  Exfoliated chromium triiodide (CrI$_3$) is a layered van der Waals (vdW)
magnetic insulator that consists of ferromagnetic layers coupled through
antiferromagnetic interlayer exchange. The resulting permutations of magnetic
configurations combined with the underlying crystal symmetry produces tunable
magneto-optical phenomena that is unique to the two-dimensional (2D) limit.
Here, we report the direct observation of 2D magnons through magneto-Raman
spectroscopy with optical selection rules that are strictly determined by the
honeycomb lattice and magnetic states of atomically thin CrI$_3$. In
monolayers, we observe an acoustic magnon mode of ~0.3 meV with
cross-circularly polarized selection rules locked to the magnetization
direction. These unique selection rules arise from the discrete conservation of
angular momentum of photons and magnons dictated by threefold rotational
symmetry in a rotational analogue to Umklapp scattering. In bilayers, by tuning
between the layered antiferromagnetic and ferromagnetic-like states, we observe
the switching of two magnon modes. The bilayer structure also enables Raman
activity from the optical magnon mode at ~17 meV (~4.2 THz) that is otherwise
Raman-silent in the monolayer. From these measurements, we quantitatively
extract the spin wave gap, magnetic anisotropy, intralayer and interlayer
exchange constants, and establish 2D magnets as a new system for exploring
magnon physics.
