Spin waves are collective perturbations in the orientation of the magnetic
moments in magnetically ordered materials. Their rich phenomenology is
intrinsically three dimensional, from the trajectory of the spin precession
during their propagation, to the profiles of the spin-wave mode throughout the
volume of the magnetic system. This gives rise to novel complex phenomena with
high potential for applications in the field of magnonics. However, the
three-dimensional imaging of spin waves, key to understanding and harnessing
these phenomena, has so far not been possible. Here, we image the
three-dimensional dynamics of spin waves excited in a synthetic
antiferromagnet, with nanoscale spatial resolution and sub-ns temporal
resolution, using time-resolved magnetic laminography. In this way, we map the
distribution of the spin-wave modes throughout the volume of the structure,
revealing unexpected depth-dependent profiles originating from the interlayer
dipolar interaction. We experimentally demonstrate the existence of complex
three-dimensional interference patterns, and analyze them via micromagnetic
modelling. We find that these patterns are generated by the superposition of
spin waves with non-uniform amplitude profiles, and that their features can be
controlled by tuning the composition and structure of the magnetic system. Our
results open unforeseen possibilities for the study of complex spin-wave modes
and their interaction within nanostructures, and for the generation and
manipulation of three-dimensional spin-wave landscapes for the design of novel
functions in magnonic devices.Comment: 15 pages, 4 figure