Surface Verwey Transition in Magnetite

We report density functional studies of the (001) surface of magnetite that account for local Coulomb interactions. Iron cations in the surface layers exhibit charge and $t_{2g}$ orbital ordering that is coupled with the lattice strains. Orbital ordering is present for various surface stoichiometries and causes opening of the band gap $E_g\sim 0.3\mathrm{eV}$ at the surface, such that the (001) surface of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ remains insulating also in the high temperature cubic phase. The $(\sqrt{2}\times \sqrt{2})R45°$ surface reconstruction is related to orbital ordering.

Figure 1

Surface energy diagram for the (001) face of ${\mathrm{Fe}}_3{\mathrm{O}}_4$. The UHV conditions correspond to ${\mu }_{\mathrm{O}}\approx -2\mathrm{eV}$. Symbols are explained in the text, and $\mathrm{Fe}(A)d+\mathrm{O}$ stands for the oxygen atom adsorbed on the surface tetrahedral iron.

Figure 2

Electronic density of states projected on the $\mathrm{Fe}(B)$ $d$ orbitals for the first (a) and second (b) surface layer. Dashed line in (a) represents density of states for the bulk. In (b) dashed and solid lines represent two types of Fe cations. The total density of states of two surface layers and for all models considered in this Letter (c).

Figure 3

Electron density integrated around localized state $E-E_{\mathrm{F}}=-0.5\mathrm{eV}$ (a) octahedral termination $\mathrm{Fe}(B)$; (b) $0.5\mathrm{Fe}(A)$ termination; (c) oxygen vacancy on the octahedral termination; (d) tetrahedral termination $\mathrm{Fe}(A)d$. Large (blue) spheres are for $\mathrm{Fe}(B)$ cations, small (white) represent $\mathrm{Fe}(A)$, and medium (red) are for oxygen. Only the two topmost surface layers of the single $(\sqrt{2}\times \sqrt{2})R45°$ surface cell are shown for clarity. The surface is parallel to the picture plane. $\mathrm{Fe}(A)$ cations above octahedral layer in (b) and (d) are marked with black dots.