Electric Field Induced Kerr Rotation on Metallic Surfaces.

We investigate the electric field-induced Kerr rotation on metallic surfaces using ab-initio calculations of the full nonlocal dielectric tensor and its modulation under a biased electric field. We demonstrate that the optoelectric tensor comprises extrinsic and intrinsic components with distinct symmetry properties under time reversal. Focusing on Pt films of varying thickness, we reveal significant inter-layer and inter-subband transition contributions to both components. In order to calculate the optical propagation through a complex medium with nonlocal two-point dielectric tensor, we developed an exact scattering approach to solve Maxwell's equations. Using this method, we calculate the electric field-induced Kerr rotation for both s- and p-polarized incident light versus optical frequency. Our theoretical predictions agree well with experimental results across different Pt film thicknesses and optical frequencies. By varying Pt film thickness, we show that the characteristic length of the Kerr rotation is primarily determined by the optical skin depth, while the optically active region near the surface that is responsible for the current-induced Kerr rotation is limited to a few nm thicknesses. Importantly, we find that the intrinsic contribution to Kerr rotation, even under time-reversal symmetry, is comparable in magnitude to the extrinsic contribution. These findings provide new insights into the microscopic origins of current-induced Kerr rotation.