Spin-state crossover of iron in lower-mantle minerals: Results of DFT+U investigations

Results of several first-principles calculations on the spin-state crossover of iron in lower-mantle minerals have been reviewed. The LDA+U method gives desirable atomic and electronic structure in ferropericlase, (Mg,Fe)O. Both low-spin and high-spin ferropericlase are insulating. Jahn-Teller distortion is observed around iron in the high-spin state. A vibrational virtual crystal model (VVCM) permitted calculations of thermodynamic properties of this system at lower mantle conditions. Predictions are overall in good agreement with several experimental data sets. They display anomalies in the bulk modulus and allowed predictions of anomalies in thermodynamic properties and of the elastic signature of this phase in the mantle. An intriguing possibility of a viscosity anomaly caused by this crossover in the mantle has been raised. Improvements in these calculations to go beyond the ideal HS-LS solid solution are still desirable, as well as self-consistent calculations of the Hubbard U. These upgrades should improve agreement between predictions and measurements of crossover pressure ranges. (Mg,Fe)SiO₃ perovskite is a more difficult system to investigate, therefore more controversial. Currently, there is lack of consensus regarding the existence of IS iron in perovskite. AU calculations, irrespective of exchange-correlation functional used, agree on one issue: the IS state is not energetically competitive and no HS-to-IS crossover is expected to occur at lowermantle pressures. The calculated HS-LS crossover pressure in ferrous iron strongly depends on the exchange-correlation functional (LDA, GGA, or DFT+U), and on the iron distribution in the supercell. This makes it more difficult to compare results with or interpret experimental data. A non-ideal HS-LS solid solution treatment appears to be essential for this system. On the positive side, the HS-LS crossover does not appear to affect the compressibility of this system to experimentally detectable levels. In the lower mantle, the change in compressibility of this system should be even less detectable. A thorough study of ferric iron using a more appropriate exchange-correlation functional or the DFT+U method is still needed for more extensive comparison between experimental data and theoretical results. (Mg,Fe)SiO₃ post-perovskite is the least understood phase. Existing experimental data appear contradictory, and computational work is limited. The spin-state crossover in (Mg,Fe) SiO₃-post-perovskite is still a wide open question.