The existence of the magnetostatic surface spin waves in ferromagnets, known as Damon-Eshbach mode, was recently demonstrated to originate from the topology of the dipole-dipole interaction. In this work, we study the topological characteristics of magnons in easy-axis antiferromagnets with uniaxial anisotropy. The dipolar spin waves are found to be, driven by the dipole-dipole interaction, in a topological nodal-line semimetal phase, which hosts Damon-Eshbach-type surface modes due to the bulk-edge correspondence. The long wavelength character of dipolar spin waves makes our proposal valid for any natural uniaxial easy-axis antiferromagnet, and thus enriches the candidates of topological magnonic materials. In contrast to the nonreciprocal property in ferromagnetic case, the surface modes with opposite momentum coexist at each surface, but with different chiralities. Such a chirality-momentum or spin-momentum locking, similar to that of electronic surface states in topological insulators, offers the opportunity to design novel chirality-based magnonic devices in antiferromagnets.
