Synthesis of band and model Hamiltonian theory for hybridizing cerium systems

The unusual magnetic behavior of the heavier Ce monopnictides may be understood on the basis of a model Hamiltonian for a system of moderately delocalized f states hybridizing with band states. The parameters entering the theory have previously been taken as phenomenological input. We present a first-principles calculation of the parameters in the model Hamiltonian based on self-consistent, warped--muffin-tin, linear muffin-tin-orbital (LMTO) band structures calculated for CeBi, CeSb, CeAs, and CeP. With the self-consistent potential, we calculate the bands and the band-f hybridization matrix element entering the Anderson lattice Hamiltonian. The band-f hybridization potential is derived from the 4${f}_{5/2}$ resonance in the potential surrounding a Ce site; the f-state energy with respect to the band Fermi energy and the f-f correlation energy U are estimated by averaging f-state eigenvalues of ${f}^{0}$, ${f}^{1}$, and ${f}^{2}$ Ce configurations. The result is used to calculate the anomalous crystal-field splitting of the Ce 4${f}_{5/2}$ manifold predicted by the model Hamiltonian for the Ce monopnictides. Due to the structure of the cubic symmetry group, band-f hybridization has a greater effect on the ${\ensuremath{\Gamma}}_{8}$ quartet than on the ${\ensuremath{\Gamma}}_{7}$ doublet of the 4${f}_{5/2}$ manifold, and the reduction of the splitting of the crystal-field levels from that expected on extrapolation from the isostructural heavier rare-earth monopnictides may be understood quantitatively on this basis. Our quantitative results are in good agreement with experimental values. We also calculate the range functions describing the anisotropic magnetic behavior of CeBi and CeSb, in fair agreement with phenomenological parameters fitted to data on those materials.