Phonon softening and anomalous mode near thexc=0.5quantum critical point inCa2−xSrxRuO4

Abstract

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