Recently, it was predicted that nonreciprocal magneto-electric effect in antiferromagnetic multilayered metamaterials occurs in two distinct versions. One is the conventional axion response, while another one is dual axion response captured by electrodynamics with magnetic charge. Here we investigate a model condensed matter system of spins coupled through antiferromagnetic exchange interaction and derive its effective electromagnetic properties. We predict that this system gives rise to the emergent dual axion field, support our conclusion by numerical simulations and put forward candidate materials.