<p>Effective axion fields emerge in condensed matter and photonic systems with broken parity and time-reversal symmetries resulting in nonreciprocal optical phenomena. Here, we predict a distinct type of electromagnetic response which has the same symmetry properties as an axion one, manifests itself only at the boundaries of the material and features the same coupling to incident plane waves. However, the response to the external sources introduced inside is profoundly different, allowing one to distinguish the predicted dual axion field experimentally. We prove that the behavior of such materials is captured by electrodynamics with magnetic charge, put forward a specific metamaterial realizing this physics and suggest possible experiments to observe it. We anticipate that this response is general and occurs in a variety of photonic and condensed matter structures.</p>