Evolution of charge-density-wave soft phonon modes in ${\mathrm{Pd}}_x{\mathrm{ErTe}}_3$

Abstract

We investigated the lattice dynamics of quasi-two-dimensional Pd-intercalated ${\mathrm{ErTe}}_3$ in relation to its charge-density-wave (CDW) transitions by means of x-ray diffuse and meV-resolution inelastic x-ray scattering. In pristine ${\mathrm{ErTe}}_3$, CDW order develops at orthogonal in-plane wave vectors ${\mathrm{q}}_1^c=(0,0,0.29)$ (the $c\text{-}\mathrm{CDW}$) and ${\mathrm{q}}_2^a=(0.31,0,0)$ (the $a\text{-}\mathrm{CDW}$), with transition temperatures $T_1^c=270$ K and $T_2^a=160$ K, respectively. Remarkably, we observe diffuse x-ray scattering already near the higher transition temperature $T_1^c$ along $a\text{-}\mathrm{CDW}$ but at a slightly different wave vector ${\mathrm{q}}_1^a=(0.29,0,0)$. Inelastic x-ray scattering for ${\mathrm{Pd}}_{0.01}{\mathrm{ErTe}}_3$ shows that a partial phonon softening at ${\mathrm{q}}_1^a$, underscoring the strong competition between ordering tendencies along the nearly equivalent in-plane axes of the orthorhombic lattice. For intercalation levels $x\ge 0.02$, the $a\text{-}\mathrm{CDW}$ state is suppressed. Nevertheless, a similar correlation between phonon softening and diffuse scattering persists along the $[100]$ direction, again observed at ${\mathrm{q}}_1^a=(0.29,0,0)$ and $T_1^c$. These findings suggest that the $a\text{-}\mathrm{CDW}$ is fully suppressed for $x\ge 0.02$, and that the residual diffuse scattering at ${\mathrm{q}}_1^a$ originates from the partial phonon softening associated with the $c\text{-}\mathrm{CDW}$, reflected by the near equality of the absolute size of ${\mathrm{q}}_1^c$ and ${\mathrm{q}}_1^a$.

10 pages, 5 figures