Critical Dynamics above the Incommensurate Phase Transition of Rb
                    <sub>2</sub>
                    ZnCl
                    <sub>4</sub>
                    Studied by NMR

Holzer, K.-P.; Petersson, J.; Schüssler, D.; Walisch, R.; Hacker, Ulrich; Michel, D.

doi:10.1209/0295-5075/31/4/005

Cited by 17 publications

(16 citation statements)

References 18 publications

(8 reference statements)

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“…T\\ is expected to be negligible in the total T\ because Tu > 100 s can be estimated from the observed T\ at 370 K. ( was obtained, from the slope of logTi vs. loge plots, to be 0.62 ± 0.03 in a temperature range of 7 K above the transition (Figure 2). This value coincides with that obtained in Cs2CdBr 4 [3] and agrees well with the theoretical value of 0.625 [13] calculated for the three-dimensional ATF-model with which the driving interaction of the N-IC phase transition is predicted [2]. The deviation of the observed T\ values from the calculated ones at temperatures higher than 7 K above the phase transition is attributable to the contribution from T\\.…”

Section: Normal (N) Phasesupporting

confidence: 90%

A¹³³Cs NMR Spin-Lattice Relaxation Study in Incommensurate Cs₂CdI₄

Suzuki

Ishimaru

Ikeda

2000

Zeitschrift Für Naturforschung A

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133Cs NMR spin-lattice relaxation times(Ti) in crystalline Cs 2 CdI 4 were measured at 225 -373 K. The critical exponent ( of T\ observed near the normal-incommensurate transition in the normal phase was determined to be 0.62 ± 0.03, in good agreement with the predicted value for three-dimensional XK-model. The frequency dependent T\ in the incommensurate phase could be explained by the fluctuation of amplitudon and small gap phason.

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Section: Normal (N) Phasesupporting

confidence: 90%

A¹³³Cs NMR Spin-Lattice Relaxation Study in Incommensurate Cs₂CdI₄

Suzuki

Ishimaru

Ikeda

2000

Zeitschrift Für Naturforschung A

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“…Consequently, in BCPS there is no transition to the slow motion limit which for instance is well known to occur in another system 20,21 and thus the soft-mode frequency stays well above the NQR frequency of about 35 MHz. Following the previous argumentation, 20,21 this means that the phason gap frequency in the IC phase is also well above this value. This result is contradictory to a previous one 11 stating that in the IC phase the 1 H NMR T 1 is frequency dependent down to 500 kHz indicating a phason gap frequency below this value.…”

Section: CL Nqr Spin-lattice Relaxationmentioning

confidence: 91%

Evidence for nonclassical critical behavior of a one-dimensional incommensurately modulated crystal: A35ClNQR study of bis(4-chlorophenyl)sulfone

Decker

Petersson

2000

Phys. Rev. B

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The temperature dependence of 35 Cl nuclear quadrupole resonance ͑NQR͒ spectra and the respective spinlattice relaxation times have been measured between room temperature and 120 K on high quality single crystals of bis͑4-chlorophenyl͒sulfone ͓͑C 6 H 4 Cl͒ 2 SO 2 ͔. Spectra with the typical incommensurate edge singularities were found at temperatures below the transition temperature T i into the incommensurate ͑IC͒ phase. This holds in particular for temperatures very close to T i . The exponent describing the temperature dependence of the distance between the edge singularities of the incommensurate spectrum is near T i about 0.35 Ϯ0.03 which is identified with the critical exponent ␤ of the order parameter. Above T i a considerable critical contribution to the spin-lattice relaxation rate 1/T 1 is detected which can be described by some critical exponent of about 0.69Ϯ0.02. The data are interpreted in terms of the three-dimensional ͑3D͒ XY model. In the IC phase T 1 stays low indicating a considerable influence of the phason excitations on every part of the IC spectrum. Contrary to the behavior of other systems the minimum of T 1 does not occur at T i . Rather, it is shifted some degrees from T i to lower temperatures. 2D 35 Cl NQR exchange spectra show no indication for large scale fluctuations of the modulation wave above about 500 Hz.

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“…For this case of OP dynamics, a direct process for the relaxation of the nuclear spin system is reasonably assumed. Precise 87 Rb-T 1 measurements [12] indeed proved both assumptions to hold for RZC above T i . Since the phason and amplitudon modes evolve from the relaxatory soft mode on passing from the N to the IC phase, we adopt both these assumptions as a general basis for interpreting quantitatively our experimental results in the IC phase.…”

Section: Low-frequency Phason and Amplitudonmentioning

confidence: 73%

Low-Frequency Phason and Amplitudon Dynamics in the Incommensurate Phase ofRb2ZnCl4

et al. 1997

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It is shown that the phason-induced 87 Rb NMR spin-lattice relaxation rate in the incommensurate phase of Rb 2 ZnCl 4 depends on the Larmor frequency, whereas the amplitudon-induced rate does not. The results are described consistently by relaxatory phason and amplitudon fluctuations. The relaxatory phason gap is found to be on the order of magnitude of about 10 MHz, in contrast to previous estimates from NMR studies. Our data also allow a determination of the temperature dependence of the amplitudon relaxation frequency. [S0031-9007 (97)02732-4] PACS numbers: 64.70.Rh, 64.60.Cn, 76.60.EsSome insulating crystals pass over from a hightemperature normal ͑N͒ phase to a structurally incommensurately (IC) modulated phase at a certain temperature T i . In the IC phase, at least one physical quantity is modulated in such a way that the characteristic wave vector q i is not a rational multiple of the reciprocal lattice vectors of the N phase. As a consequence, the initial phase of the modulation wave is arbitrary, and the IC structure is continuously degenerate with respect to a phase shift [1,2]. Thus, special low-energy excitations termed "phasons" are present in IC systems. The continuum theory of IC phases predicts the existence of a gapless phason mode. It is usually assumed, however, that in a real crystal various effects lead to a nonzero gap in the phason excitation spectrum. It is this characteristic phason dynamics which is the most fascinating feature of incommensurate crystals and which is the subject of this Letter.The incommensurate modulation wave is in most cases, at least close to T i , a single harmonic function of space ("plane wave limit", PWL). It can be represented by an order parameter (OP) with two thermodynamic degrees of freedom, e.g., amplitude and initial phase. The normal modes of the OP are given by its longitudinal and transversal components P 1 and P 2 , respectively, in the complex OP plane [2]. In first-order approximation, the fluctuations of P 1 and P 2 can be identified with those of amplitude and phase giving rise to the terms "amplitudon" and "phason" fluctuations [1,2].In most cases, the IC phase transforms into a commensurate (C) phase at a temperature T c , T i . For the prototypic system Rb 2 ZnCl 4 (RZC) the IC phase is stable between T i 303 K and T c 195 K, where a lock-in transition to a ferroelectric C phase takes place with a triplication of the unit cell with respect to the N phase [1,3]. As a characteristic precursor effect of the IC-C phase transition, a so-called soliton structure is formed. Soliton effects have been observed in RZC in a temperature region of about 40 K above T c [3]. In the following, however, we will restrict the discussion to the PWL. Quadrupolar perturbed nuclear magnetic resonance (NMR) has been proved to be an accurate and sensitive tool for investigating IC phases [1]. While the spectrum of NMR frequencies is determined by the static part of the electric field gradient (EFG), its fluctuating part is related to the probabilities of transitions be...

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Critical Dynamics above the Incommensurate Phase Transition of Rb ₂ ZnCl ₄ Studied by NMR

Abstract: Order parameter (OP) fluctuations are studied in the normal (N) phase of the 0 Les Editions de Physique

Cited by 17 publications

References 18 publications

A¹³³Cs NMR Spin-Lattice Relaxation Study in Incommensurate Cs₂CdI₄

A¹³³Cs NMR Spin-Lattice Relaxation Study in Incommensurate Cs₂CdI₄

Evidence for nonclassical critical behavior of a one-dimensional incommensurately modulated crystal: A35ClNQR study of bis(4-chlorophenyl)sulfone

Low-Frequency Phason and Amplitudon Dynamics in the Incommensurate Phase ofRb2ZnCl4

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Critical Dynamics above the Incommensurate Phase Transition of Rb 2 ZnCl 4 Studied by NMR

Abstract: Order parameter (OP) fluctuations are studied in the normal (N) phase of the 0 Les Editions de Physique

Cited by 17 publications

References 18 publications

A133Cs NMR Spin-Lattice Relaxation Study in Incommensurate Cs2CdI4

A133Cs NMR Spin-Lattice Relaxation Study in Incommensurate Cs2CdI4

Evidence for nonclassical critical behavior of a one-dimensional incommensurately modulated crystal: A35ClNQR study of bis(4-chlorophenyl)sulfone

Low-Frequency Phason and Amplitudon Dynamics in the Incommensurate Phase ofRb2ZnCl4

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Critical Dynamics above the Incommensurate Phase Transition of Rb ₂ ZnCl ₄ Studied by NMR

A¹³³Cs NMR Spin-Lattice Relaxation Study in Incommensurate Cs₂CdI₄

A¹³³Cs NMR Spin-Lattice Relaxation Study in Incommensurate Cs₂CdI₄