Electronic structures and phonon free energies of LaCoO3using hybrid-exchange density functional theory

Abstract

Hybrid-exchange density functional theory has been used to model the electronic structure of LaCoO${}_{3}$. Based on a rhombohedral unit cell of $R\overline{3}c$ symmetry containing two Co atoms we find a mixed spin phase, comprising alternating low and high spin Co${}^{+3}$ ions, with a total energy at 0 K just 57 meV per formula unit above that of a nonmagnetic semiconducting ground state. In the mixed spin phase the high-spin Co${}^{+3}$ ions have spin moments of $3.1\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ and the state is insulating with a band gap of 2.2 eV. Our calculations suggest that the effective on-site Coulomb repulsion energy ${U}_{\mathrm{eff}}$ on Co${}^{+3}$ ions is spin dependent. The ${U}_{\mathrm{eff}}$ on Co${}^{+3}$ ions is 7.1 eV and 8.5 eV for the nonmagnetic ground state and for the magnetic high spin state, respectively. For the mixed spin state, two different ${U}_{\mathrm{eff}}$ are estimated for two Co${}^{+3}$ ions in the unit cell having different spin states, 8.0 eV for the high-spin Co${}^{+3}$ ion and 7.0 eV for the low-spin Co${}^{+3}$ ion. An estimate of the harmonic phonon free energy suggests that this mixed spin phase would become the more stable phase as the temperature increases, which is consistent with experimental evidence. An alternative intermediate spin state is higher in energy at all temperatures.