Relativistic extension of the spin-polarized local-density-functional theory: Study of the electronic and magnetic properties of the rare-earth ions

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Abstract
We have extended the von Barth–Hedin local-spin-density theory to treat the relativistic spin-polarized case as proposed by Doniach and Sommers. This extension permits us to do actual numerical calculations on atomic and solid-state systems. A technique for integrating the resulting coupled Dirac equations is presented. As a test the theory is applied to the study of the magnetic and electronic properties of some rare-earth ions. We analyze the relativistic and spin-polarization effects on the 4f spin densities and evaluate the polarization effect on the core electrons. Tables of form factors for the first seven rare-earth ions are also presented.