Lifetimes and inelastic mean free path of low-energy excited electrons in Fe, Ni, Pt, and Au:Ab initio GW+Tcalculations

Abstract

We present the results of the $\mathrm{GW}+\mathrm{T}$ ab initio calculations for the inelastic lifetimes and mean free path (IMFP) of low-energy excited electrons in Fe, Ni, Pt, and Au. For Fe and Ni we show that the $T$-matrix terms, incorporating the Stoner's excitations and spin-wave emission, contribute to the IMFP of the spin-minority electrons with excitation energy below $1.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, whereas the GW term dominates at higher energy. We find that the spin dependence of IMFP in Ni is governed mainly by the spin dependence of lifetimes, but in Fe it relates mainly to the spin dependence of group velocities. We show that the ``random $k$'' model of the electron decay with fixed matrix element well agrees with the GW term of the lifetimes thus showing that the energy and spin dependence of the lifetimes are determined mainly by the convolutions of densities of states. For Au the inclusion of $T$-matrix terms with electron-hole scattering greatly reduces the calculated IMFP, bringing them into better agreement with experimental data.