Spin-Flip Diffusion Length in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>5</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:math> Transition Metal Elements: A First-Principles Benchmark
Rohit Nair, Ehsan Barati, Kriti Gupta, Zhe Yuan, Paul J. Kelly
Abstract
Little is known about the spin-flip diffusion length ${l}_{\mathrm{sf}}$, 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 ${l}_{\mathrm{sf}}$ that result from electron-phonon scattering as a function of temperature for all $5d$ transition metal elements. ${l}_{\mathrm{sf}}$ 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 ${\mathrm{\ensuremath{\Theta}}}_{\mathrm{sH}}$ that characterizes the efficiency of the spin Hall effect, we show that the products $\ensuremath{\rho}(T){l}_{\mathrm{sf}}(T)$ and ${\mathrm{\ensuremath{\Theta}}}_{\mathrm{sH}}(T){l}_{\mathrm{sf}}(T)$ are constant.