Spin Relaxation and Diffusion in Monolayer 1T'-WTe$_2$ from First-Principles

Understanding spin relaxation in topological systems such as quantum spin-hall (QSH) insulator is critical for realizing coherent transport at high temperature. WTe$_{2}$, known as a QSH insulator with a high transition temperature of 100K, is an important test-bed of unveiling spin relaxation mechanism in topological materials. In this work, we employ our recently-developed \emph{ab initio} density-matrix dynamics approach to investigate spin relaxation mechanism, and calculate spin lifetime and diffusion length of monolayer 1T'-WTe$_{2}$, at finite temperature under an external electric field. We found the spin lifetime of electrons have the largest anisotropy when measuring along the canted-spin-texture direction. Moreover, we found an opposite trend between spin and carrier relaxation against applied electric field. Most importantly, the relaxation mechanism under intermediate electric field around 1V/nm can not be explained by either Eillot-Yafet or Dyakonov-Perel models, which highlights the generality of our \emph{ab initio} density-matrix framework. We then proposed analytical models to explain its mechanism and compare well with \emph{ab initio} results at small and large electric field. We predict that spin lifetime and spin diffusion length of bulk-state electrons are $\sim$1 ps and $\sim$30 nm at room temperature respectively, suggesting its promise for spintronic applications.