Massive Dirac magnons in the three-dimensional honeycomb magnetic oxide [Formula: see text]

Two dimensional honeycomb ferromagnets host massless Dirac magnons which are a bosonic analogue of Dirac fermions in graphene. The Dirac magnons may become massive and topological when the time reversal symmetry breaks and an energy gap opens up at the Dirac point, which was experimentally observed in [Formula: see text]-based van der Waals magnets. Here, we investigate the spin wave excitations in the 3d magnetic oxide [Formula: see text] with [Formula: see text] electrons ([Formula: see text]). Using inelastic neutron scattering, we observe two magnon bands separated by a 1.2-meV gap at the Dirac points indicating that its Dirac magnons are massive. Using the linear spin-wave and density functional theory calculations, we find that the spin-orbit-coupled antisymmetric Dzyaloshinskii-Moriya exchanges can best account for the observed Dirac gap opening. The associated Berry curvature and Chern number ([Formula: see text]) indicate that [Formula: see text] hosts topological spin excitations via time-reversal symmetry breaking of Dirac magnons.