Spin-flip exchange scattering of low-energy electrons in ferromagnetic iron

We present a theory of spin-flip exchange scattering of low-energy electrons, directed at the ferromagnetic transition metals, with application to Fe. The model used employs a tight-binding description of the paramagnetic spd bands. Ferromagnetic exchange splitting of the bands is achieved by including on-site Coulomb repulsion between electrons in $3d$ orbitals, which is treated in a mean-field approximation. The low-energy electron interacts with the metal electrons via the Coulomb interaction, and the magnetic excitations in the metal are treated within the random-phase approximation. Both spin waves and Stoner excitations contribute to the energy loss of the low-energy electron. We show that the relative importance of these two loss mechanisms is influenced very importantly by the degree of localization of the $3d$ orbital. We also present results based on the use of accurate wave functions. These show that spin-wave loss peaks should be prominent features in spin-polarized electron energy-loss spectra.