# Influence of spin-orbit coupling on spin-dependent transport

The drive to increase the density and speed of magnetic forms of data storage has focused attention on how magnetization changes in response to external fields and currents, on shorter length and time scales. The time decay of a magnetization precession is described using the Landau-Lifshitz-Gilbert equation in terms of a dimensionless parameter α while its spatial decay is described using a diffusion equation in terms of a spin accumulation that is the difference between the spin-dependent electrochemical potentials for up and down spins, and a spin-flip diffusion length l_{sf}. The parameters α and l_{sf }are determined by a small coupling between the spin and orbital degrees of freedom of the transition metal d states, as is the resistivity ρ. Using a formulation of first-principles scattering theory that includes disorder and spin-orbit coupling on an equal footing, we calculate the resistivity ρ (Fig.1) and, for the first time, the spin-flip diffusion length l_{sf} and Gilbert damping parameter α (Fig.2) 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 ρ=3.50.15 μΩcm, l_{sf }=5.50.3 nm, and α=0.00460.0001 compared to experimental low-temperature values in the range 4.2–4.8 μΩcm for ρ, 5.0–6.0 nm for l_{sf}, and 0.004-0.013 for α, indicating that the theoretical formalism captures the most important contributions to these parameters.

Anton A. Starikov, Paul J. Kelly, Arne Brataas, Yaroslav Tserkovnyak, and Gerrit E.W. Bauer, *Unified First-Principles Study of Gilbert Damping, Spin-Flip Diffusion, and Resistivity in Transition Metal Alloys,* Phys. Rev. Lett. **105**, 236601 (2010).

**Figure 1. **Calculated resistivity as a function of the concentration x for fcc Ni_{1-x}Fe_{x} binary alloys with (solid line) and without (dashed-dotted line) spin-orbit coupling. Low-temperature experimental results are shown as symbols. The composition Ni_{80}Fe_{20} is indicated by a vertical dashed line. Inset: resistance of Cu|Ni_{80}Fe_{20}|Cu as a function of the thickness of the alloy layer. Dots indicate the calculated values averaged over five configurations, while the solid line is a linear fit.

**Figure 2. **Calculated zero-temperature (solid line) and experimental room-temperature (symbols) values of the Gilbert damping parameter as a function of the concentration x for fcc Ni_{1-x}Fe_{x} binary alloys. Inset: total damping of Cu|Ni_{80}Fe_{20}|Cu as a function of the thickness of the alloy layer. Dots indicate the calculated values averaged over five configurations, while the solid line is a linear fit.