Projector augmented-wave method: application to relativistic spin-density functional theory

Applying the projector augmented--wave (PAW) method to relativistic spin--density functional theory (RSDFT) we derive PAW Dirac--Kohn--Sham equations for four--component spinor pseudo wavefunctions. The PAW freedom to add a vanishing operator inside the PAW spheres allows us to transform these PAW Dirac--like equations into PAW Pauli--like equations for two--component spinor pseudo wavefunctions. With these wavefunctions, we get the frozen--core energy as well as the charge and magnetization densities of RSDFT, with errors comparable to the largest between $1/c^2$ and the transferability error of the PAW data sets. Presently, the latter limits the accuracy of the calculations, not the use of the Pauli--like equations. The theory is validated by applications to isolated atoms of Fe, Pt, and Au, and to the band structure of fcc--Pt, fcc--Au, and ferromagnetic bcc--Fe.