Relativistic current- and spin-density functional theory and its application to f-electron systems

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In order to calculate the electronic structure for f-electron compounds, in which the f electrons are itinerant and responsible to magnetism, it is necessary to take into account the magnetic effects that originate from the spin polarization and the orbital current besides relativistic effects. For a system of interacting electrons in an external electromagnetic field, a non-relativistic current- and spin-density functional theory of Vignale and Rasolt (1987) is generalized to a relativistic current- and spin-density functional theory. A generalized Hohenberg-Kohn theorem is shown to hold, and a single-particle equation of the Kohn-Sham-Dirac type is derived.By choosing the charge density and the magnetization density as the two basic variables, a single-particle equation is derived in a form suitable to an isolated atom or ion. In the single-particle equation, the magnetic interaction is expressed in a form similar to the Zeeman term in which the spin and the orbital angular momenta couple with an effective magnetic field. The effect of the orbital current is included implicitly through the spin-orbit interaction and explicitly through the Zeeman term in which the spin and the orbital angular momenta couple with an effective magnetic field. The effective magnetic field is given by the variation of the exchange and correlation energy functional with respect to the magnetization density that consists of the spin and the orbital angular momentum density, and should be determined self-consistently. The single-particle equation is applied to an atomic structure calculation for the trivalent ions of the lanthanide series, and the total spin and the orbital angular momenta are found to obey Hund's rules well.This new theoretical scheme provides a good basis for a quantitative calculation of the electronic structure for the f-electron systems.