  We show that the regime of strong-light matter coupling with remarkable
magnetic properties can be realized in systems based on monolayers of chromium
triiodide (CrI3). This two-dimensional material combines the presence of
ferromagnetic ordering with the possibility of forming strongly-bound excitonic
complexes even at room temperature. Using microscopic first-principle
calculations we reveal a rich spectrum of optical transitions, corresponding to
both Wannier- and Frenkel-type excitons, including those containing electrons
with a negative effective mass. We show that excitons of different
polarizations efficiently hybridize with a photonic mode of a planar
microcavity, and due to the peculiar selection rules polariton modes become
well resolved in circular polarizations. The combination of very 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 CrI3 an excellent
platform for magnetopolaritonic applications.
