The theory of the ferromagnetism of conduction electrons at low temperatures

A theory is presented in which the effect of spin waves on the single-particle states of conduction electrons is obtained as well as the effect of the conduction electrons on the spin waves. Green function techniques are employed. The Hamiltonian is taken to contain the single-particle energies of the conduction electrons in the absence of interactions, the Coulomb interaction between electrons in Wannier states centred on the same lattice site C, and the interatomic exchange terms Jij. Interband integrals are neglected. The chain of equations for the single-particle Green functions is decoupled in such a way as to include the effects of the spin waves in the single-particle Green functions. The theory is worked out on the assumption that C is very much greater than the band width and the Jij so that at T ═ 0 the double occupation of Wannier orbital states is the minimum possible. The resulting single-particle occupation numbers are linear combinations of Fermi-Dirac functions. The low temperature spontaneous magnetization ξ is found to be a product of a spin-wave magnetization and a single-particle magnetization ξs.p., and so contains terms varying as T1 and T1, and T2 if both spin sub-bands are partially occupied in the ground state. The low temperature specific heat contains T and T1 terms. The results of the Heisenberg model are obtained in the appropriate limit. Expressions for the spin-wave energy and its temperature dependence are discussed.