  We have performed a layer-resolved, microscopic study of interactions between
domain walls in two magnetic layers separated by a non-magnetic one, using
high-resolution x-ray photoemission electron microscopy. Domain walls in the
hard magnetic Co layer of a Co/Al2O3/FeNi trilayer with in-plane uniaxial
anisotropy strongly modify the local magnetization direction in the soft
magnetic FeNi layer. The stray fields associated to the domain walls lead to an
antiparallel coupling between the local Co and FeNi moments. For domain walls
parallel to the easy magnetization axis this interaction is limited to the
domain wall region itself. For strongly charged (head-on or tail-to-tail)
walls, the antiparallel coupling dominates the interaction over radial
distances up to several micrometers from the centre of the domain wall.
