Spin Transition in Magnesiowüstite in Earth’s Lower Mantle

Iron in the major lower mantle (LM) minerals undergoes a high spin (HS) to low spin (LS) transition at relevant pressures (23–135 GPa). Previous failures of standard first principles approaches to describe this phenomenon have hindered its investigation and the clarification of important consequences. Using a rotationally invariant formulation of $\mathrm{LDA}+U$ we report a successful study of this transition in low solute concentration magnesiowüstite, $({\mathrm{Mg}}_{1-x}{\mathrm{Fe}}_x)\mathrm{O}$, ($x<0.2$), the second most abundant LM phase. We show that the HS-LS transition goes through an insulating (semiconducting) intermediate mixed spins (MS) state without discontinuous changes in properties, as seen experimentally. We show that the HS state crosses over smoothly to the LS state passing through an insulating MS state where properties change continuously, as seen experimentally.

Figure 1

Computed Hubbard $U$ as function of pressure for ferromagnetic HS and LS states. $U$s for antiferromagnetically ordered spins fall within these same ranges. $U_{\mathrm{HS}}=-[0.15V-7.92]\pm 0.2\mathrm{eV}$ and $U_{\mathrm{LS}}=-[0.06V-5.61]\pm 0.2\mathrm{eV}$, where $V$ is the volume per formula unit in $\AA$ [3]. Variations of $U$ within these ranges have minor influence on the structural properties. Open circle is $U$ for HS iron in FeO [12].

Figure 2

Pseudocharge densities around ferrous iron in Mw with $X_{\mathrm{Fe}}=12.5\%$. These are isosurfaces with $\rho =0.3\mathrm{e}/{\AA }^3$ for majority (a) and minority HS (b), and majority and minority LS (c). Depiction of the polyhedral volume collapse across the spin transition (d). Six caps surrounding the ferrous ion belong to oxygens.

Figure 3

Static enthalpy differences between LS and HS phases at three different iron concentrations (a). Enthalpy differences in Mw with $X_{\mathrm{Fe}}=18.75\%$, between states with various fractions of coexisting HS and LS irons, $n=n_{\mathrm{LS}}/(n_{\mathrm{HS}}+n_{\mathrm{LS}})$, and the HS state (b). The reference green line corresponds to the enthalpy of all irons in the HS state ($n=0$). Pressure-volume curves for the same $n$s (c) shown in (b). Experimental results [3] at 300 K for Mw with $X_{\mathrm{Fe}}=17\%$ are represented by $+$.

Figure 4

Spin cross over in Mw with $X_{\mathrm{Fe}}=18.75\%$. $n$ is the fraction of LS irons. Experimental transition pressures at 300 K in Mw with $X_{\mathrm{Fe}}=17\%$ are from x-ray emission spectroscopy. They are denoted by gray [2] and white [3] arrows, respectively. The gray line is a lower mantle geotherm [20]. For reference, the melting temperature of MgO at ambient pressure is $\sim 3100\mathrm{K}$ increasing to $\sim 4000\mathrm{K}$ at $\sim 33\mathrm{GPa}$ [25].