{T}_{1}$ in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The $1/{T}_{1}$ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter $K$ . We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the $1/{T}_{1}$ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate $1/{T}_{1}$ in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The $1/{T}_{1}$ is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter $K$. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the $1/{T}_{1}$ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.

arXiv:1902.07361Physical review. B./Physical review. BMay 28, 20192 citations

We investigate NMR relaxation rates

1∕{T}_{1}

of quantum spin chains in magnetic fields. Universal properties for the divergence behavior of

1∕{T}_{1}

are obtained in the Tomonaga-Luttinger-liquid state. The results are discussed in comparison with experimental results.

\frac{1}{2}

zigzag chains. In this Rapid Communication, we point out that the temperature dependence of the NMR relaxation rate

1/{T}_{1}

in these multipolar TLLs is qualitatively different from that in more conventional TLLs of one-dimensional quantum magnets (e.g., the spin-

\frac{1}{2}

Heisenberg chain);

1/{T}_{1}

decreases with lowering temperature in multipolar TLL. We also discuss low-energy features in spin dynamical structure factors which are characteristic of the multipolar TLL phases.

{}_{2}

-4SC(NH

{}_{2}

)

{}_{2}

(DTN), made of weakly coupled spin

S=1

chains, interchain coupling plays an important role at low temperature as it leads to antiferromagnetic long-range order below

1

K, corresponding to a Bose-Einstein condensate of magnons. Using time-dependent numerical simulations at finite temperature, the authors compute here the nuclear magnetic resonance (NMR) relaxation rate

1/{T}_{1}

, a key experimental quantity, and address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime in purely

1

D quantum spins chains. They also comment on the experimental observation of the TLL regime, possibly masked by

3

D long-range order in materials such as DTN.

1/{T}_{1}

can involve an indirect but clear signature of the field-induced spin nematic or multipolar Tomonaga-Luttinger (TL) liquid phase [M. Sato, T. Momoi, and A. Furusaki, Phys. Rev. B 79, 060406(R) (2009)]. In this paper, we evaluate accurately the field and temperature dependence of

1/{T}_{1}

in spin-

\frac{1}{2}

frustrated

{J}_{1}

{J}_{2}

chains combining field-theoretical techniques with numerical data. Our results demonstrate that isotherms of

1/{T}_{1}

as a function of magnetic field also exhibit distinctive nonmonotonic behavior in spin nematic TL liquid, in contrast with the standard TL liquid in the spin-

\frac{1}{2}

Heisenberg chain. The relevance of our results to quasi-one-dimensional edge-sharing cuprate magnets, such as

{\mathrm{LiCuVO}}_{4}

, is discussed.

({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}

. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

^{13}\mathrm{C}

nuclear magnetic resonance relaxation rate ${T}_{1}^{\ensuremath{-}1}$, and the field theoretical approach in the Luttinger liquid regime was performed. We found very good agreement between experiment and theory in the investigated temperature and field range. Our results demonstrate how spin-spin interactions strongly affect the spin dynamics of Heisenberg spin chain compounds in the vicinity of the quantum critical point.

We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate

1/{T}_{1}

in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The

1/{T}_{1}

is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter

K

. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the

1/{T}_{1}

experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.