  We study experimentally the processes of parametric excitation in microscopic
magnetically saturated disks of nanometer-thick Yttrium Iron Garnet. We show
that, depending on the relative orientation between the parametric pumping
field and the static magnetization, excitation of either degenerate or
non-degenerate magnon pairs is possible. In the latter case, which is
particularly important for applications associated with the realization of
computation in the reciprocal space, a single-frequency pumping can generate
pairs of magnons whose frequencies correspond to different eigenmodes of the
disk. We show that, depending on the size of the disk and the modes involved,
the frequency difference in a pair can vary in the range 0.1-0.8 GHz. We
demonstrate that in this system, one can easily realize a practically important
situation where several magnon pairs share the same mode. We also observe the
simultaneous generation of up to six different modes using a fixed-frequency
monochromatic pumping. Our experimental findings are supported by numerical
calculations that allow us to unambiguously identify the excited modes. Our
results open new possibilities for the implementation of reciprocal-space
computing making use of low damping magnetic insulators.
