Symmetry-induced tunable and diverse spin textures in Janus monolayers of gold chalcogenides

Recent works have predicted monolayer gold selenide to be stable and easily exfoliable, with excellent potential optoelectronic applications. However, the presence of an inversion center prevents it from showing any spin-orbit splitting, limiting its use in the field of spintronics. In this study, we sulfurize one of the selenium layers of AuSe to construct the Janus ${\mathrm{Au}}_{2}\mathrm{SSe}$ monolayer with a low ${C}_{s}$ point group symmetry to tackle this problem. Unlike the conventional Janus structures, the two chalcogen atoms of ${\mathrm{Au}}_{2}\mathrm{SSe}$ are not mirror-symmetric, giving rise to both in-plane and out-of-plane spin polarizations. These spin polarizations, in turn, generate diverse spin-orbit coupling effects at different high-symmetry points in the Brillouin zone, namely, the linear-in-$k$ anisotropic Dresselhaus effect at the $\mathrm{\ensuremath{\Gamma}}$ point, the Zeeman-like effect at the conduction band minima, and the symmetry-induced persistent spin texture at the $X$ point. The observed spin-orbit effects have been explained by considering the variation in the strength of the SOC parameters in a ${C}_{s}$ symmetric spin-orbit coupling Hamiltonian. Additionally, these effects can be further influenced by changing the chalcogen atoms in the Janus structures without changing the system symmetry. Both the Zeeman-like and persistent spin splittings consist of momentum-independent canted spins in the ${S}_{x}\text{\ensuremath{-}}{S}_{z}$ plane and can be tuned using in-plane and out-of-plane strains, making the Janus ${\mathrm{Au}}_{2}\mathrm{SSe}$ structure ideal for realizing spin-based applications.