Thermal fluctuations of charge-density waves studied by NMR

Abstract

Thermal fluctuations of a pinned incommensurate charge-density wave in zero external electric field were studied by NMR. Low-frequency random incoherent fluctuations of the amplitude and phase of the modulation wave affect the shape of the homogeneous decay of the transverse nuclear-spin magnetization. Phase fluctuations induce a characteristic exponential decay with the exponent proportional to the time variable as ${t}^{3/2}$ whereas the amplitude fluctuations result in a decay linear in t. The two types of fluctuations show very different temperature behavior. The phase fluctuations exhibit a weak T dependence and are present in the whole incommensurate phase, whereas the amplitude fluctuations are significant only in the close vicinity of the Peierls transition temperature, where they behave critically. The above effects are predicted on the basis of Landau theory using the assumption that the spectral density of phase fluctuations exhibits a central peak to account for the slow relaxational processes and memory effects in the presence of impurities. Theoretical predictions are compared to the ${}^{87}\mathrm{Rb}$ NMR experiment in blue bronze ${\mathrm{Rb}}_{0.3}{\mathrm{MoO}}_{3},$ and a good agreement between the theory and experiment was found. The results show that the thermally induced phase fluctuations are slow and take place on a spatial scale of a small fraction of the charge-density-wave wavelength, thus on the subnanometric scale.