We have investigated the magnetic ground state of metals using an idealized theory of magnetism based on the Ruderman-Kittel-Yosida indirect exchange interaction. The preliminary, but suggestive, results reported here are for simple cubic structures and spherical Fermi surface. We find that as the number of electrons is increased, ferromagnetism is replaced by two different antiferromagnetic structures before the Néel state is finally obtained. The first transition occurs at kFa∼0.5π (kF=Fermi wave vector, a=lattice constant) at which value the rapid changeover occurs, from ferromagnetism to an antiferromagnetic structure of planes of uniform magnetization, which point along alternating directions. These planes lie perpendicular to the (1, 0, 0) axis at first, then abruptly change over to the (1, 1, 0) axis at kFa∼0.7π. The new configuration remains the ground state until kFa is further increased to 0.85π. But, at that value a final transition occurs to the Néel state. The Néel state (where every spin is surrounded by antiparallel nearest neighbors) then becomes increasingly stable and reaches maximum stability when the Fermi surface touches the zone boundary at kFa=π. It appears from our calculations that the above-mentioned states are the only stable spiral configurations in the simple cubic lattice without the introduction of anisotropy or nonlinearity into the theory. © 1962 The American Physical Society.