Symmetry-resolved elastic anomalies in spin-crossover cobaltite LaCoO$_3$

Ultrasound velocity measurements of the pseudo-cubic spin-crossover cobaltite LaCoO$_3$ and the lightly Ni-substituted La(Co$_{0.99}$Ni$_{0.01}$)O$_3$ reveal two types of symmetry-resolved elastic anomaly in the insulating paramagnetic state that are commonly observed in these compounds. The temperature dependence of the bulk modulus exhibits Curie-type softening upon cooling below 300 K down to $\sim$70 K, indicating the presence of isostructural lattice instability arising from orbital fluctuations. The temperature dependence of the tetragonal and trigonal shear moduli exhibits unusual hardening upon cooling below 300 K, indicating the occurrence of elasticity crossover arising from the spin crossover. The present study also reveals that the isostructural lattice instability in LaCoO$_3$ is sensitively suppressed with the Ni substitution, indicating the suppression of orbital fluctuations with the light Ni substitution. This Ni substitution effect in LaCoO$_3$ can be explained on the basis that the isostructural lattice instability arises from the coupling of the lattice to the Co spin state fluctuating between the high-spin state and intermediate-spin state.