A. Franchini

Surface and gap intrinsic localized modes in one-dimensional III-V semiconductors

A theoretical investigation has been made of intrinsic localized vibrational modes in an anharmonic one-dimensional diatomic lattice with alternating force constants coupling successive neighbours. This system simulates a row of atoms in the 111 direction of a III-V semiconductor. Specific calculations have been carried out for GaN, because it has a large gap between acoustic and optical branches. We study small-amplitude atom vibrations (up to 0.4 A), accessible to experimental detection, in order to legitimize the expansion of the full potential to include cubic and quartic terms. We consider then nearest-neighbour interactions through harmonic as well as cubic and quartic anharmonic interactions to study the interplay between cubic and quartic terms in the frequencies of the localized modes. The force constants were determined empirically by fitting the longitudinal branches in the -L direction of GaN. We have studied both gap and surface intrinsic localized modes. Zinc-blende-structure chains are of particular interest, because the lack of inversion symmetry prevents the classification of the modes as even or odd parity. Nevertheless, modes were found that closely resemble the even- or odd-parity modes of an NaCl-structure chain. Their frequencies lie inside the gap for GaN. The absence of inversion symmetry permits a variety of surface modes to exist, depending on whether the bond at the surface is strong or weak and the atom at the surface is light or heavy. All surface mode frequencies for GaN lie inside the gap as found with the use of the full potential.

Surface resonant phonons of Ag(110)

Abstract A study of the dynamics of the Ag(110) surface in the ḡGȲ direction is presented. The experimental TOF spectra show the existence of two low frequency modes with high scattering intensity and a dispersionless high frequency mode with a smaller intensity. The theoretical analysis based on a force constant model that contains long-range central interactions and short-range angular forces explains accurately both the dispersions and the scattering intensities of the three modes in terms of resonant and localized vibrations related to the modifications of the surface force constants caused by the different role played by the many-body forces in the surface region.

Debye-Waller factor for He/Pt(111)

Abstract We report accurate measurements of the dependence of the specular reflectivity on surface temperature and on incident angle, for He scattering off Pt(111). The usual Debye-Waller formula with a Beeby correction fits the data, provided that the effective well depth is adjusted. We show that a full calculation of the Debye-Waller exponent also reproduces the data. The inelastic atom-surface interaction and the surface phonon spectrum used in the calculation are the ones that reproduce the time-of-flight data obtained in separate experiments. No further adjustable parameters are needed.

Theory of inelastic Ne scattering from the Ni(111) surface

The recent inelastic Ne scattering data for Ni(111) by Feuerbacher and Willis are theoretically analyzed in the framework of the distorted wave Born approximation. A Ne-surface soft potential model is inferred from two-body Ne-Ni interactions and the many-body effects due to the phonon-induced surface electron charge redistribution are qualitatively described by three-body forces. The surface-projected phonon densities for the Ni(111) surface are calculated from a force constant model including three-body forces. The cut-off produced by the softness of the Ne-Ni potential accounts for the observed cross-over from Rayleigh-wave to bulk phonon scattering regimes. The one-phonon picture correlates well with experiments for outgoing angles slightly apart from the specular condition (Rayleigh-wave regime) whereas for larger deviations from the specular condition (bulk phonon regime) multiphonon contributions are important.

Theory of intrinsic localized modes in diatomic chains: beyond the rotating wave approximation

Intrinsic localized modes in the gap of a diatomic chain with free ends are discussed in detail by going beyond the rotating wave approximation. We include in the time dependence of the displacements terms up to cos (2ωt). We consider a finite chain of particles interacting with nearest-neighbour interactions. We study amplitudes of the intrinsic localized modes smaller than 0.25 A. In this range of amplitudes the full potential can be well represented by an expansion in powers of the displacements up to fourth-order terms. The use of a force constant model allows us to simplify the problem. As a test case we consider a chain of LiI atoms. We found intrinsic localized modes in the gap. The amplitudes of the first harmonic term (cos (ωt)) are of even or odd parity, whereas we prove that the amplitudes of the static part and those of the second harmonic can have only even symmetry. The main result of the paper is that the amplitudes associated with the second harmonic are two or three orders of magnitude less than those of the first harmonic. Furthermore, the frequency of the localized modes are modified by less than 1% by the inclusion of the second harmonic.

Inelastic scattering of helium atoms from the phonons of the reconstructed Au(111) surface

We present inelastic atom-surface phonon scattering time-of-flight spectra for the reconstructed Au(111) surface. The shapes of the spectra are compared with calculated reflection coefficients based on a simplified lattice dynamical model for the reconstructed surface. The force constants were determined from a best fit of the surface phonon dispersion curves and the lateral atom-atom interactions in the surface layer were found to be 30% of the bulk value. The theoretical spectra reproduce the overall lineshape of the experimental spectra and reveal additional features which can be attributed to the reconstruction of the surface layer with respect to the substrate.

Localized spin modes in ferromagnetic cylindrical dots with in-plane magnetization

A study of spin localized excitations in ferromagnetic tangentially magnetized dots of cylindrical shape and of nanometric size is presented. A recently formulated variational theory permits us to study the most representative localized spin modes of the spectrum. One of these, the fundamental mode, is mainly localized in the central part of the dot endfaces and is analogous to the Kittel uniform mode in ellipsoids. We also investigate the dynamical properties of spin modes localized in the lateral part of the dot endfaces along the direction of the applied magnetic field, studying the dependence of their localization on the variational parameter and the applied magnetic field. Finally, a comparison of the calculated frequencies of some of these localized modes with available experimental data is performed.

Surface phonon calculations of the Ni (111) surface with adsorbed oxigen

Abstract In the framework of a central and angular force constant model we have evaluated the phonon spectrum and the loss function of the Ni (111) surface with p(2×2) and ( 3 × 3 )R30° adsorbed lattices of Oxigen. The calculations compare well with recent EELS experimental data. We give reason of the different origin of the weaks observed in the measured spectra in terms of either the modes of the substrate or of the modes induced by the adsorbate.

Surface Phonon Calculations in Metals and Comparison with Experimental Techniques

There has been considerable recent progresses in the experimental techniques to detect surface phonons over the entire Brillouin zone for noble and transition metals with the high resolution electron energy loss spectroscopy and with the inelastic atomic scattering. However the cross sections are in general not strictly proportional to the density of states so that in the interpretation of the experimental spectra it is necessary a knowledge of the scattering mechanisms.

Theory of one-phonon scattering of atoms from metal surfaces: Application to He/Ag(111)

Abstract We present explicit expressions for one-phonon scattering of atoms from metal surfaces, within the distorted wave Born approximation by including Van der Waals forces. A comparison is made with the recent high-resolution time of flight spectra for He/Ag(1 1 1). We explain in quantitative terms the position and the intensity of the peaks due to scattering from the Rayleigh wave of silver. Also the bulk phonons contribute to the spectra, but the calculated intensities underestimate the data.