MAGNETIC-PROPERTIES OF F-ELECTRON SYSTEMS IN SPIN-POLARIZED RELATIVISTIC DENSITY-FUNCTIONAL THEORY

The magnetic ground state of the series of lanthanide and actinide tri valent ions is investigated by means of spin-polarized relativistic sp in-density functional theory. In the local density functional approxim ation (LDA) an internal effective magnetic field due to exchange and c orrelation couples to the spin degrees of freedom. The resulting set o f coupled Dirac equations yields ground-state multiplets that obey the well-known Hund's rules. This remarkable result comes about by the co upling of the j = l + 1/2 with the j = l - 1/2 states due to the excha nge-correlation potential that is, as usual, the functional derivative of the exchange-correlation energy with respect to the spin magnetic moment. The effect of the coupling is shown to depend on the varying r elative strengths of spin-orbit coupling and exchange splitting within the f series. Since in the f levels the internal exchange splitting d ominates rather than the spin-orbit splitting, the energy level scheme is that of the Paschen-Back effect, and thus features of the Russell- Saunders coupling persist in spite of relativistic effects.