The presence of chalcogen vacancies in monolayer transition metal dichalcogenides (TMDs) leads to excitons with mixed localized-delocalized character and to reduced valley selectivity. Recent experimental advances in defect design in TMDs allow for a close examination of such mixed exciton states as a function of their degree of circular polarization under external magnetic fields, revealing strongly varying defect-induced magnetic properties. A theoretical understanding of these observations and their physical origins demands a predictive, structure-sensitive theory. In this work, we study the effect of chalcogen vacancies on the exciton magnetic properties in monolayer ${\mathrm{MoS}}_2$. Using many-body perturbation theory, we show how the complex excitonic picture associated with the presence of defects—with reduced valley and spin selectivity due to hybridized electron-hole transitions—leads to a structurally controllable exciton magnetic response. We find a variety of $g$-factors with changing magnitudes and sign depending on the exciton energy and character. Our findings suggest a pathway to tune the nature of the excitons—and by that their magneto-optical properties—through defect architecture.

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• Defects
• Excitons
• Magneto-optics
• Transition metal dichalcogenides
• Ab initio calculations
• Many-body techniques