Abstract
A detailed investigation is made of the coefficient
C
in the energy
CK
2
of a spin wave of small wave vector K in a ferromagnetic cubic metal. It is assumed that the spins of all particles, within the energy band system considered, are alined in the ground state. An exact expression is obtained for
C
on the basis of one plausible assumption, that the inverse lifetime of a spin wave tends to zero faster than
K
2
as
K
→ 0. This expression is examined in detail for a one-band model with short-range inter-particle interactions and it consists of three terms. The first two terms are closely related to the well known r. p. a. formula for
C
although the second term is modified in an important way. In particular this modification is shown to take account of two-particle correlations of the type considered by Kanamori, but adapted to the ferromagnetic situation, and of magnon-electron scattering. The third term in
C
is completely new but is generally expected to be smaller than the second term. In an Appendix contact is made with Nagaoka’s work on spin wave energies in a nearly half-filled band.
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5. Low-Temperature Properties of Nearly Ferromagnetic Fermi Liquids
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