Scaling of intrinsic Gilbert damping with spin-orbital coupling strength

We have experimentally and theoretically investigated the dependence of the intrinsic Gilbert damping parameter $\alpha_0$ on the spin-orbital coupling strength $\xi$ by using L1$_{\mathrm{0}}$ ordered FePd$_{\mathrm{1-x}}$Pt$_{\mathrm{x}}$ ternary alloy films with perpendicular magnetic anisotropy. With the time-resolved magneto-optical Kerr effect, $\alpha_0$ is found to increase by more than a factor of ten when $x$ varies from 0 to 1.0. Since changes of other leading parameters are found to be neglected, the $\alpha_0$ has for the first time been proven to be proportional to $\xi^2$.