Effect of $c\left(2\times 2\right)$-CO overlayer on the phonons of Cu(001): A first-principles study

We have examined the effect of a $c\left(2\times 2\right)$-CO overlayer on the surface phonons of the Cu(001) substrate by applying density-functional perturbation theory with both the local density approximation and generalized-gradient approximation (GGA) embodied in the Hedin-Lundqvist and the Perdew-Burke-Ernzerhof functionals, respectively. Our GGA results trace the Rayleigh wave softening detected by helium atom scattering (HAS) experiments to changes in the force constants between Cu surface atoms brought about by CO chemisorption and not merely to the effect of CO mass load on half of the surface atoms. The calculated surface phonon-dispersion curves reveal changes in the polarization of some modes, the most consequential of which is for those originally along the $\overline{Y}$ direction of the clean surface Brillouin zone (SBZ) that are backfolded along the $\overline{\Delta }$ direction of the chemisorbed SBZ. The $S_1$ mode along the $\overline{Y}$ direction of the $1\times 1$ SBZ—where it has mixed vertical and shear-horizontal polarization—, for example, is backfolded as a longitudinal-vertical mode, thereby indicating that $S_1$—predicted a long time back along $\overline{\Delta }$ for the clean surface—may be indirectly assessed in the vicinity of $\overline{X}$ upon CO adsorption by standard planar scattering techniques. These findings further suggest that some of the energy losses detected by HAS along $\overline{\Delta }$—originally interpreted as multiphonon excitations of the adlayer frustrated translation mode—may actually correspond to backfolded substrate surface modes.

Figure 1

(a) The top view of the surface shows CO (gray circles) and first (filled circles) and second (open circles) layer atoms of Cu(100). The $1\times 1$ (dashed line) and the $c\left(2\times 2\right)$ (solid line) surface unit cells are underlined. (b) The corresponding $\left(1\times 1\right)$ (dotted line) and $c\left(2\times 2\right)$ surface Brillouin zones (solid line) showing the $\overline{\Gamma }$, $\overline{X}$, and $\overline{M}$ points and the $\overline{\Delta }$, $\overline{\Sigma }$, and $\overline{Y}$ directions.

Figure 2

GGA-PBE phonon dispersion of Cu(100), modeled by a 50-layer slab. Theoretical surface modes (filled circles) are compared with HAS (open triangles) and electron-energy-loss spectroscopy (EELS) (open circles) measurements taken from Refs. 39, 40, 42, 46.

Figure 3

GGA-PBE phonon dispersion of $c\left(2\times 2\right)$-CO/Cu(100), modeled by a Cu 50-layer slab. Note that the dispersion curves of the high-lying modes, which correspond to the C-O stretch and the Cu-CO stretch modes, are omitted in this figure since the emphasis here is on the modes of the substrate. Filled circles denote theoretical surface modes. Experimental data are taken from Ref. 17: filled circles and triangles were associated with multiphonon processes. Open circles correspond to the substrate Rayleigh wave. Squares were associated with the FT mode of CO on the perfect $c\left(2\times 2\right)$ structure (filled) and on defects in the adlayer at lower coverage (open).