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

Abstract

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.

NMR line shape analysis in the incommensurate phase of bis(4‐chlorophenyl)sulfone

“…Although, as outlined in Section 2, the conditions for the 35 Cl NMR experiments are rather difficult because of the large 35 Cl quadrupole resonance frequency in BCPS, also 35 Cl NMR measurements could be realised over a wide range of frequencies [17]. Recent 35 Cl NMR spin-lattice rate measurements [18] have nicely confirmed that critical exponent is identical with that value derived from the NQR measurements [16]. Moreover, it could be shown in the 35 Cl relaxation time measurements made at different various external dc magnetic fields that the critical frequency for the order parameter fluctuations is so high that the limit of fast fluctuations is always valid if we approach the phase transition from the direction of higher temperatures.…”

“…Deuteron [13] and proton [14] NMR spin-lattice relaxation times have been measured with the aim to investigate the mechanism of the phase transition which is related to the molecular twisting motion of the two phenyl rings. In 35 Cl NQR measurements line shape profiles were measured which are typical for the phase transition into the IC phase and a strong critical contribution to the 35 Cl-NQR spinlattice relaxation rate was found in the proximity of the N-IC phase transition [15,16]. The critical exponent derived is in agreement with predictions of the renormalisation group theory [16].…”

“…In 35 Cl NQR measurements line shape profiles were measured which are typical for the phase transition into the IC phase and a strong critical contribution to the 35 Cl-NQR spinlattice relaxation rate was found in the proximity of the N-IC phase transition [15,16]. The critical exponent derived is in agreement with predictions of the renormalisation group theory [16]. NQR line shape measurements allowed the estimation of the phase transition temperature T i .…”

“…The substance was purified for about ten times using a home-built zone melting oven. Large single crystals (>10 cm Cl NQR spectra [16] at room temperature in comparison to other materials proves the high quality of the samples. 35 Cl NMR studies are very suitable for a study of the IC modulation because the largest principal axis Z of the quadrupole coupling tensor (QCT) is parallel to the S-Cl axis [17].…”

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

“…Some of them were limited to the study of the spin-lattice relaxation time [5][6][7] and phase transitions [7,8]. The variation of the 35 Cl spin-lattice relaxation rate over the incommensurate NQR frequency distribution in BCPS has been measured at various temperatures by Schneider et al [9], Pusiol et al [6], Blinc et al [5], and Decker and Petersson [7]. The characteristic features of the variation of the effective spin-lattice relaxation rate T --1 over the incommensurate NQR frequency distribution were explained in terms of competing phason and amplitudon contributions.…”