Effect ofc(2×2)-CO overlayer on the phonons of Cu(001): A first-principles study

Abstract

We have examined the effect of a $c(2\ifmmode\times\else\texttimes\fi{}2)$-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 $\overline{\ensuremath{\Delta}}$ direction of the chemisorbed SBZ. The ${S}_{1}$ mode along the $\overline{Y}$ direction of the $1\ifmmode\times\else\texttimes\fi{}1$ 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 $\overline{\ensuremath{\Delta}}$ 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 $\overline{\ensuremath{\Delta}}$---originally interpreted as multiphonon excitations of the adlayer frustrated translation mode---may actually correspond to backfolded substrate surface modes.