Figure 1

(a) Bulk unit cell for the room-temperature phase of Fe${}_3$O${}_4$. (b) Top view of the distorted $B$-layer model for the $\left(\sqrt{2}\times \sqrt{2}\right)R{45}^{\circ }$ reconstructed Fe${}_3$O${}_4$(001) surface. In the surface layer (left of the dashed line), pairs of surface Fe($B$)${}^{3+}$ cations relax perpendicular to the Fe($B$) row direction producing inequivalent narrow “$n$” and wide “$w$” sections. In the second layer, a bimodal charge order exists with formal Fe($B$)${}^{2+}$ and Fe($B$)${}^{3+}$ cations underneath the surface oxygen in the narrow and wide regions of the unit cell, respectively.Reuse & Permissions

Figure 2

(a) Overview STM image of the as-prepared Fe${}_3$O${}_4$(001) surface. A row of protrusions runs across the lower terrace terminating at step edges (indicated by the arrows). (b) High-resolution STM image of the area contained within the square in panel (a). On either side of the row of protrusions, the $\left(\sqrt{2}\times \sqrt{2}\right)R{45}^{\circ }$ reconstruction is out of phase by half a unit cell as indicated by the cyan and yellow lines, which pass through wide $w$ sections of the reconstruction in each domain. Hydroxyl groups appear as bright protrusions on the Fe($B$) rows (dashed oval). (c) Representative stretch of an APDB imaged with atomic resolution. Following the $w$ and $n$ sections of the surface reconstruction perpendicular to the Fe($B$) row, it is clear that the APDBs are formed where two $n$ sections meet. The circles indicate the position of the subsurface Fe($A$) atoms with positions that are not affected by the APDB. The bright protrusions located at the APDB are due to adsorbed hydroxyl groups. (d) Schematic of the APDB structure assuming the distorted $B$-layer model of the $\left(\sqrt{2}\times \sqrt{2}\right)R{45}^{\circ }$ reconstruction. The undulating rows of surface Fe($B$) atoms observed by STM are drawn as gray lines, whereas the subsurface Fe($B$) atoms are indicated by 2 and 3 (their formal oxidation state). The scheme demonstrates that the $n$-$n$ junction is consistent with four Fe${}^{2+}$ cations in a row in the second layer (highlighted yellow).Reuse & Permissions

Figure 3

(a) STM image of the Fe${}_3$O${}_4$(001) surface following 1-keV Ar${}^{+}$ sputtering (15 min) and 300 °C annealing (20 min) in a 2 × 10${}^{-6}$-mbar O${}_2$ background. Many small terraces are formed, in contrast to the samples annealed at 700 °C, which are largely flat (compare Fig. 2). (b) STM image of two small terraces that are not joined at any point. Lines connecting all of the wide sections of the lattice distortion on each terrace demonstrate that the terraces are out of phase by half a surface unit cell. The $\left(\sqrt{2}\times \sqrt{2}\right)R{45}^{\circ }$ surface unit cell is indicated by the red square.Reuse & Permissions

Figure 4

Simulated STM images. (a) A clean surface with a $\left(\sqrt{2}\times \sqrt{2}\right)R{45}^{\circ }$ reconstruction. This image reproduces the undulating rows of Fe($B$) atoms as observed experimentally. (b) Schematic of the 3 × 3 unit cell used to calculate the APDB structure. The numbers show the nominal charge state imposed on the second layer Fe($B$) atoms using $U_{\mathrm{eff}}$. (c) A clean surface with APDB. This image clearly shows the narrow-narrow junction at the APDB, which is marked by the dashed yellow line. Due to the small unit cell, a periodic array of APDBs is present. (d) A row of hydrogen atoms adsorbed to surface oxygen atoms at the APDB. The adjacent Fe($B$) atoms, which reside between the narrow-narrow junction at the APDB, are reduced to Fe${}^{2+}$ and appear as bright spots in the simulated STM image.Reuse & Permissions