Spin dependence of the inelastic electron mean free path in Fe and Ni: Explicit calculations and implications

We present explicit calculations of the dependence of the inelastic electron mean free path on spin direction and energy, for propagation in the bulk of the ferromagnetic metals Fe and Ni. The substrate electrons are modeled within the framework of an empirical tight-binding description of the $3d,$ $4s,$ and $4p$ bands combined with intra-atomic Coulomb interactions between electrons in the $3d$ shell. The analysis of spin-flip contributions to the inelastic mean free path incorporates the role of spin-wave emission. We discuss the energy variation of the spin asymmetry in the mean free path, along with other issues. For electrons a few eV above the vacuum level, we find that the mean free path of minority-spin electrons is very short.