We have measured the magnetic susceptibility of the ${\mathrm{Rb}}_x\mathrm{W}{\mathrm{O}}_3$ compound $(0.20⩽x⩽0.33)$ and examined its structural properties and lattice dynamics, using elastic and inelastic neutron scattering (INS) experiments, in order to gain further insight into the unusual features of its superconducting state, namely, (i) the stabilizing effect resulting from the reduction of rubidium content, i.e., of the conduction electron density [what we shall name the “$T_c$ $\left(x\right)$ paradox”], and (ii) the destabilizing effect of the ordering of the Rb ions. We also performed density-functional calculations of the phonon dispersion in the “stoichiometric” ${\mathrm{Rb}}_{0.33}\mathrm{W}{\mathrm{O}}_3$ and ${\mathrm{Cs}}_{0.33}\mathrm{W}{\mathrm{O}}_3$ to identify the main features of the phonon spectra. These calculations give a very satisfactory description of the INS data and confirm the assignment to these bronzes of a lower (orthorhombic) symmetry than previously proposed. Our results contradict the previous interpretations of the $T_c$ $\left(x\right)$ paradox and of the ordering effect: (i) no general softening of the lattice accompanies the increase of the Rb-vacancy population and (ii) no general decrease of the electron density of states $D_{\mathrm{EF}}$ distinguishes the ordered nonsuperconducting ${\mathrm{Rb}}_{0.25}\mathrm{W}{\mathrm{O}}_3$ from its neighboring disordered parents. It appears, therefore, that the electron-electron coupling in this system probably proceeds through well-defined electronic states and phonons. This is a feature these “hexagonal” tungsten bronzes (HTB) apparently share with several high-$T_c$ materials. We discuss what could be the mechanisms responsible for the very selective electron-phonon coupling in the HTB.

• Received 4 April 2007

DOI:https://doi.org/10.1103/PhysRevB.76.174511