Band theory of ferromagnetism, antiferromagnetism, and spin waves

Intra-atomic exchange (Hund's rule mechanism) and Heisenberg nearest-neighbor exchange are examined for their role in the ferromagnetism of metals with degenerate bands. The equations of motion of spin waves valid near T=0°K are derived, and a number of branches are found. When the equations are solved in the approximation that kғ<<size of the Brillouin zone, the spin waves all have positive energy, and have wave vectors not exceeding 0.9kғ in magnitude. When the electrons approximately half-fill the Brillouin zone, it is possible for some spin waves to have negative energy, and for an antiferromagnetic state to become stable. This is not proved, but indicated on the basis of an earlier calculation that also showed that ferromagnetism is less stable against antiferromagnetism in face-centered cubic materials than in either the simple, or body-centered cubic structures.