First-principles investigation of the spin state of ferrous iron in MgSiO$_3$ under pressure*

We present a density functional study of the pressure induced spin transition in ferrous iron in MgSiO$_3$ perovskite and post-perovskite. We address the influence of iron concentration and configuration (structural and magnetic), as well as technical issues such as the nature of the exchange correlation (XC) functional (LDA versus PBE-GGA) on the spin transition pressure. Supercells containing up to 160 atoms were adopted to tackle these issues. We show that there are preferred configurations for high-spin and low-spin iron and that the spin transition pressure depends strongly on iron concentration and XC functionals. We also address the possibility of a structural change accompanying the spin transition.