Dirac magnons in collinear antiferromagnets

We study the topological properties of magnon excitations in a large class of Heisenberg spin systems in three dimensions, where the ground state configuration is collinear and invariant under magnetic group symmetry $P*T$, a composite symmetry of time-reversal followed by space inversion. We prove that in these systems, ``Dirac points'' are symmetry-protected at band crossing between optical magnon bands, and the corresponding topological surface states have equal energy contours in the shape of non-contractible arcs, unseen in known topological materials. As a concrete example, we study a $J_1$-$J_2$ model for spin-web compound, and show the presence of the Dirac magnons using spin wave approximation.