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arXiv:0810.1403 · Physical Review B

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

Published Feb 13, 2009• 82 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.79.060406

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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.
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.
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.
At low temperature, critical one-dimensional (1D) quantum systems, such as spin chains, are theoretically described by the Tomonaga-Luttinger liquid (TLL) theory. In realistic quasi-1D materials, however, residual couplings are always present, and these systems eventually escape the theoretical 1D world to get eventually ordered at lower temperature. In order to define a genuine ``1D temperature window'' in quasi-1D systems for dynamical quantities such as the NMR relaxation rate or the dynamical structure factor that is probed by inelastic neutron scattering, the authors present a comprehensive theoretical study based on analytical as well as numerical approaches. They are able to describe the full temperature crossover for weakly coupled chains and, in particular, the universal 1D window where the TLL picture can be experimentally observed.
Repulsive Tomonaga-Luttinger Liquid in Quasi-one-dimensional Alternating Spin-1/21/21/2 Antiferromagnet NaVOPO4_44​
We probe the magnetic field-induced Tomonaga-Luttinger liquid (TLL) state in the bond-alternating spin-1/21/21/2 antiferromagnetic (AFM) chain compound NaVOPO4_44​ using thermodynamic as well as local μμμSR and 31^{31}31P NMR probes down to milli-K temperatures in magnetic fields up to 14~T. The μμμSR and NMR relaxation rates in the gapless TLL regime decay slowly following characteristic power-law behaviour, enabling us to directly determine the interaction parameter KKK as a function of the magnetic field. These estimates are cross-checked using magnetization and specific heat data. The field-dependent KKK lies in the range of 0.4<K<10.4 < K < 10.4<K<1 and indicates repulsive nature of interactions between the spinless fermions, in line with the theoretical predictions. This renders NaVOPO4_44​ the first experimental realization of TLL with repulsive fermionic interactions in hitherto studied S=1/2S=1/2S=1/2 bond-alternating AFM-AFM chain compounds.
Frustrated spin systems can show phases with spontaneous breaking of spin-rotational symmetry without the formation of local magnetic order. We study the dynamic response of the spin-nematic phase of one-dimensional spin-1/21/21/2 systems, characterized by slow large-distance decay of quadrupolar correlations, by numerically computing one-spin and two-spin dynamical structure factors at zero temperature using time-dependent density matrix renormalization group methods. We interpret the results in terms of an effective theory of gapped magnon excitations interacting with a quasicondensate of bound magnon pairs. This employs an extension of the well-known Tomonaga-Luttinger liquid theory which includes the magnon states as a mobile impurity. A good qualitative understanding of the characteristic thresholds and their intensity in the structure factors is obtained this way. Our results are useful in the interpretation of inelastic neutron scattering and resonant inelastic x-ray scattering experiments.
We present NMR measurements of a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)2CuBr4 under magnetic fields up to 15 T in the temperature range from 1.2 K down to 50 mK. From the splitting of NMR lines, we determine the phase boundary and the order parameter of the low-temperature (three-dimensional) long-range-ordered phase. In the Tomonaga-Luttinger regime above the ordered phase, NMR relaxation reflects characteristic power-law decay of spin correlation functions as 1/T1∝T(1/2K-1), which allows us to determine the interaction parameter K as a function of field. We find that field-dependent K varies within the 1<K<2 range, which signifies attractive interaction between the spinless fermions in the Tomonaga-Luttinger liquid.