Role of d orbitals in the Rashba-type spin splitting for noble-metal surfaces

TL;DR

This study reveals that d-orbitals play a crucial role in the Rashba-type spin splitting of noble-metal surfaces, with spin-orbit interaction in the d-channel being the key factor influencing the splitting and spin orientation.

Contribution

It demonstrates that d-channel spin-orbit interaction, rather than p-channel, primarily governs the Rashba spin splitting in noble-metal surface states, highlighting the importance of d-orbitals.

Findings

d-channel SOI determines spin splitting and direction

Small d-orbital character varies linearly with momentum

Doping affects d-orbital contribution and spin splitting

Abstract

We investigate the Rashba-type spin splitting in the Shockley surface states on Au(111) and Ag(111) surfaces, based on first-principles calculations. By turning on and off spin-orbit interaction (SOI) partly, we show that although the surface states are mainly of p-orbital character with only small d-orbital one, d-channel SOI determines the splitting and the spin direction while p-channel SOI has minor and negative effects. The small d-orbital character of the surface states, present even without SOI, varies linearly with the crystal momentum k, resulting in the linear k dependence of the splitting, the Hallmark of the Rashba type. As a way to perturb the d-orbital character of the surface states, we discuss effects of electron and hole doping to the Au(111) surface.