Critical x-ray scattering at the Peierls transition of the blue bronze.

Abstract

We report on the temperature evolution of the 2${k}_{F}$ charge-density wave (CDW) in the blue bronze ${\mathrm{K}}_{0.3}$${\mathrm{MoO}}_{3}$. Using detailed profile analysis of the x-ray scattering, we were able to deduce: (i) from the temperature dependence of the peak intensity the square of the order parameter in the ordered phase (T${T}_{c}$) and the CDW static susceptibility in the disordered phase (T>${T}_{c}$); (ii) from the temperature variation of the scattering width, the correlation lengths of the CDW above ${T}_{c}$. Close to the Peierls transition (${T}_{c}$\ensuremath{\approxeq}180 K), these variations were, respectively, parametrized by the power laws (${T}_{c}$-T${)}^{2\ensuremath{\beta}}$, (T-${T}_{c}$${)}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$, and (T-${T}_{c}$${)}^{\mathrm{\ensuremath{-}}\ensuremath{\nu}}$ with \ensuremath{\beta}\ensuremath{\approxeq}0.31, \ensuremath{\gamma}\ensuremath{\approxeq}1.33, and \ensuremath{\nu}\ensuremath{\approxeq}0.68. The experimental values of these exponents indicate the existence of a three-dimensional (3D) regime of critical fluctuations, compatible with an order parameter of dimension n=2. At about 20 K above ${T}_{c}$ we observed a crossover into a regime characterized by quasi-two-dimensional fluctuations, which survive at least up to room temperature.