Magnetic order beyond RKKY in the classical Kondo lattice

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