  We present first principles calculations of the two-particle excitation
spectrum of CrI$_3$ using many-body perturbation theory including spin-orbit
coupling. Specifically, we solve the Bethe-Salpeter equation, which is
equivalent to summing up all ladder diagrams with static screening and it is
shown that excitons as well as magnons can be extracted seamlessly from the
calculations. The resulting optical absorption spectrum as well as the magnon
dispersion agree very well with recent measurements and we extract the
amplitude for optical excitation of magnons resulting from spin-orbit
interactions. Importantly, the results do not rely on any assumptions on the
microscopic magnetic interactions such as Dzyaloshinskii-Moriya (DM), Kitaev or
biquadratic interactions and we obtain a model independent estimate of the gap
between acoustic and optical magnons of 0.3 meV. In addition, we resolve the
magnon wavefunction in terms of band transitions and show that the magnon
carries a spin that is significantly smaller than $\hbar$. This highlights the
importance of terms that do not commute with $S^z$ in any Heisenberg model
description.
