Magnetic properties of f-electron systems in spin-polarized relativistic density functional theory

The magnetic ground state of the series of lanthanide and actinide trivalent ions is investigated by means of spin-polarized relativistic spin-density functional theory. In the local density functional approximation (LDA) an internal effective magnetic field due to exchange and correlation couples to the spin degrees of freedom. The resulting set of coupled Dirac equations yields ground-state multiplets that obey the well-known Hund's rules. This remarkable result comes about by the coupling of the j = l + 1/2 with the j = l - 1/2 states due to the exchange-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 relative strengths of spin-orbit coupling and exchange splitting within the f series. Since in the f levels the internal exchange splitting dominates 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.