  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.
