  Spin waves in the type-III ordered antiferromagnetic state of the frustrated
$t$-$t'$ Hubbard model on the fcc lattice are calculated to investigate
finite-$U$-induced competing interaction and frustration effects on magnetic
excitations and instabilities. Particularly strong competing interactions
generated due to interplay of fcc lattice geometry and magnetic order result in
significant spin wave softening. The calculated spin wave dispersion is found
to be in qualitative agreement with the measured spin wave dispersion in the
pyrite mineral $\rm Mn S_2$ obtained from inelastic neutron scattering
experiments. Instabilities to other magnetic orders (type I, type II, spiral,
non-collinear), as signalled by spin wave energies turning negative, are also
discussed.
