NMR evidence for universal nonclassical critical behavior of incommensurately modulated crystals

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

doi:10.1103/physrevlett.71.89

Cited by 27 publications

(14 citation statements)

References 16 publications

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“…Accordingly, within the limits of experimental accuracy, BCPS fits to the universal critical behavior known from other one-dimensionally modulated IC systems. [2][3][4] On the basis of the same arguments one can understand the increase of the apparent critical exponent becoming obvious in Fig. 3 at increasing distance from T i .…”

Section: Discussionmentioning

confidence: 61%

“…An analysis of the temperature dependence of this effective additional relaxation mechanism therefore can be reasonably achieved: Assuming as usual two independent processes the measured relaxation rate T 1 Ϫ1 is represented as the sum of a critical relaxation rate T 1c Ϫ1 and a noncritical one. The latter can be obtained by fitting the values measured at higher temperatures where the background mechanism is dominating to the smoothly varying function aT 2 Ϫb where a and b are positive constants. This relation was derived previously for quadrupolar relaxation by two phonon Raman processes.…”

Section: CL Nqr Spin-lattice Relaxationmentioning

confidence: 99%

“…This is contradictory to the fact that many substances different in composition and structure but equally characterized by the occurrence of an one-dimensional incommensurate modulation can be described by the same critical exponents of the 3D XY model as required by the universality hypothesis. 2 This model is characterized by a two-dimensional order pa-rameter with three-dimensional interactions and consequently applies to a one-dimensionally incommensurately modulated lattice. Note, moreover, that the critical behavior of a substance is generally assumed to be strongly influenced by imperfections and that its accurate detection at so big distances from T i may be subject to some doubts.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 61%

Section: CL Nqr Spin-lattice Relaxationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…This value agrees well with the value 0.62±0.02 reported previously in Cs 2 CdBr 4 1) and is close to the theoretical value of ζ = 0.625 for the threedimensional XY model. [20][21][22] Cowley and Bruce predict that the three-dimensional XY model is acceptable for …”

Section: Normal (N) Phasementioning

confidence: 97%

Studies on¹³³Cs NMR Spectra and Spin-Lattice Relaxation Times in Incommensurate Cs₂HgCl₄

2000

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133 Cs NMR spectra and the spin-lattice relaxation times, T 1 , in Cs 2 HgCl 4 crystals were measured in the ranges of 160-361 K and 160-371 K, respectively. The central lines of the spectra show small splittings characteristic of the incommensurate (IC) phase. The splitting increases with decreasing temperature. The critical exponent ζ of T 1 at the phase transition from normal (N) to IC phase was determined to be 0.615±0.025 in the high-temperature side of the transition, which is in good agreement with the three-dimensional XY model predicting the one-dimensional modulation wave in the IC phase. The frequency dependence of T 1 in the IC phase can be explained by the fluctuations of phason with a small gap, 0-5 MHz, and amplitudon. ment disorders in HgCl 2− 4 complex anions and one of the crystallographically inequivalent two Cs cations. It has been presumed that the ferroelectric commensurate (C) phase below T C without centrosymmetry have a point symmetry mm2, 4) but detailed studies on structures below T C have not been reported. 35 Cl NQR, 12) dielectric and Raman scattering 8) measurements revealed a different result that the IC phase appears between T IC and T C1 . 12) From the optical polarization measurement, the low-temperature phase immediately below T C1 is anticipated to be a ferroelastic C phase analogous to that in Cs 2 MBr 4 (M=Cd, Hg). §2. Experimental Cs 2 HgCl 4 crystals were grown by cooling a molten mixture containing stoichiometric amounts of CsCl (purity 99.9%) and HgCl 2 (purity 99.9%) purchased from Wako Pure Chemical Industries, Ltd. The crystalline powder obtained was dried in vacuo and then sealed in glass tubes with nitrogen gas for differential thermal analysis (DTA) and NMR measurements.DTA was measured between 120 and 300 K to confirm the phase transitions reported previously. The sample temperature was determined within ±0.2 K using a chromel-constantan thermocouple. The measurement of 133 Cs NMR T 1 was performed with a Bruker MSL-300 spectrometer at frequency of 39.4 MHz in the range 160-371 K and also with a Bruker MSL-400 spectrometer at 52.5 MHz in 196-215 K. 133 Cs NMR spectra were recorded by a Bruker MSL-300 using a saturated CsCl aqueous solution as a standard of frequency shift. The sample temperature was controlled within ±0.5 K by Bruker VT-1000 temperature controller and determined by a copper-constantan thermocouple with the same accuracy. The uncertainty in the T 1 measurement is estimated to be within 5%. §3. Results DTA thermograms on heating displayed endother- §1. IntroductionMany compounds belonging to the A 2 BX 4 family with the pseudo-hexagonal β-K 2 SO 4 type structure (P nma) form incommensurate (IC) phases at low temperatures. We reported lattice dynamics in IC phases of Cs 2 MBr 4 (M=Cd and Hg) studied by 133 Cs NMR. 1) The critical exponents obtained at the phase transitions from normal to incommensurate (N-IC) phase correspond to the three-dimensional XY and the mean field models for Cd and Hg compounds, respectively. This difference seems to be expl...

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“…It is the aim of this study to further contribute to a deeper understanding of this problem. Since it has been found by other authors [17,18] that Cl nuclear spin moments and other nuclei with quadrupole moments like 87 Rb [19,20] are very sensitive local probes to investigate small structural changes at the phase transition and to study critical fluctuations in IC systems close to T i , we try to apply 35 Cl NMR measurements for that purpose. In case of BCPS the problem in that respect is that the quadrupole frequency for the nuclei Cl (ca.…”

Section: Introductionmentioning

confidence: 99%

35Cl Nuclear Magnetic Resonance Study in Bis(4-Chlorophenyl)Sulphone [(ClC6H4)2SO2]

Taye

Michel

2002

phys. stat. sol. (b)

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Cl NMR measurements of the central transitions (--1/2 $ +1/2) on a multidomain crystal of bis(4-chlorophenyl)sulphone (BCPS) were performed at room temperature. The quadrupole tensors and the temperature dependence of the 35 Cl NMR resonance frequencies have been analysed. Since the Larmor frequency n L is of comparable size with the quadrupole frequency n Q an exact solution of the problem of the eigenvalues for a system of spins with I = 3/2 in presence of an external magnetic field was necessary in order to evaluate the principal values, the directions of the principal axes, and the asymmetry parameter h of the quadrupole coupling tensor from the angular dependent NMR spectra. The conclusions from the NMR measurements are in very good agreement with the results of the 35 Cl nuclear quadrupole resonance (NQR) and the X-ray diffraction (XRD) studies on BCPS.

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NMR evidence for universal nonclassical critical behavior of incommensurately modulated crystals

Cited by 27 publications

References 16 publications

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

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

Studies on¹³³Cs NMR Spectra and Spin-Lattice Relaxation Times in Incommensurate Cs₂HgCl₄

35Cl Nuclear Magnetic Resonance Study in Bis(4-Chlorophenyl)Sulphone [(ClC6H4)2SO2]

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NMR evidence for universal nonclassical critical behavior of incommensurately modulated crystals

Cited by 27 publications

References 16 publications

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

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

Studies on133Cs NMR Spectra and Spin-Lattice Relaxation Times in Incommensurate Cs2HgCl4

35Cl Nuclear Magnetic Resonance Study in Bis(4-Chlorophenyl)Sulphone [(ClC6H4)2SO2]

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Studies on¹³³Cs NMR Spectra and Spin-Lattice Relaxation Times in Incommensurate Cs₂HgCl₄