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 ($T_c$≊180 K), these variations were, respectively, parametrized by the power laws ($T_c$-T${)}^{2\beta }$, (T-$T_c$ ${)}^{\mathrm{-}\gamma }$, and (T-$T_c$ ${)}^{\mathrm{-}\nu }$ with β≊0.31, γ≊1.33, and ν≊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.