  We present a comprehensive study of the magnetic exchange Hamiltonian of
elemental Gadolinium. We use neutron scattering to measure the magnon spectrum
over the entire Brillouin zone, and fit the excitations to a spin wave model to
extract the first 26 nearest neighbor magnetic exchange interactions with
rigorously defined uncertainty. We find these exchange interactions to follow
RKKY behavior, oscillating from ferromagnetic to antiferromagnetic as a
function of distance. Finally, we discuss the topological features and
degeneracies in Gd, and HCP ferromagnets in general. We show theoretically how,
with asymmetric exchange, topological properties could be tuned with a magnetic
field.
