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Hone, Daniel; Scherer, C.; Borsa, F.

doi:10.1103/physrevb.9.965

Cited by 94 publications

(29 citation statements)

References 19 publications

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“…Sachdev 7 determined the temperature dependence of the NMR spinlattice ͑1/T 1 ͒ and the Gaussian spin-spin ͑1/T 2G ͒ relaxation rates for half-integer spin chains for k B T / J Ӷ 1 as 1/T 1 = constant and 1 / T 2G ϰ 1/ ͱ T. Quantum Monte Carlo calculations by Sandvik 8 support these results over an appropriate temperature range. These results are at variance from those for classical spin chains S = ϱ, where theory predicts 9 1/T 1 and 1 / T 2G ϰ T −3/2 .…”

Section: Introductioncontrasting

confidence: 52%

Study of one-dimensional nature ofS=1∕2(Sr,Ba)2
Nath
¹
,
Mahajan
²
,
Büttgen
³

et al. 2005
Phys. Rev. B
68
18
58
1
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The magnetic behavior of the low-dimensional phosphates ͑Sr, Ba͒ 2 Cu͑PO 4 ͒ 2 and BaCuP 2 O 7 was investigated by means of magnetic susceptibility and 31 P nuclear magnetic resonance ͑NMR͒ measurements. We present here the NMR shift, the spin-lattice ͑1/T 1 ͒, and spin-spin ͑1/T 2 ͒ relaxation-rate data over a wide temperature range 0.02 K ഛ T ഛ 300 K. The temperature dependence of the NMR shift K͑T͒ is well described by the S =1/2 Heisenberg antiferromagnetic chain model ͓D. C. Johnston, R. K. Kremer, M. Troyer, X. Wang, A. Klümper, S. L. Bud'ko, A. F. Panchula, and P. C. Canfield, Phys. Rev. B 61, 9558 ͑2000͔͒ with an intrachain exchange of J / k B Ӎ 165, 151, and 108 K in Sr 2 Cu͑PO 4 ͒ 2 , Ba 2 Cu͑PO 4 ͒ 2 , and BaCuP 2 O 7 , respectively. Deviations from Johnston's expression are seen for all these compounds in the T dependence of K͑T͒ at low temperatures. 31 P is located symmetrically between the Cu ions and fluctuations of the staggered susceptibility at q = / a should be filtered out due to vanishing of the geometrical form factor. However, the qualitative temperature dependence of our 31 P NMR 1 / T 1 indicates that relaxation due to fluctuations around q = / a ͑but / a͒ have the same T dependence as those at q = / a and apparently dominate. Our measurements suggest the presence of magnetic ordering at 0.85 K in BaCuP 2 O 7 ͑J / k B Ӎ 108 K͒ and a clear indication of a phase transition ͑divergence͒ in 1 / T 1 ͑T͒, 1/T 2 ͑T͒, and a change of the line shape is observed. This enables us to investigate the one-dimensional ͑1D͒ behavior over a wide temperature range. We find that 1 / T 1 is nearly T independent at low temperatures ͑1 Kഛ T ഛ 10 K͒, which is theoretically expected for 1D chains when relaxation is dominated by fluctuations of the staggered susceptibility. At high temperatures, 1 / T 1 varies nearly linearly with temperature, which accounts for contribution of the uniform susceptibility.

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Section: Introductioncontrasting

confidence: 52%

Study of one-dimensional nature ofS=1∕2(Sr,Ba)2
Nath
¹
,
Mahajan
²
,
Büttgen
³

et al. 2005
Phys. Rev. B
68
18
58
1
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“…By various investigations on different s = 1 2 AF compounds it has been found that the relaxation time T 2 at small magnetic fields and low T has only a very weak temperature dependence (Ehrenfreund et al 1973, Azevedo et al 1979, Groen et al 1978, 1979, 1980). For the s = 5 2 AF TMMC, on the other hand, Richards and Borsa (1974) and Hone et al (1974) have observed that T 1 has a very strong temperature dependence in agreement with a diverging F µµ (ω = 0) for T → 0. In view of the increasing number of available quasi-1D AF compounds with different spin quantum numbers it would be interesting to investigate such s-dependent effects more systematically.…”

Section: Isotropic S ≥mentioning

confidence: 71%

Quantum spin dynamics of the one-dimensional planar antiferromagnet

Müller

Thomas

Puga

et al. 1981

J. Phys. C: Solid State Phys.

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The T = 0 dynamics of the one-dimensional s = 1 2 planar anti ferromagnet is studied by an approach which consists of exact analytic calculations in the Bethe formalism and numerical finite-chain calculations on rings up to 10 spins. Our method makes use of well known critical exponents for the correlation functions and of exact sum rules. We obtain approximate analytic expressions for both the out-of-plane and the inplane dynamic structure factors, and for related quantities such as integrated intensities, susceptibilities and autocorrelation functions. The results are discussed in relation to possible experiments on quasi-1D magnetic compounds at low T . Our calculations make clear that the T = 0 dynamic structure factors are dominated by two-parameter continua of excitations rather than by single branches of spin-waves as predicted by classical spin-wave theory. By varying the planar anisotropy the autocorrelation functions display interesting features in their long-time asymptotic behaviour, such as a crossover from a uniform power-law decay to an oscillatory decay and a crossover between oscillatory decays with different frequencies. We conjecture a possibility of approaching the classical limit s = ∞ starting from the quantum limit s = 1 2 . This provides a qualitative, and in some aspects even quantitative, understanding of the dynamical behaviour of s > 1 2 systems in terms of a quantum approach.

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“…8,9) Here we estimate such a contribution to (1/T 1 ) 0 . The cutoff effect is taken into account phenomenologically by multiplying the exponential decay to the longitudinal diffusive spin correlation function as S z q (t)S z −q (0) ∝ exp(−D s q 2 t) exp(−ω c t) where ω c is the cutoff frequency.…”

Section: )mentioning

confidence: 99%

“…8,9,10,11,12,13) As to the S = 1/2 chain, an analysis of the ω dependence of 1/T 1 at the Cu site in Sr 2 CuO 3 based on the classical spin-diffusion theory gives an unusually high value of the spin diffusion constant compared with the classical value. 14) This suggests the absence of spin diffusion in the low-temperature limit in consistency with the field-theoretical 2) and perturbative 3) approaches.…”

Section: §1 Introductionmentioning

confidence: 99%

Spin Diffusion in theS=1/2 Quasi One-Dimensional Antiferromagnet α-VO(PO₃)₂via³¹P NMR

et al. 2001

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Low-frequency spin dynamics in the S = 1/2 antiferromagnetic spin-chain compound α-VO(PO3)2 has been studied by means of 31 P NMR. The nuclear spin-lattice relaxation rate 1/T1 at the P site exhibits H −1/2 dependence on the applied magnetic field (H) at temperatures (T ) well above the intrachain coupling strength J/kB = 3.50 K indicating one-dimensional diffusive spin dynamics. The diffusive contribution to 1/T1 decreases on cooling as electronic spins acquire short-range antiferromagnetic correlations within the chain, and vanishes almost entirely around T ≈ J/kB. This is accompanied by an apparent increase of the spin-diffusion constant from the value expected in the classical limit. On the other hand, the field-independent part of 1/T1 increases with decreasing temperature, which may be a precursor for the true long-range antiferromagnetic ordering found below TN = 1.93 ± 0.01 K.KEYWORDS: α-VO(PO 3 ) 2 , NMR, antiferromagnetic spin chain, nuclear spin relaxation, spin diffusion §1. Introduction There has been a continued interest in the dynamics of low-dimensional quantum antiferromagnets at finite temperatures. One of the issues which has attracted renewed attention is a problem of spin diffusion in the one-dimensional (1D) Heisenberg spin chain. It is argued from phenomenology that at high enough temperatures and at long times, the spin autocorrelation function of the 1D Heisenberg spin chain has a diffusive formleading to divergence of the spectral density at low frequencies as ω −1/2 . However, because the diffusive form (1.1) is not derived from the microscopic Hamiltonian but is a consequence of the hydrodynamical assumption for the spin-spin correlation, 1) the question on the existence of spin diffusion in 1D spin chains has been studied intensively from both theoretical and experimental viewpoints. One of the best studied theoretical models is the S = 1/2 XXZ chain represented by the Hamiltonian 2, 3, 4, 5, 6, 7)(1.2)At the isotropic point (∆ = 1) and at low enough temperatures (T ≪ J/k B ), analytical expressions for the dynamical susceptibility χ(q, ω) have been derived for q ≈ 0 and π, and are shown to have no diffusive pole at low frequencies.2) At modestly high, or much higher temperatures compared with the intrachain coupling strength J, the problem is still controversial. Although the absence * E-mail: kikuchi@ph.noda.sut.ac.jp of diffusive excitations seems to be settled for the XXZ chain with planar anisotropy (0 ≤ ∆ < 1), a definite answer for the absence (or presence) of spin diffusion at the isotropic point has not yet been given.Diffusive behavior of the spin-spin correlation has been observed experimentally in several 1D spin chains via the ω −1/2 resonance-frequency dependence of the nuclear spin-lattice relaxation rate 1/T 1 at elevated temperatures. 8,9,10,11,12,13) As to the S = 1/2 chain, an analysis of the ω dependence of 1/T 1 at the Cu site in Sr 2 CuO 3 based on the classical spin-diffusion theory gives an unusually high value of the spin diffusion constant compared with the ...

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Proton spin-lattice relaxation in TMMC [(CH3)4NMn

Cited by 94 publications

References 19 publications

Study of one-dimensional nature ofS=1∕2(Sr,Ba)2
Nath
¹
,
Mahajan
²
,
Büttgen
³

et al. 2005
Phys. Rev. B
68
18
58
1
View full text Add to dashboard Cite

Study of one-dimensional nature ofS=1∕2(Sr,Ba)2
Nath
¹
,
Mahajan
²
,
Büttgen
³

et al. 2005
Phys. Rev. B
68
18
58
1
View full text Add to dashboard Cite

Quantum spin dynamics of the one-dimensional planar antiferromagnet

Spin Diffusion in theS=1/2 Quasi One-Dimensional Antiferromagnet α-VO(PO₃)₂via³¹P NMR

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Proton spin-lattice relaxation in TMMC [(CH3)4NMn

Cited by 94 publications

References 19 publications

Study of one-dimensional nature ofS=1∕2(Sr,Ba)2Nath1, Mahajan2, Büttgen3 et al. 2005Phys. Rev. B6818581View full textAdd to dashboardCite

Study of one-dimensional nature ofS=1∕2(Sr,Ba)2Nath1, Mahajan2, Büttgen3 et al. 2005Phys. Rev. B6818581View full textAdd to dashboardCite

Quantum spin dynamics of the one-dimensional planar antiferromagnet

Spin Diffusion in theS=1/2 Quasi One-Dimensional Antiferromagnet α-VO(PO3)2via31P NMR

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Product

Resources

About

Study of one-dimensional nature ofS=1∕2(Sr,Ba)2
Nath
¹
,
Mahajan
²
,
Büttgen
³

et al. 2005
Phys. Rev. B
68
18
58
1
View full text Add to dashboard Cite

Study of one-dimensional nature ofS=1∕2(Sr,Ba)2
Nath
¹
,
Mahajan
²
,
Büttgen
³

et al. 2005
Phys. Rev. B
68
18
58
1
View full text Add to dashboard Cite

Spin Diffusion in theS=1/2 Quasi One-Dimensional Antiferromagnet α-VO(PO₃)₂via³¹P NMR