  Spin wave excitations and stability of the (0,pi) ordered SDW state are
investigated within the minimal two-band model for iron pnictides including a
Hund's coupling term. The SDW state is shown to be stable in two distinct
doping regimes --- finite hole doping in the lower SDW band for small second
neighbour hoppings, and small electron doping in the upper SDW band for
comparable first and second neighbour hoppings. In both cases, Hund's coupling
strongly stabilizes the SDW state due to generation of additional ferromagnetic
spin couplings involving the inter-orbital part of the particle-hole
propagator. Spin wave energies for the two-band model are very similar to the
one-band t-t' Hubbard model results obtained earlier, and are in agreement with
inelastic neutron scattering studies of iron pnictides.
