Influence of isolated and clustered defects on electronic and dielectric properties of wüstite

The influence of intrinsic Fe defects in FeO (either single cation vacancies or prototypical 4:1 vacancy clusters) on electronic and dielectric properties is studied within density-functional theory. The importance of local Coulomb interactions at Fe atoms is highlighted and shown to be responsible for the observed insulating Mott gap in FeO, which is reduced by the presence of defects. We investigate nonstoichiometric configurations of ${\mathrm{Fe}}_{1-x}\mathrm{O}$ with $x$ ranging from 3% to 9%, and we find the aliovalent Fe cations in both the regular and interstitial lattice sites of the considered configurations. Furthermore, we show that the trivalent Fe ions, induced by both isolated and clustered Fe vacancies, introduce the empty band states inside the insulating gap, which decreases monotonically with increasing cation vacancy concentration. The ${\mathrm{Fe}}_{1-x}\mathrm{O}$ systems with high defect content become metallic for small values of the Coulomb interaction $U$, yielding an increase in the dielectric functions and optical reflectivity at low energies, in agreement with the experimental data. Due to the crystal defects, the infrared-active transverse optic phonons split and distribute over a wide range of frequencies, clarifying the origin of the exceptionally large spectral linewidths of the dielectric loss functions observed for wüstite in recent experiments.

Figure 1

Schematic representation of the prototypical 4:1-type cluster with a single Fe ion in a tetrahedral configuration of ${\mathrm{Fe}}_{1-x}\mathrm{O}$.

Figure 2

Densities of electron states calculated for ${\mathrm{Fe}}_{1-x}\mathrm{O}$ containing 4:1-type vacancy clusters ($x=5\%$) at $U_{\mathrm{eff}}=5$ eV. Configuration with (a) interstitial ${\mathrm{Fe}}^{3+}$ ion and (b) interstitial ${\mathrm{Fe}}^{2+}$ ion. Positive (negative) values represent the spin-up (spin-down) components. The $3d$ states of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions residing in the regular ($R$) and interstitial ($I$) lattice sites are denoted by shaded areas (see the legend). The solid curve corresponds to ${\mathrm{O}}^{2-}$ states. The top of the valence band is taken as the reference energy (0 eV).

Figure 3

Magnetization isosurfaces of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{2+}$ cations in ${\mathrm{Fe}}_{1-x}\mathrm{O}$ containing 4:1-type vacancy clusters ($x=9\%$) calculated at $U_{\mathrm{eff}}=5$ eV. (a) Configuration with the ${\mathrm{Fe}}^{2+}$ ion at the $R$ site and the ${\mathrm{Fe}}^{3+}$ ion at the $I$ site, (b) configuration with the ${\mathrm{Fe}}^{2+}$ ion at the $I$ site and the ${\mathrm{Fe}}^{3+}$ ion at the $R$ site. The cation vacancies and the $R$ sites of ${\mathrm{Fe}}^{3+}$ ions are denoted, respectively, by white and red spheres, whereas the magnetization isosurface is marked in green. For clarity, the isosurfaces are drawn only for the $I$ site and one selected $R$ site. Note the relatively random distribution of ${\mathrm{Fe}}^{3+}$ ions around the 4:1 defect.

Figure 4

Influence of local interaction $U_{\mathrm{eff}}$ and vacancy concentration $x$ on the energy gap $E_g$ in ${\mathrm{Fe}}_{1-x}\mathrm{O}$. The inset shows the bandwidth ($\Delta$) of the empty states of ${\mathrm{Fe}}^{3+}$ cations as a function of increasing $x$ for $U_{\mathrm{eff}}=5$ eV. Dashed lines are guides for the eye.

Figure 5

Real and imaginary parts of dielectric function (2) vs photon energy for (a) FeO with isolated vacancies and (b) FeO with vacancy clusters. Calculations are performed with $U_{\mathrm{eff}}=5$ eV.

Figure 6

Dependence of (a) real and (b) imaginary parts of the dielectric function on $U_{\mathrm{eff}}$ for ${\mathrm{Fe}}_{1-x}\mathrm{O}$ with $x=6\%$. The values derived from the experiment (open symbols) are adopted from Ref. [20].

Figure 7

(a) Reflectivity $R\left(\omega \right)$, (b) refractive index $n\left(\omega \right)$ and extinction coefficient $k\left(\omega \right)$ of ${\mathrm{Fe}}_{1-x}\mathrm{O}$ with different nonstoichiometry. Theoretical and experimental data [24] are denoted by solid and dashed lines and symbols, respectively. Theoretical results are obtained for $U_{\mathrm{eff}}=5$ eV.

Figure 8

Theoretical infrared absorption intensities (dotted vertical lines) of ${\mathrm{Fe}}_{1-x}\mathrm{O}$ with the Fe-vacancy content of 5% (vacancy clusters) and 6% (isolated vacancies) and the Gaussian convolutions of theoretical spectra with a FWHM of 33 ${\mathrm{cm}}^{-1}$ (solid lines). The experimental dielectric loss function [22] measured at 5 K for ${\mathrm{Fe}}_{1-x}\mathrm{O}$ with $x=7–8$ % is represented by solid symbols. The frequencies ${\omega }_{\mathrm{TO}}$ correspond to the transverse-optic phonons. Theoretical results are obtained for $U_{\mathrm{eff}}=5$ eV.