  We study magnon properties in terms of spin stiffness, Curie temperatures and
magnon spectrum of Fe-Ni, Co-Ni and Fe-Co random alloys using a combination of
electronic structure calculations and atomistic spin dynamics simulations.
Influence of the disorder are studied in detail by use of large supercells with
random atomic arrangement. It is found that disorder affects the magnon
spectrum in vastly different ways depending on the system. Specifically, it is
more pronounced in Fe-Ni alloys compared to Fe-Co alloys. In particular, the
magnon spectrum at room temperature in Permalloy (Fe$_{20}$Ni$_{80}$) is found
to be rather diffuse in a large energy interval while in Fe$_{75}$Co$_{25}$ it
forms sharp branches. Fe-Co alloys are very interesting from a technological
point of view due to the combination of large Curie temperatures and very low
calculated Gilbert damping of $\sim$0.0007 at room temperature for Co
concentrations around 20--30\%.
