Atomic layers of manganese nitride, deposited on the cubic gallium nitride (111) surface, are investigated using spin polarized periodic density functional theory calculations. The adsorption of a manganese atom has been evaluated at different high symmetry sites. Incorporation into the GaN substrate by replacing gallium atoms drives the formation of a site in which the displaced Ga atom forms bonds with Ga atoms at the surface. This energetically favorable configuration shows a ferromagnetic alignment. Surface formation energy calculations demonstrate that when a full Mn ML is incorporated into the GaN structure, a Ga ML on top of a MnN bilayer may be formed for very Ga-rich conditions. On the other hand, when a full Mn ML is deposited on top of the nitrogen terminated surface, an epitaxial MnN bilayer is formed with antiferromagnetic characteristics. Density of states and partial density of states are reported to show the antiferromagnetic alignment in both structures. This behavior is mainly induced by the Mn-d orbitals.