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arXiv:1009.3206 · Physical Review B

Field and temperature dependence of NMR relaxation rate in the magnetic quadrupolar liquid phase of spin- 12 frustrated ferromagnetic chains

Masahiro Sato, Toshiya Hikihara, Tsutomu Momoi

Published Feb 10, 2011• 57 citations
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Abstract

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.

DOI
10.1103/physrevb.83.064405

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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/T11/{T}_{1}1/T1​ 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/T11/{T}_{1}1/T1​ in spin-12\frac{1}{2}21​ frustrated J1{J}_{1}J1​-J2{J}_{2}J2​ chains combining field-theoretical techniques with numerical data. Our results demonstrate that isotherms of 1/T11/{T}_{1}1/T1​ 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-12\frac{1}{2}21​ Heisenberg chain. The relevance of our results to quasi-one-dimensional edge-sharing cuprate magnets, such as LiCuVO4{\mathrm{LiCuVO}}_{4}LiCuVO4​, is discussed.
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-12\frac{1}{2}21​ zigzag chains. In this Rapid Communication, we point out that the temperature dependence of the NMR relaxation rate 1/T11/{T}_{1}1/T1​ in these multipolar TLLs is qualitatively different from that in more conventional TLLs of one-dimensional quantum magnets (e.g., the spin-12\frac{1}{2}21​ Heisenberg chain); 1/T11/{T}_{1}1/T1​ 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.
Abstract Modern theories of quantum magnetism predict exotic multipolar states in weakly interacting strongly frustrated spin-1/2 Heisenberg chains with ferromagnetic nearest neighbor (NN) inchain exchange in high magnetic fields. Experimentally these states remained elusive so far. Here we report strong indications of a magnetic field-induced nematic liquid arising above a field of ~13 T in the edge-sharing chain cuprate LiSbCuO4 ≡ LiCuSbO4. This interpretation is based on the observation of a field induced spin-gap in the measurements of the 7Li NMR spin relaxation rate T1−1 as well as a contrasting field-dependent power-law behavior of T1−1 vs. T and is further supported by static magnetization and ESR data. An underlying theoretical microscopic approach favoring a nematic scenario is based essentially on the NN XYZ exchange anisotropy within a model for frustrated spin-1/2 chains and is investigated by the DMRG technique. The employed exchange parameters are justified qualitatively by electronic structure calculations for LiCuSbO4.
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 NiCl2{}_{2}2​-4SC(NH2{}_{2}2​)2{}_{2}2​ (DTN), made of weakly coupled spin S=1S=1S=1 chains, interchain coupling plays an important role at low temperature as it leads to antiferromagnetic long-range order below 111 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/T11/{T}_{1}1/T1​, a key experimental quantity, and address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime in purely 111D quantum spins chains. They also comment on the experimental observation of the TLL regime, possibly masked by 333D long-range order in materials such as DTN.
Evidence for a magnetic field-induced "hidden" spin nematic phase in the frustrated and anisotropic spin-chain cuprate LiCuSbO4_44​
Modern theories of quantum magnetism predict exotic multipolar states in weakly interacting strongly frustrated spin-1/2 Heisenberg chains with ferromagnetic nearest neighbor (NN) inchain exchange in high magnetic fields. Experimentally these states remained elusive so far. Here we report the evidence for a long-sought magnetic field-induced nematic state arising above a field of ∼13\sim 13∼13 T in the edge-sharing chain cuprate LiSbCuO4_44​ ≡\equiv≡ LiCuSbO4_44​. This interpretation is based on the observation of a field induced spin-gap in the measurements of the 7^77Li NMR spin relaxation rate T1−1T_1^{-1}T1−1​ as well as a contrasting field-dependent power-law behavior of T1−1T_1^{-1}T1−1​ vs. TTT and is further supported by static magnetization and ESR data. An underlying theoretical microscopic approach favoring a nematic scenario is based essentially on the NN XYZ exchange anisotropy within a model for frustrated spin-1/2 chains. It is investigated by the DMRG technique. The employed exchange parameters are justified qualitatively by electronic structure calculations for LiCuSbO4_44​.
We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate 1/T11/{T}_{1}1/T1​ 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/T11/{T}_{1}1/T1​ 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 KKK. 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/T11/{T}_{1}1/T1​ experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.
We investigate NMR relaxation rates 1∕T11∕{T}_{1}1∕T1​ of quantum spin chains in magnetic fields. Universal properties for the divergence behavior of 1∕T11∕{T}_{1}1∕T1​ are obtained in the Tomonaga-Luttinger-liquid state. The results are discussed in comparison with experimental results.