Magneto-optical Kerr effect in spin split two-dimensional massive Dirac materials

TL;DR

This paper demonstrates that spin-orbit interactions and exchange spin splitting in 2D massive Dirac materials like TMDs induce a measurable magneto-optical Kerr effect, enabling detection of magnetic impurities.

Contribution

It reveals how spin-orbit coupling and magnetic exchange lead to a net Kerr effect in 2D Dirac materials, which was previously obscured by Berry curvature cancellation.

Findings

Kerr rotation depends on frequency and exchange splitting.

Substrate effects critically influence Kerr response.

Magneto-optical Kerr spectroscopy can detect single magnetic impurities.

Abstract

Two-dimensional (2D) massive Dirac electrons possess a finite Berry curvature, with Chern number $\pm 1/2$, that entails both a quantized dc Hall response and a subgap full-quarter Kerr rotation. The observation of these effects in 2D massive Dirac materials such as gapped graphene, hexagonal boron nitride or transition metal dichalcogenides (TMDs) is obscured by the fact that Dirac cones come in pairs with opposite sign Berry curvatures, leading to a vanishing Chern number. Here, we show that the presence of spin-orbit interactions, combined with an exchange spin splitting induced either by diluted magnetic impurities or by proximity to a ferromagnetic insulator, gives origin to a net magneto-optical Kerr effect in such systems. We focus on the case of TMD monolayers and study the dependence of Kerr rotation on frequency and exchange spin splitting. The role of the substrate is included in the theory and found to critically affect the results. Our calculations indicate that state-of-the-art magneto-optical Kerr spectroscopy can detect a single magnetic impurity in diluted magnetic TMDs.