Vibrational lifetimes and friction in adsorbate motion determined from quasi-elastic scattering

Multiple echoes in beam spin-echo spectroscopy and their effect on measurements of ultra-fast dynamics

Helium (³He) spin-echo is a powerful experimental technique used to probe ultra-fast atomic scale surface dynamics. The analysis of these measurements is typically performed assuming there is only a single spin-echo condition, expected to produce a constant signal for pure elastic scattering, a monotonically decaying signal for quasi-elastic scattering and oscillations from inelastic scattering events. In the present work, we show that there are in fact four spin-echoes which must be correctly accounted for, and that even in the case of elastic scattering these additional echoes lead to oscillations which could mistakenly be interpreted as being due to inelastic scattering. We demonstrate that it is possible to accurately simulate the experimental data by propagating the³He through the measured magnetic field profile of the apparatus and considering the geometry of the machine, allowing the effect of these additional echoes to be disentangled from inelastic scattering events in future³He spin-echo measurements.

Measuring surface phonons using molecular spin-echo

A new method to measure surface phonons with a molecular beam is presented. The method extends the principles of ³He spin-echo spectroscopy, to the more complex case of a molecular beam exchanging energy with the surface. Measurements are presented for inelastic scattering of D₂ from a Cu(111) surface. Similarly to helium spin-echo, experiments can be performed along optimal tilted projections making it possible to resolve energy peaks with a high energy resolution which is not restricted by the spread of energies of the incident beam. Two analysis methods for these molecular spin echo experiments are presented. A classical approach, analogous to that used for helium spin-echo, explains the most dominant excitation peaks measured, whereas a semi-classical approach allows us to identify smaller peaks which are related to the complexity of the multiple spin-rotation states which exist for molecules.

Amplitude of jump motion signatures in classical vibration-jump dynamics

The classical Langevin dynamics of a particle in a periodic potential energy landscape are studied via the intermediate scattering function (ISF). By construction, the particle performs coupled vibrational and activated jump motion with a wide separation of the vibrational period and the mean residence time between jumps. The long time limit of the ISF is a decaying tail proportional to the function that describes ideal jump motion in the absence of vibrations. The amplitude of the tail is unity in idealized jump dynamics models but is reduced from unity by the intra-well motion. Analytical estimates of the amplitude of the jump motion signature are provided by assuming a factorization of the conditional probability density of the particle position at long times, motivated by the separation of time scales associated with inter-cell and intra-cell motion. The assumption leads to a factorization of the ISF at long correlation times, where one factor is an ideal jump motion signature and the other component is the amplitude of the signature. The amplitude takes the form of a single-particle anharmonic Debye-Waller factor. The factorization approximation is exact at the diffraction conditions associated with the periodic potential. Numerical simulations of the Langevin equation in one and two spatial dimensions confirm that for a strongly corrugated potential the analytical approximation provides a good qualitative description of the trend in the jump signature amplitude, between the points where the factorization is exact.

Energy Dissipation during Diffusion at Metal Surfaces: Disentangling the Role of Phonons versus Electron-Hole Pairs

Helium spin echo experiments combined with ab initio based Langevin molecular dynamics simulations are used to quantify the adsorbate-substrate coupling during the thermal diffusion of Na atoms on Cu(111). An analysis of trajectories within the local density friction approximation allows the contribution from electron-hole pair excitations to be separated from the total energy dissipation. Despite the minimal electronic friction coefficient of Na and the relatively small mass mismatch to Cu promoting efficient phononic dissipation, about (20±5)% of the total energy loss is attributable to electronic friction. The results suggest a significant role of electronic nonadiabaticity in the rapid thermalization generally relied upon in adiabatic diffusion theories.