Spin-State Crossover and Hyperfine Interactions of Ferric Iron in ${\mathrm{MgSiO}}_3$ Perovskite

Using density functional theory plus Hubbard $U$ calculations, we show that the ground state of $(\mathrm{Mg},\mathrm{Fe})(\mathrm{Si},\mathrm{Fe}){\mathrm{O}}_3$ perovskite, the major mineral phase in Earth’s lower mantle, has high-spin ferric iron ($S=5/2$) at both dodecahedral ($A$) and octahedral ($B$) sites. With increasing pressure, the $B$-site iron undergoes a spin-state crossover to the low-spin state ($S=1/2$) between 40 and 70 GPa, while the $A$-site iron remains in the high-spin state. This $B$-site spin-state crossover is accompanied by a noticeable volume reduction and an increase in quadrupole splitting, consistent with recent x-ray diffraction and Mössbauer spectroscopy measurements. The anomalous volume reduction leads to a significant softening in bulk modulus during the crossover, suggesting a possible source of seismic-velocity anomalies in the lower mantle.

Figure 1

Atomic structure of $({\mathrm{Mg}}_{0.875}{\mathrm{Fe}}_{0.125})({\mathrm{Si}}_{0.875}{\mathrm{Fe}}_{0.125}){\mathrm{O}}_3$ Pv, configured with the shortest iron-iron distance, viewing along the [001] direction. Large (orange) and small (green) spheres represent Fe and Mg sites, respectively. Si-O and Fe-O octahedra are shown in opaque [dark (blue)] and translucent [light (orange)] colors.

Figure 2

Relative enthalpies of $({\mathrm{Mg}}_{0.875}{\mathrm{Fe}}_{0.125})({\mathrm{Si}}_{0.875}{\mathrm{Fe}}_{0.125}){\mathrm{O}}_3$ Pv in different spin states obtained using different functionals and Hubbard $U$. The reference state has HS iron in the $A$ site and LS iron in the $B$ site ($A$ HS, $B$ LS). Predicted transition pressures by $\mathrm{LDA}+U_{\mathrm{sc}}$ (a), $\mathrm{GGA}+U_{\mathrm{sc}}$ (b), and $\mathrm{GGA}+U$ with $U=4\mathrm{eV}$ (c) are 41, 70, and 29 GPa, respectively. Dashed lines in (c) correspond to antiparallel spins at $A$ and $B$ sites.

Figure 3

Calculated QSs of (a) ferrous iron [27] and (b) ferric iron in ${\mathrm{MgSiO}}_3$ Pv. Letters $A$ and $B$ in (b) refer to iron-occupying site. Arrows in (c) indicate the measured effect of pressure on QSs [16, 18, 30].

Figure 4

Compression curves (a) and bulk modulus (b) of $({\mathrm{Mg}}_{1-x}{\mathrm{Fe}}_x)({\mathrm{Si}}_{1-x}{\mathrm{Fe}}_x){\mathrm{O}}_3$ Pv computed with $\mathrm{LDA}+U_{\mathrm{sc}}$ ($x=0.125$) and room-temperature measurements ($x=0.1$) [30]. Both the measured and calculated compression curves exhibit a clear reduction accompanying the $B$-site HS-LS crossover, which leads to a softening in bulk modulus shown in (b).