Electronic structure, magnetism, and optical properties ofFe2SiO4fayalite at ambient and high pressures: AGGA+Ustudy

Abstract

The electronic structure, magnetism, and optical properties of ${\mathrm{Fe}}_{2}{\mathrm{SiO}}_{4}$ fayalite, the iron-rich end member of the olivine-type silicate, one of the most abundant minerals in Earth's upper mantle, have been studied by density-functional theory within the generalized gradient approximation (GGA) with the on-site Coulomb energy $U=4.5\mathrm{eV}$ taken into account $(\mathrm{GGA}+U).$ The stable insulating antiferromagnetic solution with an energy gap $\ensuremath{\sim}1.49\mathrm{eV}$ and a spin magnetic moment of $3.65{\ensuremath{\mu}}_{B}$ and an orbital magnetic moment of $0.044{\ensuremath{\mu}}_{B}$ per iron atom is obtained. It is found that the gap opening in this fayalite results mainly from the strong on-site Coulomb interaction on the iron atoms. In this band structure, the top of valence bands consists mainly of the $3d$ orbitals of Fe2 atoms, and the bottom of the conduction bands is mainly composed of the $3d$ orbitals of Fe1 atoms. Therefore, since the electronic transition from the Fe2 $3d$ to Fe1 $3d$ states is weak, significant electronic transitions would appear only about 1 eV above the absorption edge when Fe-O orbitals are involved in the final states. In addition, our band-structure calculations can explain the observed phenomena including redshift near the absorption edge and the decrease of the electrical resistivity of ${\mathrm{Fe}}_{2}{\mathrm{SiO}}_{4}$ upon compression. The calculated Fe p partial density of states agree well with Fe K-edge x-ray absorption spectrum. The calculated lattice constants and atomic coordinates for ${\mathrm{Fe}}_{2}{\mathrm{SiO}}_{4}$ fayalite in orthorhombic structure are in good agreement with experiments.