Exploring nonlinear Rashba effect and spin Hall conductivity in Janus MXenes W2COX (X = S, Se, Te)

Rashba spin-orbit coupling (RSOC) facilitates spin manipulation without relying on an external magnetic field, opening up exciting possibilities for advanced spintronic devices. In this work, we examine the effects of crystal momentum ($k$) nonlinearity and anisotropy on the conventional Rashba effect, with a particular focus on their impact on the spin Hall conductivity (SHC) in a newly predicted family of 2D Janus materials, W$_2$COX (X = S, Se, Te). Using first-principles density functional theory calculations, we confirm the dynamical and mechanical stability of the studied 2D materials. Strikingly, this materials family exhibits pronounced nonlinear Rashba spin splitting at the $\Gamma$ point of Brillouin zone near the Fermi level, which cannot be adequately described by the linear-$k$ Rashba model. Therefore, third-order momentum contributions ({$k^3$}) must be incorporated into the Rashba Hamiltonian. Our analysis reveals that among the studied systems, W$_2$COS exhibits the highest {$k^3$} contribution of $-45.9$\,eV\,{\AA$^3$}, despite having the lowest linear Rashba constant. A detailed analysis of electronic structure reveals topological nontrivial behaviour in these 2D materials, yielding sizable SHC that is primarily governed by the nonlinear Rashba effect. Notably, these materials also exhibit large spin Hall angle (0.018 -- 2.5), which is comparable to that of in bulk topological insulators like Bi$_2$Se$_3$ and Bi$_2$Te$_3$, and surpassing those in narrow bandgap bulk semiconductors GeTe and SnTe, as well as heavy metals such as Pt. Sizable SHC, large spin Hall angles, and the ability to tune SHC via electric fields without altering the topological properties, rooted in the crystal field splitting, underscore the potential of these materials for spintronic applications.