We study the Kondo lattice model of band electrons coupled to classical
spins, in three dimensions, using a combination of variational calculation and
Monte Carlo. We use the weak coupling `RKKY' window and the strong coupling
regime as benchmarks, but focus on the physically relevant intermediate
coupling regime. Even for modest electron-spin coupling the phase boundaries
move away from the RKKY results, the non interacting Fermi surface no longer
dictates magnetic order, and weak coupling `spiral' phases give way to
collinear order. We use these results to revisit the classic problem of 4f
magnetism and demonstrate how both electronic structure and coupling effects
beyond RKKY control the magnetism in these materials.Comment: 6 pages, 4 figs. Improved figures, expanded captions. To appear in
Europhys. Let