Electron-phonon coupling in ferromagnetic Fe-Co alloys from first principles

The measured magnetization dynamics of ferromagnetic iron--cobalt Fe$_{1-x}$Co$_x$ alloys show a strong dependence on the alloy composition, especially near $x=0.25$. Here, we calculate from first principles the electron-phonon coupling strength in Fe$_{1-x}$Co$_x$ alloys for compositions ranging from $x=0$ to $x=0.75$. We find a strong, spin-dependent variation of the electron-phonon coupling strength with alloy composition, with a minimum near $x=0.25$. We analyze the variation of the electron-phonon interaction with composition, as a function of electron spin, density of states, electron-phonon matrix elements, character of electron wavefunction at the Fermi level, orbital-resolved strength of the phonon perturbing potential, and phonon frequencies. We calculate the electron-phonon energy transfer coefficients, and find that they are in qualitative agreement with the phenomenological electron-phonon energy transfer coefficient deduced from magnetization dynamics experiments. Our findings show that variations in the composition of ferromagnetic alloys can significantly alter the magnetization dynamics and transport properties.