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.

Considering the before and after phonon softening, the gap in a CoO₆-octahedral crystal electric fields (CEF) and the thermally activated spin gap, were observed of ∼0.5 meV and Q ∼ 25 meV in defect-free LaCoO₃ single crystal, respectively.