Si(775)-Au atomic chains: Geometry, optical properties, and spin order

The geometry and electronic structure of self-assembled atomic scale Au wires on Si(775) are investigated within density functional theory. The calculated surface diagram indicates the existence of two stable configurations with Au coverages of 0.32 and 0.96 monolayers, respectively. The low-coverage structure is predicted to host an antiferromagnetic spin chain localized at the Si rest atom dangling bonds, while the high-coverage structure is characterized by a Au-induced $\beta \text{−}\sqrt{3}$-like structure on the terrace. These structural models are supported by the comparison of measured and calculated surface optical anisotropies.

Figure 1

Top and side view of the energetically most favored Si(775)-Au surface structures for Au coverages of (a) 0.32 ML (“dbl-Au”), (b) 0.40 ML, (c) 0.48 ML, (d) 0.56 ML, (e) 0.64 ML $[\alpha \text{−}\left(\sqrt{3}\times \sqrt{3}\right)]$, and (f) 0.96 ML $[\beta \text{−}\left(\sqrt{3}\times \sqrt{3}\right)]$. The color coding is Au atoms (yellow), Si HC and step edge atoms (red), Si adatoms (blue), and Si rest atoms (green).

Figure 2

Calculated surface phase diagram of Si(775)-Au as a function of the Au chemical potential $\mathrm{\Delta }{\mu }_{\mathrm{Au}}$ relative to its bulk value. Regions of stability for low and high coverage phases are indicated.

Figure 3

Reflectance anisotropy spectra of the Si(775)-Au surface. (a) Experimental data measured at room temperature for 0.32, 0.6, and 1.0 ML coverages of Au, along with (inset) LEED images for the 0.32 and 0.6 ML coverages. (b) Calculated spectra for the dbl-Au and $\beta \text{−}\sqrt{3}$ reconstructions, as well as for the most stable 0.56 ML model [see Fig. 1]. All spectra are computed within PBE; the LDA spectrum for dbl-Au is also shown.

Figure 4

Calculated STM images of Si(775)-Au with 0.32 ML and 0.96 ML Au coverage for empty (left) and filled (right) states. The two uppermost layers of the respective structural motif are superimposed over the STM image for better clarification.

Figure 5

Calculated band structures and density of states for the Si(775)-Au dbl-Au (a) and $\beta \text{−}\sqrt{3}$ model (c). The corresponding unfolded bands for the primitive translational symmetry are shown in (b) and (d). The Brillouin zone notation is indicated in (e). The color coding of the bands/states corresponds to Fig. 1 and indicates localization at Au atoms (yellow), Si HC atoms (red), Si adatoms (blue), and Si rest atoms (green). The point size in the unfolded band structures represents the $\times 1$ character of the respective state; cf. Ref. [38]. Yellow squares indicate ARPES data from Ref. [10]. Yellow semitransparent lines are a fit to the Au bands with a model of free electrons and two energy levels (for more details see Refs. [24, 39]).

Figure 6

Calculated spin density for (a) antiferromagnetic and (b) ferromagnetic spin ordered configurations of the dbl-Au model. Red and blue isosurfaces represent different spin orientations.

Figure 7

Calculated band structures and density of states for the Si(775)-Au dbl-Au model: (a) AFM configuration; (b), (c) the two spin channels of the FM configuration. The color coding of the bands/states corresponds to that of Figs. 1 and 5, apart from the adatom-related bands, which are not colored for better visibility.