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

TL;DR

This study explores how charge-density-wave phonon modes evolve in Pd-intercalated ErTe3, revealing competition between different CDW states and the effects of intercalation on lattice dynamics.

Contribution

It provides detailed insights into the phonon softening and diffuse scattering associated with CDW transitions in Pd_xErTe3, highlighting the suppression of one CDW state with intercalation.

Findings

Partial phonon softening at q1a indicates competition between CDW states.

Intercalation suppresses the a-CDW state for x ≥ 0.02.

Diffuse scattering persists at q1a even when the a-CDW is suppressed.

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 $\boldsymbol{\mathrm{q}}_{1}^{c} = (0, 0, 0.29)$ (the $c\text{-}\mathrm{CDW}$) and $\boldsymbol{\mathrm{q}}_{2}^{a} = (0.31, 0, 0)$ (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 $\boldsymbol{\mathrm{q}}_{1}^{a} = (0.29, 0, 0)$. Inelastic x-ray scattering for $\mathrm{Pd}_{0.01}\mathrm{ErTe}_3$ shows that a partial phonon softening at $\boldsymbol{\mathrm{q}}_{1}^{a}$, underscoring the strong competition between ordering tendencies along the nearly equivalent in-plane axes of the orthorhombic lattice. For intercalation levels $x \geq 0.02$, 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 $\boldsymbol{\mathrm{q}}_{1}^{a} = (0.29, 0, 0)$ and $T_{1}^{c}$. These findings suggest that the $a\text{-}\mathrm{CDW}$ is fully suppressed for $x \geq 0.02$, and that the residual diffuse scattering at $\boldsymbol{\mathrm{q}}_{1}^{a}$ originates from the partial phonon softening associated with the $c\text{-}\mathrm{CDW}$, reflected by the near equality of the absolute size of $\boldsymbol{\mathrm{q}}_{1}^{c}$ and $\boldsymbol{\mathrm{q}}_{1}^{a}$.