  The discovery of the Dirac electron dispersion in graphene led to the
question of the Dirac cone stability with respect to interactions. Coulomb
interactions between electrons were shown to induce a logarithmic
renormalization of the Dirac dispersion. With a rapid expansion of the list of
compounds and quasiparticle bands with linear band touching, the concept of
bosonic Dirac materials has emerged. We consider a specific case of
ferromagnets consisting of the Van der Waals-bonded stacks of honeycomb layers,
e.g chromium trihalides CrX3 (X = F, Cl, Br and I), that display two spin wave
modes with energy dispersion similar to that for the electrons in graphene. At
the single particle level, these materials resemble their fermionic
counterparts. However, how different particle statistics and interactions
affect the stability of Dirac cones has yet to be determined. To address the
role of interacting Dirac magnons, we expand the theory of ferromagnets beyond
the standard Dyson theory to a case of non-Bravais honeycomb layers. We
demonstrate that magnon-magnon interactions lead to a significant
momentum-dependent renormalization of the bare band structure in addition to
strongly momentum-dependent magnon lifetimes. We show that our theory
qualitatively accounts for hitherto unexplained anomalies in a nearly half
century old magnetic neutron scattering data for CrBr3. We also show that
honeycomb ferromagnets display dispersive surface and edge states, unlike their
electronic analogs.
