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We present a comprehensive \textit{ab initio} analysis of the spin-chargecorrelations at the Tl/Si(111) surface, where the spin-orbit interaction is sostrong that a detailed treatment of the non-collinear electron spin appearsdecisive for the correct description of the response properties. Therelativistic limit enforces a unified treatment of the spin and chargedensities as a four-vector, and the response function acquires then a4$\times$4 tensor structure. Our all-electron implementation allows to resolvethe real space structure of the possible collective modes, and demonstrates theemergence of a novel collective excitation combining transverse-spin andordinary charge oscillations of a similar order of magnitude, whose spincharacter is strongly enhanced as we approach the $q$$\rightarrow$0 momentumlimit.

Relativistic response and novel spin-charge plasmon at the Tl/Si(111) surface