  The purpose of this paper is to investigate the propagation of topological
currents along magnetic interfaces (also known as magnetic walls) of a
two-dimensional material. We consider tight-binding magnetic models associated
to generic magnetic multi-interfaces and describe the K-theoretical setting in
which a bulk-interface duality can be derived. Then, the (trivial) case of a
localized magnetic field and the (non trivial) case of the Iwatsuka magnetic
field are considered in full detail. This is a pedagogical preparatory work
that aims to anticipate the study of more complicated multi-interface magnetic
systems.
