Energy of a Bloch Wall on the Band Picture. II. Perturbation Approach

The "exchange stiffness" constant, which appears in the theory of the Bloch interdomain wall in ferromagnetics, can be calculated by computing the response of a saturated specimen to a small spatially varying perturbing field. This calculation is carried out here in the self-consistent field approximation, using running waves for the one-electron states, and the results is interpreted physically in terms of precession of the spins of moving electrons.Combination of the present theory with the Stoner-Wohlfarth model of the ferromagnetic electrons in nickel does not give satisfactory results, probably because the latter model does not approximate the actual self-consistent field solution very well. However, application of the theory to the free electron gas is of interest as a confirmation of the validity of the perturbation approach.It is shown that there exist, even in a ferromagnetic metal, quantum states orthogonal to all the low-lying states of the conventional band picture and having the properties of spin waves. The presumably universal relation between the exchange stiffness constant and the energies of spin waves of long wavelength is verified in the present approximation. It is shown that spin waves carry a current in a metal, though not in an insulator. For spin waves of long wavelength the present theory can be shown to include Slater's theory of spin waves in a ferromagnetic insulator, and a fortiori to include all previous theories based on the atomic model.