  We present the observation of a complete bandgap and collective spin wave
excitation in two-dimensional magnonic crystals comprised of arrays of
nanoscale antidots and nanodots, respectively. Considering that the frequencies
dealt with here fall in the microwave band, these findings can be used for the
development of suitable magnonic metamaterials and spin wave based signal
processing. We also present the application of a numerical procedure, to
compute the dispersion relations of spin waves for any high symmetry direction
in the first Brillouin zone. The results obtained from this procedure has been
reproduced and verified by the well established plane wave method for an
antidot lattice, when magnetization dynamics at antidot boundaries is pinned.
The micromagnetic simulation based method can also be used to obtain
iso--frequency countours of spin waves. Iso--frequency contours are analougous
of the Fermi surfaces and hence, they have the potential to radicalize our
understanding of spin wave dynamics. The physical origin of bands, partial and
full magnonic bandgaps has been explained by plotting the spatial distribution
of spin wave energy spectral density. Although, unfettered by rigid assumptions
and approximations, which afflict most analytical methods used in the study of
spin wave dynamics, micromagnetic simulations tend to be computationally
demanding. Thus, the observation of collective spin wave excitation in the case
of nanodot arrays, which can obviate the need to perform simulations may also
prove to be valuable.
