  In this Letter, we provide experimental evidence of nonlinear wave
propagation in a triangular lattice of repulsive magnets supported by an
elastic foundation of thin pillars and we interpret all the individual features
of the nonlinear wavefield through the lens of a phonon band calculation that
precisely accounts for the inter-particle repulsive forces. We confirm the
co-existence of two spectrally distinct components (homogeneous and forced) in
the wave response that is induced via second harmonic generation (SHG), a
well-known effect of quadratic nonlinearity (here embedded in the magnetic
interaction). We show that the modal and spatial characteristics of the second
harmonic components are complementary to those exhibited by the fundamental
harmonic. This endows the lattice with a functionality enrichment capability,
whereby additional modes and directivity patterns can be triggered and tuned by
merely increasing the amplitude of excitation.
