Strong effects of cation vacancies on the electronic and dynamical properties of FeO

We report pronounced modifications of the electronic and vibrational properties induced in FeO by cation vacancies, obtained within density functional theory incorporating strong local Coulomb interactions at Fe atoms. The insulating gap of FeO is reduced by about 50$\%$ due to unoccupied electronic bands introduced by trivalent Fe ions stabilized by cation vacancies. The changes in the electronic structure along with atomic displacements induced by cation vacancies affect strongly the phonon dispersions via modified force constants, including those at atoms beyond the nearest neighbors of defects. We demonstrate that theoretical phonon dispersions and their densities of states reproduce the results of inelastic neutron and nuclear resonant x-ray scattering experiments only when Fe vacancies and Coulomb interaction $U$ are both included explicitly in ab initio simulations, which also suggests that the electron-phonon coupling in FeO is strong.

Figure 1

Total orbital projected electronic DOS obtained for (a) the stoichiometric FeO, and defected Fe${}_{1-x}$O, with (b) $x=3$$\%$, and (c) $x=6$$\%$. The positive (negative) DOS represents the spin-up (spin-down) states in each case; the gaps between the valence and conduction band are indicated by dashed lines. Parameters: $U=6$ eV, $J=1$ eV.

Figure 2

Phonon dispersion relations for stoichiometric FeO (solid lines) and the relative intensities of the phonon modes in Fe${}_{1-x}$O with $x=3$$\%$, for $U=6$ eV, $J=1$ eV. The experimental data (solid squares) are adopted from Ref. 23. The highest intensity mode is taken as a reference (100$\%$); relative intensities are arranged into the following ranges indicated by the intensity of gray scale (color): 5$\%$–20$\%$ (light blue), 20$\%$–50$\%$ (cyan), 50$\%$–80$\%$ (blue), 80$\%$–100$\%$ (red). High-symmetry points are (in units of $2\pi /a$): $\Gamma =(0,0,0)$, $X=(\frac{1}{2},\frac{1}{2},0)$, $K=(\frac{3}{8},\frac{3}{8},\frac{3}{4})$, $L=(\frac{1}{2},\frac{1}{2},\frac{1}{2})$, $W=(\frac{1}{2},\frac{1}{4},\frac{3}{4})$.

Figure 3

Partial phonon DOS obtained for stoichiometric FeO (solid lines) and Fe${}_{1-x}$O with $x=6$$\%$ (shaded area) for sublattices of (a) oxygen and (b) iron ions. The experimental points in (b) are taken from the NRIXS experiment (Ref. 24). The dotted lines denote the Gaussian convolutions of our theoretical results with the experimental resolution of 2.4 meV. Parameters: $U=6$ eV, $J=1$ eV.

Figure 4

Diagonal elements $\Phi$ of the on-site force-constant matrix for distance $d/a$ from the vacancy in the Fe${}_{1-x}$O system with $x=3$$\%$. The vertical dashed lines denote ideal positions of the Fe and O atoms, whereas the horizontal solid and dashed lines stand for the respective force constants in the stoichiometric FeO. Parameters: $U=6$ eV, $J=1$ eV.