Intrinsic and extrinsic spin-orbit coupling and spin relaxation in monolayer PtSe2

Monolayer ${\mathrm{PtSe}}₂$ is a semiconducting transition-metal dichalcogenide characterized by an indirect band gap, space inversion symmetry, and high carrier mobility. Strong intrinsic spin-orbit coupling and the possibility to induce extrinsic spin-orbit fields by gating make ${\mathrm{PtSe}}₂$ attractive for fundamental spin transport studies as well as for potential spintronics applications. We perform a systematic theoretical study of the spin-orbit coupling and spin relaxation in this material. Specifically, we employ first-principles methods to obtain the basic orbital and spin-orbital properties of ${\mathrm{PtSe}}₂$, also in the presence of an external transverse electric field. We calculate the spin mixing parameters ${b}²$ and the spin-orbit fields $\mathrm{\ensuremath{\Omega}}$ for the Bloch states of electrons and holes. This information allows us to predict the spin lifetimes due to the Elliott-Yafet and D'yakonov-Perel mechanisms. We find that ${b}²$ is rather large, on the order of ${10}^{\ensuremath{-}2}$ and ${10}^{\ensuremath{-}1}$, while $\mathrm{\ensuremath{\Omega}}$ varies strongly with doping, being about ${10}³\text{--}{10}⁴\phantom{\rule{0.16em}{0ex}}{\mathrm{ns}}^{\ensuremath{-}1}$ for carrier density in the interval ${10}¹³\text{--}{10}¹⁴\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ at the electric field of 1 V/nm. We estimate the spin lifetimes to be on the picosecond level.