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

Abstract

The temperature dependence of ${}^{35}\mathrm{Cl}$ nuclear quadrupole resonance (NQR) spectra and the respective spin-lattice relaxation times have been measured between room temperature and 120 K on high quality single crystals of bis(4-chlorophenyl)sulfone $[{(\mathrm{C}}_{6}{\mathrm{H}}_{4}{\mathrm{C}\mathrm{l})}_{2}{\mathrm{SO}}_{2}].$ Spectra with the typical incommensurate edge singularities were found at temperatures below the transition temperature ${T}_{i}$ into the incommensurate (IC) 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 $0.35\ifmmode\pm\else\textpm\fi{}0.03$ which is identified with the critical exponent \ensuremath{\beta} 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 \ensuremath{\zeta} of about $0.69\ifmmode\pm\else\textpm\fi{}0.02.$ The data are interpreted in terms of the three-dimensional (3D) 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. ${2\mathrm{D}\mathrm{}}^{35}\mathrm{Cl}\mathrm{}\mathrm{NQR}$ exchange spectra show no indication for large scale fluctuations of the modulation wave above about 500 Hz.