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

Two-dimensional (2D) massive Dirac electrons possess a finite Berry curvature, with Chern number 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. We thank Allan H MacDonald, Elaine Li, Alejandro Molina-Sanchez and Joao C G Henriques for fruitful discussions. GC acknowledges Fundacao para a Ciencia e a Tecnologia (FCT) for Grant No. SFRH/BD/138806/2018. GC and JF-R acknowledge financial support from FCT through Grant No. P2020-PTDC/FIS-NAN/4662/2014. NMRP acknowledges financial support from European Commission through project 'Graphene-Driven Revolutions in ICT and Beyond' (Ref. No. 785219), FCT in the framework of Strategic Financing (Ref. No. UID/FIS/04650/2019), and COMPETE2020, PORTUGAL2020, FEDER and FCT for Grants No. PTDC/FIS-NAN/3668/2013, No. POCI-01-0145-FEDER-028114, No. POCI-01-0145-FEDER-029265 and No. PTDC/NANOPT/29265/2017. JF-R acknowledges FCT for Grant No. UTAP-EXPL/NTec/0046/2017, as well as Generalitat Valenciana funding Prometeo2017/139 and MINECO-Spain (Grant No. MAT201678625-C2).