Surface dynamics of relaxed (001) slabs of alkali halides and MgO.

Abstract

We have performed a comprehensive study of the lattice dynamics of the unrelaxed and relaxed (001) surfaces of the alkali halides and MgO. The dynamical calculations were carried out for 15-layer slabs, for which the surface relaxation had been evaluated in earlier work [F.W. de Wette, W. Kress, and U. Schr\oder, Phys. Rev. B 32, 4143 (1985)]. Both the relaxation calculations and the dynamical calculations were based on the same shell models for the alkali halides, available in the literature. The results for the surface-mode frequencies at the high-symmetry points \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}, X\ifmmode\bar\else\textasciimacron\fi{}, and M\ifmmode\bar\else\textasciimacron\fi{} of the surface Brillouin zone (SBZ) are presented, and compared with the corresponding frequencies for unrelaxed slabs. In addition, for those compounds not treated in the calculations of Chen, de Wette, and Alldredge [Phys. Rev. B 15, 1167 (1977)] for unrelaxed alkali halide slabs (NaBr, KF, KCl, KBr, KI, RbBr, and RbI) as well as for RbF, we also present dispersion-curve diagrams for wave vectors along the boundary \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} X\ifmmode\bar\else\textasciimacron\fi{} M\ifmmode\bar\else\textasciimacron\fi{} of the irreducible part of the SBZ. In general the relaxation-induced changes in the surface-mode frequencies are small; the largest changes for each compound are found for the optical surface mode with polarization perpendicular to the surface (${\mathrm{SP}}_{\mathrm{\ensuremath{\perp}}}$). Moreover, as a general rule, the effects of relaxation on the surface dynamics are largest for the heavy compounds; these have the largest ionic polarizabilities and exhibit the largest surface relaxation. The most pronounced relaxation-induced changes in the surface dynamics occur for RbF, RbBr, and RbI. In RbF the optical surface mode ${\mathrm{SP}}_{\mathrm{\ensuremath{\perp}}}^{\mathrm{\ensuremath{-}}}$, which lies in the optical-acoustical gap, undergoes a substantial upward shift as a result of the relaxation, while in RbBr and RbI the same optical surface mode ${\mathrm{SP}}_{\mathrm{\ensuremath{\perp}}}$ is pushed above the bulk continuum. These three should be the most interesting cases for experimental study by inelastic He scattering. Experimental confirmation or lack of confirmation of these predictions will provide important information about suitability of bulk interaction models for use in surface dynamical calculations.