The magnetic properties of a simple nondegenerate band with short-range intra-atomic electron-electron interactions are discussed. A generalized Hartree-Fock formalism is developed which give closed expressions for all ordered magnetic states with constant local moments lying on a conical helix. The stability of the paramagnetic and ferromagnetic states with respect to these helixes is analyzed in detail. In particular, the importance of band structure and Fermi-surface geometry is investigated. It is shown that helical and antiferromagnetic magnetic states can indeed be more favorable than a ferromagnetic state for itinerant-band electrons with short-range interactions. It is shown that umklapp processes at the zone boundaries can favor antiferromagnetic instabilities of the paramagnetic state, and necks in the Fermi surface tend to favor spin-density waves with a period determined by the diameter of the neck. Related effects also appear in investigating the transverse stability of ferromagnetic states. Detailed numerical calculations on several simple model tight-binding band structures are presented to illustrate these arguments. The effects of the shape of the density-of-states curve and band ferromagnetism are also discussed, and conditions for discontinuities in the self-constent solutions are investigated.

• Received 13 March 1967

DOI:https://doi.org/10.1103/PhysRev.164.642