  We demonstrate a microscopic magnonic-crystal waveguide produced by
nano-patterning of a 20 nm thick film of Yttrium Iron Garnet. By using the
phase-resolved micro-focus Brillouin light scattering spectroscopy, we map the
intensity and the phase of spin waves propagating in such a periodic magnetic
structure. Based on these maps, we obtain the dispersion and the attenuation
characteristics of spin waves providing detailed information about the physics
of spin-wave propagation in the magnonic crystal. We show that, in contrast to
the simplified physical picture, the maximum attenuation of spin waves is
achieved close to the edge of the magnonic band gap, which is associated with
non-trivial reflection characteristics of spin waves in non-uniform field
potentials.
