Incommensurate Moiré overlayer with strong local binding: CoO(111) bilayer on Ir(100)

Incommensurate relaxed overlayer Moiré structures are often interpreted as systems with weak lateral variations of the binding potential and thus no structural modulations in the overlayer material. We discuss here the example of a CoO(111) bilayer on Ir(100), which is a relaxed overlayer with strong structural response to the lateral modulation of interface properties but nevertheless is incommensurate. By means of density functional theory (DFT) calculations, we quantitatively reproduce all the structural parameters of the CoO(111) bilayer on Ir(100) as proposed by a recent low-energy electron diffraction analysis [Ebensperger et al., Phys. Rev. B 81, 235405 (2010)]. The calculations predict energetic degeneracies with respect to registry shifts of the CoO(111) film along [01$\overline{1}$]. Large-scale, low-temperature scanning tunneling microscopy topographies reveal that the true structure of the film is incommensurate in this direction, exhibiting a one-dimensional Moiré pattern with a period of about 9.4 $a_{\mathrm{Ir}}$. From DFT calculations for limiting (periodic) models, we can sample the potential landscape of the cobalt and oxygen atoms in the Moiré structure across the Ir(100) unit cell. We find that despite the non-commensurability of the film, the binding to the substrate is site specific with strong attraction and repulsion points for both cobalt and oxygen atoms, leading to severe local distortions in the film. The lateral modulation of the structural elements within the oxide film can be understood as a combination of the lateral variation in the Co-Ir binding potential and additional O-Ir binding.

Figure 1

Schematic model of the starting configurations for the calculations. The flat CoO bilayer film with $c$($10\times 2$) periodicity with respect to Ir(100) and a primitive unit cell are displayed. Small yellow (bright) spheres denote cobalt atoms, large blueish (gray) spheres denote oxygen atoms, and even larger light gray spheres denote iridium atoms of the uppermost layer. Oxygen atoms shaded darker are closer to the substrate in the corrugated starting configuration. The unit cell contains nine Co and nine O atoms, aligned parallel to the [01$\overline{1}$] directions and perfectly row-matched in the [011] direction. (a) The registry of the film is chosen symmetric to a first-layer Ir top site, i.e., there is a mirror plane (green line) intersecting a Co, an O, and a first-layer Ir atom [“mirror-top” (MT) model]. (b) Same as (a) but with $\sim$0.15 Å lateral shift of the CoO with respect to the substrate. The film is now symmetric to a first-layer Ir bridge site, i.e., the mirror plane intersects a Co, an O, and a second-layer Ir atom [“mirror-bridge” (MB) model].

Figure 2

Vertical coordinates of Co and O atoms parallel to the [01$\overline{1}$] direction for different values of $U$$-$$J$ in the DFT+$U$ calculations. Closed symbols denote the vertical positions of the Co atoms (left axis), open symbols those of the O atoms. The experimentally determined values from Ref. 19 are plotted for comparison. Only the positions in one half of the MT unit cell are shown.

Figure 3

Top and side views of the CoO-$c$($10\times 2$) Ir(100) (a) MT and (b) MB structures including structural parameters and spin orientations as determined by the DFT+$U$ calculations. (Experimental values taken from Ref. 19 are given in brackets.) The different types of atoms are displayed as in Fig. 1 and the magnetization direction of the Co atoms is indicated by different coloring and a dot for the down configuration. Oxygen atoms near Ir top sites (shaded darker) lie between the Co layer, while those in the vicinity of Ir bridge positions (shaded lighter) occupy sites above the Co atoms.

Figure 4

PBE calculated vertical coordinates of Co and O atoms for different magnetic configurations parallel to the [01$\overline{1}$] direction. Closed symbols denote the vertical positions of the Co atoms (right axis), open symbols those of the O atoms. “Nonmag.” refers to a nonmagnetic calculation, “mag.” to the magnetic configuration shown in Fig. 3, and “mag. alt.” to the same configuration but with the spins of Co1 and Co2 switched. The experimentally determined values from Ref. 19 are plotted for comparison. Only the positions in one half of the MT unit cell are shown.

Figure 5

Left: Calculated STM images for the MT and MB configurations of the CoO film for two different bias voltages and tip-surface distances. Right: Corresponding experimental STM images taken at the given tunneling parameters. The inset in (h) displays a vacancy at the high-lying oxygen site.

Figure 6

(a) Atomically resolved STM image (100 $\times$ 60 Å). The CoO film appears inhomogeneous both in the number of maxima and size of apparent unit cells. (b) Large-scale STM topography (300 $\times$ 250 Å) demonstrating the Moiré structure of the CoO film on Ir(100).

Figure 7

Compilation of reduced atomic coordinates (modulo substrate unit vectors) of Co and O taken from DFT calculations for both registries visualizing the Co and O traces across the Ir(100) unit cell in the Moiré structure. The triangles drawn in denote certain adsorption sites of oxygen (for details, see text).