ORBITAL POLARIZATION IN METALLIC F-ELECTRON SYSTEMS

The orbital polarization (OP) in systems with an open f shell is analyzed by means of several theoretical tools. The delocalization-localization transition (DLT) is considered as a redistribution of electrons within the f shell whereas the total f occupation is approximately constant. A qualitative analysis of the many-orbital Hubbard-Kanamori model both within a weak-coupling Hartree-Fock approximation (WCHFA) and a strong-coupling mean-field-approximation (SCMFA) perturbation theory is presented. The WCHFA analysis shows that the DLT is only possible in the beginning and the end of a series and may occur only when the bandwidth is of the order of Hubbard U. Band structure calculations within a tight-binding scheme (TB) and a linear-muffin-tin-orbital (LMTO) method with Hubbard-Kanamori corrections to the potential are performed for U, Th, and the α and γ phases of Ce. In this analysis we find that the theory tends to overestimate the stability of the localized state. For Ce metal the transition from itinerant to localized 4f states takes place already for a Hubbard U of ∼2.7 eV. A comparison of a TB energy band scheme with the LMTO method for implementing the Hubbard-Kanamori corrections is also performed. The TB scheme gives a sharper transition, whereas allowing for renormalization of the hopping and mixing parameters in the LMTO method makes the transition smoother. An analysis of the Ce (nf∼1) 4f states within the perturbation theory around the atomic limit is also performed both within the Hubbard I approximation as well as within the strong-coupling mean-field approximation. The Hubbard I solution shows that when the f-electron number deviates slightly from 1 the energy difference between the OP and the paramagnetic metallic state is very small. In this analysis we show that the Hubbard U does not enter the criterion for OP. The reason for this is that in both phases the lower Hubbard band is occupied while the upper one gives only a small difference in the kinetic energy. The SCMFA improves the Hubbard I solution, taking into account exchangelike shifts of the centers of the bands. In this analysis we find that at a filling larger than the critical one (n1.07) the ground state is a Pauli paramagnet, while at smaller fillings the orbital polarized solution has lower energy. © 1995 The American Physical Society.