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arXiv:cond-mat/0511004 · Physical Review Letters

Tomonaga-Luttinger Liquid in a Quasi-One-Dimensional S=1 Antiferromagnet Observed by Specific Heat Measurements

Masayuki Hagiwara, H. Tsujii, Costel R. Rotundu, B. Andraka, Y. Takano, Naoyuki Tateiwa, T. C. Kobayashi, T. Suzuki, Sei-ichiro Suga

Published Apr 12, 2006• 28 citations
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Abstract

Specific-heat experiments on single crystals of the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9H24N4)(NO2)ClO2 (NTENP) have been performed in magnetic fields applied both parallel and perpendicular to the spin chains. We have found for the parallel field configuration that the magnetic specific heat (C(mag)) is proportional to temperature (T) above a critical field H(c), at which the energy gap vanishes, in a temperature region above that of the long-range ordered state. The ratio C(mag)/T increases as the magnetic field approaches H(c) from above. The data are in good quantitative agreement with the prediction of the c= 1 conformal field theory in conjunction with the velocity of the excitations calculated by a numerical diagonalization, providing conclusive evidence for a Tomonaga-Luttinger liquid.

DOI
10.1103/physrevlett.96.147203

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Specific-heat experiments on single crystals of the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9H24N4)(NO2)ClO2 (NTENP) have been performed in magnetic fields applied both parallel and perpendicular to the spin chains. We have found for the parallel field configuration that the magnetic specific heat (C(mag)) is proportional to temperature (T) above a critical field H(c), at which the energy gap vanishes, in a temperature region above that of the long-range ordered state. The ratio C(mag)/T increases as the magnetic field approaches H(c) from above. The data are in good quantitative agreement with the prediction of the c= 1 conformal field theory in conjunction with the velocity of the excitations calculated by a numerical diagonalization, providing conclusive evidence for a Tomonaga-Luttinger liquid.
Motivated by recent studies on the quasi-one-dimensional (1D) antiferromagnet BaCo2V2O8, we investigate the Tomonaga-Luttinger-liquid properties of the 1D S=1/2 XXZ Heisenberg-Ising model in magnetic fields. By using the Bethe ansatz solution, thermodynamic quantities and the divergence exponent of the NMR relaxation rate are calculated. We observe a magnetization minimum as a function of temperature (T) close to the critical field. As the magnetic field approaches the critical field, the minimum temperature asymptotically approaches the universal relation in agreement with the recent results by Maeda et al. in Phys. Rev. Lett. 99 (2007) 057205. We observe T-linear specific heat below the temperature of the magnetization minimum. The field dependence of its coefficient agrees with the results based on conformal field theory. The field dependence of the divergence exponent of the NMR relaxation rate with decreasing temperature is obtained, indicating a change in the critical properties. The results are discussed in connection with experiments on BaCo2V2O8.
Dynamics of S=1S=1S=1 antiferromagnetic bond-alternating chains in the dimer phase, in the vicinity of the critical point with the Haldane phase, is studied by a field theoretical method. This model is considered to represent the compound Ni(C9{}_{9}9​H24{}_{24}24​N4{}_{4}4​)(NO2{}_{2}2​)ClO4{}_{4}4​ (abbreviated as NTENP). We derive a sine-Gordon (SG) field theory as a low-energy effective model of this system, starting from a Tomonaga-Luttinger liquid at the critical point. Using the exact solution of the SG theory, we give a field theoretical picture of the low-energy excitation spectrum of NTENP. Results derived from our picture are in a good agreement with results of inelastic neutron scattering experiments on NTENP and numerical calculation of the dynamical structure factor. Furthermore, on the basis of the obtained theoretical picture, we predict that the sharp peaks corresponding to a single elementary excitation are absent in the Raman scattering spectrum of NTENP in contrast to the inelastic neutron scattering spectrum.
The ground state phase diagrams and thermodynamic properties of a spin-1 bond-alternating Heisenberg antiferromagnetic chain with a single-ion anisotropy in longitudinal and transverse magnetic fields are investigated jointly by means of the infinite time evolving block decimation, the linearized tensor renormalization group, and the density matrix renormalization group methods. It is found that in the magnetic field--bond alternating ratio plane six phases such as singlet dimer, Haldane, two Tomonaga-Luttinger liquid, 1/2 magnetization plateau, and spin-polarized phases are identified in a longitudinal field, while in a transverse field there are five phases including singlet dimer, Haldane, Z2{Z}_{2}Z2​ symmetry breaking, quasi-1/2 magnetization plateau, and quasi-spin-polarized phases. A reentrant behavior of the staggered magnetization in a transverse field is observed. The quantum critical behaviors in longitudinal and transverse magnetic fields are disclosed to fall into different universality classes with corresponding conformal field central charge c=1c=1c=1 and 1/21/21/2, respectively. The experimental data of the compound NTENP under both longitudinal and transverse magnetic fields are nicely fitted, and the Luttinger liquid behavior of low-temperature specific heat experimentally observed is also confirmed.
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.
Inelastic neutron scattering experiments on the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependence of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q(parallel) = pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev, Phys. Rev. B 68, 134438 (2003)].
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{\mathrm{NaVOPO}}_{4}NaVOPO4​ using thermodynamic as well as local $\ensuremath{\mu}\mathrm{SR}$ and 31P^{31}\mathrm{P}31P NMR probes down to mK temperatures in magnetic fields up to 14 T. The $\ensuremath{\mu}\mathrm{SR}$ and NMR relaxation rates in the gapless TLL regime decay slowly following characteristic power-law behavior, enabling us to directly determine the interaction parameter KKK as a function of the magnetic field. These estimates are crosschecked 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 the repulsive nature of interactions between the spinless fermions, in line with the theoretical predictions. This renders NaVOPO4{\mathrm{NaVOPO}}_{4}NaVOPO4​ 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.