Elastic properties of the transition metal oxides Ca$_{2-x}$Sr$_{x}$RuO$_{4}$

Layered perovskite ruthenates have attracted considerable interest since the discovery of superconductivity in Sr$_{2}$RuO$_{4}$, the only copper-free superconductor isostructural to the cuprates. Among the doped varieties of Sr$_{2}$RuO$_{4}$, the Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ series is heavily studied, as it connects the Mott insulator Ca$_{2}$RuO$_{4}$ with the superconductor Sr$_{2}$RuO$_{4}$ and exhibits a variety of physical properties. The current work focuses on the elastic properties of Ca$_{2-x}$Sr$_{x}$RuO$_{4. }$Resonant Ultrasound Spectroscopy (RUS) has been used to study the elastic response of the samples, and results are presented for single crystals with x = 0.2, 0.3, 0.4, 0.5, 1, 1.5, 1.9 and 2.0. The temperature-dependence of the elastic behavior is found to be quite unusual and reflects the rich phase diagram of these materials. Almost all measured Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ samples show a soft phonon mode at low temperatures, which is believed to be associated with the dynamics of the RuO$_{6}$ octahedra.