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.