Critical statics and dynamics of the one-dimensionally incommensurately modulated crystalRb2ZnBr4studied by NMR

Abstract

The critical statics and dynamics of the prototype incommensurate crystal ${\mathrm{Rb}}_{2}{\mathrm{ZnBr}}_{4}$ is investigated by nuclear-magnetization relaxation measurements in quadrupolar-perturbed nuclear magnetic resonance of ${}^{87}\mathrm{Rb}.$ Within the frame of the so-called conventional model and for an order-disorder phase-transition mechanism a general relationship is established between the anomalous behavior of the nuclear spin-lattice relaxation rate and the critical behavior of the crystal under investigation, which is assumed to be generally a nonclassical one. Based on this approach the experimental data can be consistently interpreted. The critical exponents derived fit nicely to the universality class of the three-dimensional XY model. The characteristic frequency of the critical dynamics of the order parameter (OP) slows down below the Larmor frequency used in the ${}^{87}\mathrm{Rb}$ nuclear-magnetic-resonance relaxation-time measurements. In this particular case one can derive the characteristic frequency of the critical dynamics of the OP above ${T}_{i}$ and of the phason below ${T}_{i}$ from the Larmor frequency dependence of ${T}_{i}.$ The amplitudon mode behaves like a usual soft mode whereas the phason mode stays soft in the entire incommensurately modulated phase. The latter can be described by a very small frequency gap below about 0.4 MHz. The critical behavior is discussed in a general context.