Evolution of charge density wave soft phonon modes in Pd x ErTe 3

We investigated the lattice dynamics of quasi-two-dimensional Pd-intercalated ErTe₃ in relation to its charge-density-wave (CDW) transitions by means of x-ray diffuse and meV-resolution inelastic x-ray scattering. In pristine ErTe₃, CDW order develops at orthogonal in-plane wave vectors q₁ᶜ = (0, 0, 0.29) (the c-CDW) and q₂ᵃ = (0.31, 0, 0) (the a-CDW), with transition temperatures T₁ᶜ = 270 K and T₂ᵃ = 160 K, respectively. Remarkably, we observe diffuse x-ray scattering already near the higher transition temperature T₁ᶜ along a-CDW but at a slightly different wave vector q₁ᵃ = (0.29, 0, 0). Inelastic x-ray scattering for Pd0.01ErTe₃ shows that a partial phonon softening at q₁ᵃ, underscoring the strong competition between ordering tendencies along the nearly equivalent in-plane axes of the orthorhombic lattice. For intercalation levels x ≥ 0.02, the a-CDW state is suppressed. Nevertheless, a similar correlation between phonon softening and diffuse scattering persists along the $[100]$ direction, again observed at q₁ᵃ = (0.29, 0, 0) and T₁ᶜ. These findings suggest that the a-CDW is fully suppressed for x ≥ 0.02, and that the residual diffuse scattering at q₁ᵃ originates from the partial phonon softening associated with the c-CDW, reflected by the near equality of the absolute size of q₁ᶜ and q₁ᵃ.