Nonmagnetic and ferromagnetic fcc cerium studied with one-electron methods

Density functional theory was used to study the nonmagnetic (NM) and ferromagnetic (FM) phases of face-centered cubic cerium. Functionals of four levels of approximation for the exchange-correlation energy were used: LDA, PBE, LDA/PBE + $U$, and YS-PBEh. The latter two contain an adjustable parameter, the onsite Coulomb repulsion parameter $U$ for LDA/PBE + $U$, and the fraction ${\alpha }_{\text{x}}$ of Hartree-Fock exchange for YS-PBEh, which were varied in order to study their influence on the results. By supposing that, as a first approximation, the NM and FM solutions can be identified to the observed $\alpha$ and $\gamma$ phases, respectively, it is concluded that while a small value of $U$ or ${\alpha }_{\text{x}}$ leads to the correct trend for the stability ordering of the two phases, larger values are necessary for a more appropriate (but still not satisfying) description of the electronic structure.

Figure 1

The spin-majority $4f$-electron density at an isovalue of 0.1 electron/bohr${}^3$ for the (a) FM1, (b) FM2, (c) FM3, and (d) NM phases obtained from PBE + $U$ with $U=4.3$ eV and SOC. The shown axes are those of the conventional cubic fcc unit cell.

Figure 2

Total energy of the FM (blue solid curve) and NM (red dashed curve) phases of cerium versus the lattice constant calculated with different functionals. The vertical dotted lines indicate the experimental values of the $\alpha$ (4.85 Å) and $\gamma$ (5.16 Å) phases. The zero of the energy was set at the minimum of the most stable phase. Note that the scale on the energy axis is different for each functional. The results for PBE and PBE + $U$ include SOC effects.

Figure 3

Total and $4f$ one-spin density of states for the NM phase of cerium. The results for PBE and PBE + $U$ include SOC effects. The Fermi energy is set at $E=0$ eV.

Figure 4

Total and $4f$ spin-majority (upwards) and spin-minority (downwards) density of states for the FM phase of cerium. The FM state is FM2 for PBE + $U$ with $U=4.3$ eV and FM1 in the other cases. The results for PBE + $U$ include SOC effects. The Fermi energy is set at $E=0$ eV.

Figure 5

Total and $4f$ spin-majority (upwards) and spin-minority (downwards) density of states for the three FM phases of cerium as obtained from PBE + $U$ ($U=4.3$ eV) with SOC. The Fermi energy is set at $E=0$ eV.