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 $l_{\mathrm{sf}}$, and Gilbert damping parameter $\alpha$ for ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x$ substitutional alloys as a function of $x$. For the technologically important ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ alloy, Permalloy, we calculate values of $\rho =3.5\pm 0.15\mu \Omega \mathrm{cm}$, $l_{\mathrm{sf}}=5.5\pm 0.3\mathrm{nm}$, and $\alpha =0.0046\pm 0.0001$ compared to experimental low-temperature values in the range $4.2–4.8\mu \Omega \mathrm{cm}$ for $\rho$, 5.0–6.0 nm for $l_{\mathrm{sf}}$, and 0.004–0.013 for $\alpha$, indicating that the theoretical formalism captures the most important contributions to these parameters.

Figure 1

Calculated resistivity as a function of the concentration $x$ for fcc ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x$ binary alloys with (solid line) and without (dashed-dotted line) SOC. Low-temperature experimental results are shown as symbols [15]. The composition ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ is indicated by a vertical dashed line. Inset: resistance of $\mathrm{Cu}|{\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}|\mathrm{Cu}$ 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 ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x$ binary alloys [21, 22, 23]. Inset: total damping of $\mathrm{Cu}|{\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}|\mathrm{Cu}$ 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 3

Fractional spin-current densities for electrons injected at $z=0$ from Cu into ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ alloy. Symbols indicate calculated values, while the solid lines are fits to Eq. (6).

Figure 4

Spin-diffusion length (solid line) and polarization $\beta$ as a function of the concentration $x$ for ${\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x$ binary alloys.