We show that the regime of strong light-matter coupling with remarkable magnetic properties can be implemented in systems based on monolayers of chromium triiodide (${\mathrm{CrI}}_3$). This two-dimensional material combines the presence of strongly bound excitonic complexes with ferromagnetic ordering below the Curie temperature. Using microscopic first-principles calculations, we reveal a rich spectrum of optical transitions corresponding to both Wannier- and Frenkel-type excitons, including those containing electrons with an effective negative mass. We show that excitons of different polarizations efficiently hybridize with a photonic mode of a planar microcavity. Due to the peculiar selection rules, polariton modes become well resolved in circular polarizations. The strong optical oscillator strength of excitons and cavity confinement leads to large values of the Rabi splitting, reaching 35 meV for a single monolayer and giant Zeeman splitting between polariton modes of up to 20 meV. This makes ${\mathrm{CrI}}_3$ an excellent platform for magnetopolaritonic applications.

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• Exciton polariton
• Excitons
• Magneto-optics
• Polaritons
• 2-dimensional systems
• Magnetic semiconductors
• Bethe-Salpeter equation
• Green's function methods
• Many-body techniques