The low-lying magnetic excitation spectrum of rare-earth metals is derived
within an adiabatic approach on the basis of spin-density-functional theory
. The treatment accounts for conduction-electron spin intersite exchange, o
n-site exchange between conduction and f electrons, on-site spin-orbit inte
raction, and crystal-field interaction. It is shown that the finiteness of
the f-d interaction, that is a possible noncollinearity of conduction elect
ron and f spins at the same site, plays an essential role for the magnon di
spersion, and a simple Heisenberg model for the total site spin does not ap
ply. The obtained magnon spectra are in semiquantitative agreement with exp
erimental data, where the latter are available. Main sources of discrepancy
might be incomplete knowledge of the crystal-field parameters and the negl
ect of intersite correlations of the fast conduction-electron motion.