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LaCoO$_3$ exhibits two crossovers at T$_{SS} \approx$ 100 K and T$_{MI} \approx$ 500 K observed in various physical properties such as thermal expansion and electric susceptibility. These crossovers are typically associated with the temperature dependent population of excited spin states of the Co$^{3+}$ ion, which evolves upon heating from the low-spin (LS), S = 0, to high-spin (HS), S = 2, configuration. Since the CoO$_6$ octahedra expands around the larger HS sites, a static LS-HS order was proposed by Goodenough in the 1960's [1] but was never confirmed experimentally. More recent models suggest that spin states form a 3D checkerboard-type short range order near the room temperature, which is formed due to different sizes of these spin states [2-4]. A corresponding dynamic distortion of the crystal lattice mimics closely the Co-O breathing mode. Using inelastic neutron scattering to study the lattice dynamics of LaCoO$_3$ over a wide temperature range, 5 K ≤ T ≤ 700 K, we find strong phonon renormalization of low- as well as high-energy phonon modes with periodicities corresponding to the proposed superlattice.
[1] P. M. Raccah and J. B. Goodenough, Physical Review 155, 932 (1967).
[2] J. Kuneš and V. Křápek, Physical Review Letters 106, 256401 (2011).
[3] V. Křápek et al., Physical Review B 86, 195104 (2012).
[4] J. Kuneš et al., Physical Review B 89, 115134 (2014).
