First-principles study of intermediate-spin ferrous iron in the Earth's lower mantle

Spin crossover of iron is of central importance in solid Earth geophysics. It impacts all physical properties of minerals that altogether constitute $\sim 95$ vol\% of the Earth's lower mantle: ferropericlase [(Mg,Fe)O] and Fe-bearing magnesium silicate (MgSiO$_3$) perovskite. Despite great strides made in the past decade, the existence of intermediate-spin (IS) state in ferrous iron (Fe$^{2+}$) (with total electron spin $S=1$) and its possible role in the pressure-induced spin crossover in these lower-mantle minerals still remain controversial. Using density functional theory $+$ self-consistent Hubbard $U$ (DFT$+U_{sc}$) calculations, we investigate all possible types of IS states of Fe$^{2+}$ in (Mg,Fe)O and (Mg,Fe)SiO$_3$ perovskite. Among the possible IS states in these minerals, the most probable IS state has an electronic configuration that significantly reduces the electron overlap and the iron nuclear quadrupole splitting (QS). These most probable IS states, however, are still energetically disfavored, and their QSs are inconsistent with M\"{o}ssbauer spectra. We therefore conclude that IS Fe$^{2+}$ is highly unlikely in the Earth's lower mantle.