Ferromagnetism and Spin Waves in the Band Theory
Abstract
Intraatomic exchange (Hund's rule mechanism) and Heisenberg nearestneighbor exchange are examined for their role in the ferromagnetism of metals with degenerate bands. We examine the ground state, and find there is ferromagnetism once the largest eigenvalue j_{00} of the exchange matrix exceeds 1/2 ×No. of atoms/density of states at the Fermi surface. We then find several spinwave spectra, of which one "acoustic" and at least one "optical" spectrum have infinite lifetime in the random phase approximation. The initial parabolic behavior of the acoustic spectrum yields Bloch's T^{32} low at low temperature. There is a maximum wave vector beyond which no spinwave solutions exist, corresponding to a minimum wavelength of at least several atomic distances. Formulas are given, and the copious numerical results calculated by W. Doherty on the IBM7094 computer are summarized in graphs and tables. The ferromagnetic ground state is stable versus antiferromagnetic states only so long as umklapp is neglected. Because umklapp is most important in halffilled bands, we find qualitative agreement with previous calculations that antiferromagnetism can result in this case.
 Publication:

Physical Review
 Pub Date:
 December 1963
 DOI:
 10.1103/PhysRev.132.2521
 Bibcode:
 1963PhRv..132.2521M