Calculating spin transport properties from first principles: spin currents

Abstract

Local charge and spin currents are evaluated from the solutions of fully relativistic quantum mechanical scattering calculations for systems that include temperature-induced lattice and spin disorder as well as intrinsic alloy disorder. This makes it possible to determine material-specific spin transport parameters at finite temperatures. Illustrations are given for a number of important materials and parameters at 300 K. The spin-flip diffusion length $l_{\rm sf}$ of Pt is determined from the exponential decay of a spin current injected into a long length of thermally disordered Pt; we find $l_{\rm sf}^{\rm Pt}= 5.3\pm0.4 \,$nm. For the ferromagnetic substitutional disordered alloy Permalloy (Py), we inject currents that are fully polarized parallel and antiparallel to the magnetization and calculate $l_{\rm sf}$ from the exponential decay of their difference; we find $l_{\rm sf}^{\rm Py}= 2.8 \pm 0.1 \,$nm. The transport polarization $β$ is found from the asymptotic polarization of a charge current in a long length of Py to be $β= 0.75 \pm 0.01$. The spin Hall angle $Θ_{\rm sH}$ is determined from the transverse spin current induced by the passage of a longitudinal charge current in thermally disordered Pt; our best estimate is $Θ_{\rm sH}^{\rm Pt}=4.5 \pm 1 \%$ corresponding to the experimental room temperature bulk resistivity $ρ=10.8 μΩ\,$cm.