Spatio-temporal spin transport with electron-phonon scattering from first principles

Accurate prediction of key spin quantities such as spin lifetime and spin diffusion length is important in designing materials in the field of spintronics. We combine density-matrix quantum dynamics with semi-classical spatial transport within the Wigner function formalism, to simulate spatio-temporal spin transport in realistic device geometries. This approach accounts for coherent and incoherent processes at device length scales. Using this framework, we show incoherent spin transport results for graphene-hBN, accounting for first-principles electron-phonon coupling within a Lindbladian framework. We study the effect of scattering strength on spin lifetime and spin diffusion length and observe a Dyakonov-Perel (DP) region with a scattering-independent spin diffusion length of 30 microns in good agreement with experiment. We also derive our analytical model for the transport in the DP region and obtain spatial spin profile and spin diffusion lengths in agreement with simulation.