Phonon softening and anomalous mode near the xc=0.5 quantum critical point in Ca2-xSrxRuO4

Inelastic neutron scattering is used to measure the temperature-dependent phonon dispersion in Ca{sub 2-x}Sr{sub x}RuO{sub 4} (x = 0.4,0.6). The in-plane {Sigma}{sub 4} octahedral tilt mode softens significantly at the zone boundary of the high-temperature tetragonal (HTT) I4{sub 1}/acd structure as the temperature approaches the transition to a low-temperature orthorhombic (LTO) Pbca phase. This behavior is similar to that in La{sub 2}CuO{sub 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 {Sigma}{sub 4}, albeit with similar dispersion. This anomalous phonon mode never softens below {approx} 5 meV, even for temperatures below the HTT-LTO transition. This mode is attributed to the presence of intrinsic structural disorder within the I4{sub 1}/acd tetragonal structure of the doped ruthenate.