First-principles study of the gap in the spin excitation spectrum of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mtext>CrI</mml:mtext><mml:mn>3</mml:mn></mml:msub></mml:math> honeycomb ferromagnet

The nature of the gap observed at the zone border in the spin excitation spectrum of ${\mathrm{CrI}}_{3}$ quasi-two-dimensional single crystals is still controversial. We perform first-principles calculations based on time-dependent density functional perturbation theory, which indicate that the observed gap results from a combination of spin-orbit and interlayer interaction effects. The former give rise to the anisotropic spin-spin interactions that are responsible for its very existence, while the latter determine both its displacement from the $K$ point of the Brillouin zone, due to the in-plane lattice distortions induced by them, and an enhancement of its magnitude, in agreement with experiments and previous theoretical work based on a lattice model.