Exchange Narrowing ofdBands in Ferromagnets

Abstract

A semiphenomenological Hamiltonian based on the generalized Hartree-Fock equations for a two-component spinor is developed which describes the interaction of an electron in the $d$ band with the spin waves of a ferromagnet. Solutions to the effective Hamiltonian are examined in the tight-binding approximation using a self-consistent separation of the electron and spin-wave variables. The dynamic interaction of the electron with the spin waves gives rise to a band-narrowing factor $\exp (-\zeta )$ analogous to that obtained by Yamashita and Kurosawa for the polaron. $\zeta$ increases with temperature and estimates show that it may be on the order of unity for a typical ferromagnet at low temperatures.