Abstract
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.