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-wave-functions. The PAW freedom to add a vanishing operator inside the PAW spheres allows us to transform these PAW Dirac-type equations into PAW Pauli-type equations for two-component spinor pseudo-wave-functions. With these wave functions, we get the frozen-core energy as well as the charge and magnetization densities of RSDFT, with errors comparable to the largest between 1/c² and the transferability error of the PAW data sets. Presently, the latter limits the accuracy of the calculations, not the use of the Pauli-type 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.