Current-Induced Circular Dichroism on Metallic Surfaces: A First-Principles Study

TL;DR

This study uses first-principles calculations to analyze the current-induced optical response and orbital magnetization at metallic surfaces, revealing significant differences between theoretical models and emphasizing the importance of accurate descriptions.

Contribution

It provides a detailed first-principles comparison of gauge-invariant self-rotation and atom-centered approximation methods for current-induced orbital magnetization in metallic films.

Findings

Self-rotation contribution is larger than ACA orbital moments by an order of magnitude.

Finite-size effects significantly influence the orbital magnetization.

Surface accumulation saturates at a length scale comparable to the mean free path.

Abstract

We use {\it ab initio} calculations to understand the current-induced optical response and orbital moment accumulation at the surfaces of metallic films. These two quantities are related by a sum rule that equates the circular dichroic absorption integrated over frequency to the gauge-invariant self-rotation contribution to the orbital magnetization, $\vec{M}_{\rm SR}$. In typical ferromagnets, $\vec{M}_{\rm SR}$ is a good approximation to the total orbital magnetization. We compute the current-induced $\vec{M}_{\rm SR}$ for a Pt thin film and compare it to the current-induced orbital moment accumulation calculated with the atom-centered approximation (ACA). We find significant differences: the size of $\vec{M}_{\rm SR}$ is, in general, larger than the ACA orbital moment accumulation by an order of magnitude and includes substantial finite-size effects. The differences between the two quantities caution against interpreting optical measurements with models utilizing the ACA. Finally, we compute the total $\vec{M}_{\rm SR}$ and ACA orbital moment accumulation as a function of layer thickness. For both quantities, the length scale at which the total surface accumulation saturates is on the order of the mean free path and longer than the length scale of their spatial profiles.