Microscopic theory of surface phonons in Al(100): Mechanisms for the anomalous behavior of the dispersion curves for large wave vectors

The frequencies of surface phonons measured on the (100) surface of fcc metals are higher than the values obtained from bulk force constants. We study the origin of this ``anomaly'' for Al(100) via a first-principles calculation of the interatomic force constants and surface-phonon dispersion relations to second order in the pseudopotential. The key quantity behind the anomaly turns out to be the force constant coupling nearest neighbors in the outmost atomic layer for displacements orthogonal to the bond and to the surface. This conclusion differs from mechanisms proposed for simple models, i.e., surface stress and force-constant stiffening.