A unified first-principles study of Gilbert damping, spin-flip diffusion and resistivity in transition metal alloys

Using a formulation of first-principles scattering theory that includes disorder and spin-orbit coupling on an equal footing, we calculate the resistivity $rho$, spin flip diffusion length $l_{sf}$ and the Gilbert damping parameter $alpha$ for Ni$_{1-x}$Fe$_x$ substitutional alloys as a function of $x$. For the technologically important Ni$_{80}$Fe$_{20}$ alloy, permalloy, we calculate values of $rho = 3.5 pm 0.15$ $mu$Ohm-cm, $l_{sf}=5.5 pm 0.3$ nm, and $alpha= 0.0046 pm 0.0001$ compared to experimental low-temperature values in the range $4.2-4.8$ $mu$Ohm-cm for $rho$, $5.0-6.0$ nm for $l_{sf}$, and $0.004-0.013$ for $alpha$ indicating that the theoretical formalism captures the most important contributions to these parameters.