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.