  The Landau-Lifshitz-Gilbert damping parameter is typically assumed to be a
local quantity, independent of magnetic configuration. To test the validity of
this assumption we calculate the precession damping rate of small amplitude
non-uniform mode magnons in iron, cobalt, and nickel. At scattering rates
expected near and above room temperature, little change in the damping rate is
found as the magnon wavelength is decreased from infinity to a length shorter
than features probed in recent experiments. This result indicates that
non-local effects due to the presence of weakly non-uniform modes, expected in
real devices, should not appreciably affect the dynamic response of the element
at typical operating temperatures. Conversely, at scattering rates expected in
very pure samples around cryogenic temperatures, non-local effects result in an
order of magnitude decrease in damping rates for magnons with wavelengths
commensurate with domain wall widths. While this low temperature result is
likely of little practical importance, it provides an experimentally testable
prediction of the non-local contribution of the spin-orbit torque-correlation
model of precession damping. None of these results exhibit strong dependence on
the magnon propagation direction.
