Scaling law for Rashba-type spin splitting in quantum-well films

We use laser-based spin- and angle-resolved photoemission spectroscopy (laser-SARPES) with high resolution experimentally determine, for the first time, Rashba parameters of quantum-well states (QWSs) systematically changing film thickness quantum numbers, through observation Ag films grown on an Au(111) substrate. The data are very well reproduced by theoretical calculations based density functional theory. Most importantly, we find a scaling law parameter (${\ensuremath{\alpha}}_{\mathrm{R}}$) that magnitude ${\ensuremath{\alpha}}_{\mathrm{R}}$ is scaled charge at interface spin-orbit coupling ratio between substrate, it expressed single straight line regardless numbers. new finding not only crucial to understand effect in QWSs but also gives foundation growth engineering fine-tune spin splitting 2D heterostructure systems.