Spin-orbit splitting of image states

TL;DR

This paper investigates the impact of spin-orbit interaction on image state electrons at metal surfaces, revealing Rashba-like dispersions and quantifying splittings that are experimentally observable and related to surface spin-flip scattering.

Contribution

It extends the phase-accumulation model to include spin-orbit effects, providing a quantitative description of spin-orbit splittings in image states on metal surfaces.

Findings

Spin-orbit splittings range from 38-88 meV Å in magnitude.

Splittings vary with quantum number as 1/(n+a)^3.

Splittings are larger than some exchange-splittings and comparable to linewidths.

Abstract

We quantify the effect of the spin-orbit interaction on the Rydberg-like series of image state electrons at the (111) and (001) surface of Ir, Pt and Au. Using relativistic multiple-scattering methods we find Rashba-like dispersions with Delta E(K)=gamma K with values of gamma for n=1 states in the range 38-88 meV Angstrom. Extending the phase-accumulation model to include spin-orbit scattering we find that the splittings vary like 1/(n+a)^3 where a is the quantum defect and that they are related to the probability of spin-flip scattering at the surface. The splittings should be observable experimentally being larger in magnitude than some exchange-splittings that have been resolved by inverse photoemission, and are comparable to linewidths from inelastic lifetimes.