The spin-orbit-phonon coupling and crystalline elasticity of LaCoO₃ perovskite

Based on an integrated study of magnetic susceptibility, specific heat, and thermal expansion of single-crystal LaCoO₃ free from cobalt and oxygen vacancies, two narrow spin gaps are identified before and after the phonon softening of gap size ΔE ∼ 0.5 meV in a CoO₆-octahedral crystal electric field (CEF) and the thermally activated spin gap Q ∼ 25 meV, respectively. Significant excitation of Co³⁺ spins from a low-spin (LS) to a high-spin (HS) state is confirmed by the thermal activation behavior of spin susceptibility χ ^S of energy gap Q ∼ 25 meV, which follows a two-level Boltzmann distribution to saturate at a level of 50% LS/50% HS statistically above ∼200 K, without the inclusion of a postulated intermediate spin (IS) state. A threefold increase in the thermal expansion; coefficient (α) across the same temperature range as that of thermally activated HS population growth is identified, which implies the non-trivial spin-orbit-phonon coupling caused the bond length of Co^3+(LS↔HS)-O fluctuation and the local lattice distortion. The unusually narrow gap of ΔE ∼ 0.5 meV for the CoO₆ octahedral CEF between e_g-t_2g indicates a more isotropic negative charge distribution within the octahedral CEF environment, which is verified by the Electron Energy Loss Spectroscopy (EELS) study to show nontrivial La-O covalency.