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