Spin-flip diffusion length in 5d transition metal elements: a first-principles benchmark

Little is known about the spin-flip diffusion length $l_{\rm sf}$, one of the most important material parameters in the field of spintronics. We use a density-functional-theory based scattering approach to determine values of $l_{\rm sf}$ that result from electron-phonon scattering as a function of temperature for all 5d transition metal elements. $l_{\rm sf}$ does not decrease monotonically with the atomic number Z but is found to be inversely proportional to the density of states at the Fermi level. By using the same local current methodology to calculate the spin Hall angle $\Theta_{\rm sH}$ that characterizes the efficiency of the spin Hall effect, we show that the products $\rho(T)l_{\rm sf}(T)$ and $\Theta_{\rm sH}(T)l_{\rm sf}(T)$ are constant.