Electronic and optical properties of the ${\text{Mg}}_{2-x}{\text{Fe}}_x{\text{SiO}}_4$ spinel: From band insulator to Mott insulator

The crystal properties and electronic structure of ${\text{Mg}}_{2-x}{\text{Fe}}_x{\text{SiO}}_4$ spinel have been studied using the density-functional theory including the local Hubbard interaction $U$ within the generalized gradient approximation. The lattice constant depends linearly on increasing iron concentration $x$ in agreement with the Vegard’s law. The contributions of the $\text{Fe}\left(t_{2g}\right)$ and $\text{Fe}\left(e_g\right)$ orbitals to the electronic density of states have been determined and their crucial role in the band-gap formation has been elucidated. We explain the decrease in the insulating gap with increasing iron concentration on the basis of the Mott-Hubbard picture of correlated insulators. Thus, it was revealed that the electronic structure of ${\text{Mg}}_{2-x}{\text{Fe}}_x{\text{SiO}}_4$ evolves from the band insulator found in ${\text{Mg}}_2{\text{SiO}}_4$ to the Mott insulator with increasing iron concentration. We present also the absorption spectra derived from the complex dielectric tensor, which are in good qualitative agreement with the previously reported experimental data for a wide range of energies.

Figure 1

(Color online) The crystal structure of ${\text{Mg}}_{2-x}{\text{Fe}}_x{\text{SiO}}_4$. The dark (green) balls representing the Mg or Fe atoms and the ${\text{SiO}}_4$ tetrahedra are shown in (a). In (b) the metal ions are presented in corners of tetrahedra as dark (green) balls. The oxygen atoms are shown here as light (yellow) balls and form octahedra around the metal ions.

Figure 2

(Color online) Lattice constant, enthalpy, and average magnetic moment as functions of Fe concentration $x$. Triangles and squares represent the values obtained for the FM and AFM configurations, respectively. Solid lines were obtained by the linear regression of the calculated data.

Figure 3

(Color online) Comparison of the spin-projected EDOS of ${\text{Mg}}_2{\text{SiO}}_4$ (a) with the one obtained for ${\text{Mg}}_{1.875}{\text{Fe}}_{0.125}{\text{SiO}}_4$ $\left(x=0.125\right)$, i.e., for one Fe atom in the supercell shown in Fig. 1: (b) $U=0$, and (c) $U=4.5\text{eV}$. The energy $E=0$ corresponds to the highest occupied $p$-state in ${\text{Mg}}_2{\text{SiO}}_4$.

Figure 4

(Color online) The electronic structure of ${\text{Mg}}_{2-x}{\text{Fe}}_x{\text{SiO}}_4$ spinel for different Fe concentrations $x$ in the FM state obtained for $U=4.5\text{eV}$ and $J=0.9\text{eV}$.

Figure 5

(Color online) Electronic structure of ${\text{Mg}}_{2-x}{\text{Fe}}_x{\text{SiO}}_4$ for the AFM state with two Fe concentrations $x=1$ (top) and $x=2$ (bottom).

Figure 6

(Color online) Comparison of the EDOS for ${\text{MgFeSiO}}_4$ $\left(x=1\right)$ obtained in: (a) the GGA, i.e., neglecting local Coulomb interactions $\left(U=0\right)$ and (b) for realistic local Coulomb interactions with $U=4.5\text{eV}$.

Figure 7

(Color online) Dependence of the energy gap on the Fe concentration. Triangles up and down are the values of the gap for the FM state obtained directly from EDOS and calculated from Eq. (12), respectively. Squares and circles represent the insulating gaps for the AFM configuration obtained from EDOS and from Eq. (12), respectively. The lines connecting the average values of the gap are guides to the eye.

Figure 8

(Color online) Dependence of the energy band gap $E_g$ on pressure $p$, as obtained for ${\text{Fe}}_2{\text{SiO}}_4$ for the AFM (solid line) and FM (dashed line) configuration.

Figure 9

Absorption intensity $\alpha$ for ${\text{Mg}}_{1.875}{\text{Fe}}_{0.125}{\text{SiO}}_4$ as obtained: (a) for $U=4.5\text{eV}$ in a wide energy range and (b) at low energies for $U=0$ (dashed line) and $U=4.5\text{eV}$ (solid line). The band gap given by $p$ states in ${\text{Mg}}_2{\text{SiO}}_4$ is indicated by the onset of absorption at $\sim 6.0\text{eV}$, as shown in (b) by dotted line. The two vertical lines in (b) denote the positions of the experimental peaks given in Ref. 17.

Figure 10

(Color online) Absorption intensity $\alpha$ as obtained for ${\text{Mg}}_{2-x}{\text{Fe}}_x{\text{SiO}}_4$ with different Fe concentration $x=2.0$, 1.0, 0.5, 0.25, and 0.125, from top to bottom.