Fluctuations of the multiplicity of Co$^{3+}$ ions and softening of the phonon spectrum of rare-earth cobalt oxides

An unconventional temperature dependence of infrared absorption spectra of rare-earth cobalt oxides LaCoO$_3$ and GdCoO$_3$ has been studied experimentally and theoretically in the temperature range of 3.2–550 K. A quite strong softening of the optical phonon mode has been detected, which cannot be explained by standard lattice anharmonicity. It has been shown that the redshift of the phonon spectrum is due to the electron–phonon coupling quadratic in the lattice displacement and to fluctuations of the multiplicity of Co$^{3+}$ ions.