Phonon softening and anomalous mode near the $x_{c}=0.5$ quantum critical point in Ca$_{2-x}$Sr$_{x}$RuO$_4$

TL;DR

This study investigates phonon behavior near the quantum critical point in Ca$_{2-x}$Sr$_{x}$RuO$_4$, revealing significant softening of tilt modes and an anomalous mode linked to structural disorder, using inelastic neutron scattering.

Contribution

It provides new insights into phonon dynamics and disorder effects near the quantum critical point in doped ruthenates, highlighting an anomalous phonon mode not observed in similar cuprates.

Findings

Significant softening of the $ ext{Sigma}_4$ tilt mode near the transition.

Observation of an anomalous phonon mode that does not soften below ~5 meV.

Presence of intrinsic structural disorder affecting phonon behavior.

Abstract

Inelastic neutron scattering is used to measure the temperature dependent phonon dispersion in Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ ($x=0.4$, 0.6). The in-plane $\Sigma_{4}$ octahedral tilt mode softens significantly at the zone boundary of the high temperature tetragonal (HTT) \textit{I4}$_{\mathit{1}}$\textit{/acd} structure as the temperature approaches the transition to a low temperature orthorhombic (LTO) \textit{Pbca} phase. This behavior is similar to that in La$_2$CuO$_4$, but a new inelastic feature that is not found in the cuprate is present. An anomalous phonon mode is observed at energy transfers greater than the $\Sigma_{4}$ albeit with similar dispersion. This anomalous phonon mode never softens below $\sim 5$ meV, even for temperatures below the HTT-LTO transition. This mode is attributed to the presence of intrinsic structural disorder within the \textit{I4}$_{\mathit{1}}$\textit{/acd} tetragonal structure of the doped ruthenate.