Thickness dependence of surface Rashba spin-momentum coupling

Here we present findings indicating that Rashba spin-momentum coupling (RSMC), traditionally believed to be confined within the Fermi wavelength from the surface, displays a thickness dependence in metallic thin films. Specifically, we observed that in Au films thinner than a critical thickness of 4 nm, and in Pt films thinner than 5 nm, quantum interference occurs between the top and bottom surface states, strongly impacting the surface spin polarization. The spin polarization gradually increases with the film thickness until it reaches these critical thresholds, beyond which it saturates. Our findings serve as examples illustrating that the characteristic length of RSMC far exceeds the Fermi wavelength, while the characteristic length has been regarded as the Fermi wavelength in spin-orbit torque measurements.