Valence fluctuations in thin films and theαandδphases of Pu metal determined by4fcore-level photoemission calculations

Abstract

The average number of 5f electrons making up the valence state in plutonium metal together with the electronic fluctuations on each metal site has been a recent subject of debate. For the ␦ phase of Pu, where compared to the ␣ phase increased localization ͑more atomiclike character͒ leads to decreased overlap and volume increase, an f count close to either 5 or 6 has been proposed depending on the type of electronic structure calculation. In order to resolve the controversy, we analyze the Pu 4f photoemission spectrum, which displays well screened and poorly screened peaks that can be used as a measure for the degree of localization. A simple analytical two-level model already shows on general grounds that the f count for Pu must be between 5 and 5.5. Furthermore, we present detailed Anderson impurity model calculations including the full multiplet structure for Pu 4f photoemission, which are compared to previous experimental results obtained from 1 to 9 monolayers thin films of Pu on Mg and from Pu metal in the ␣ and ␦ phases. The trend in the satellite to main peak intensity ratio as a function of the Pu layer thickness gives a clear indication that Pu metal has an 5f 5 like ground state. For the Pu allotropes and thicker films an f count of 5.22 is obtained with a Coulomb interaction U = 4 eV. The 5f fluctuations in Pu metal are very prominent and strongly material dependent. The calculations give a ground state with 9.6% f 4 , 58.8% f 5 , and 31.6% f 6 for the ␣ phase and 5.7% f 4 , 66.4% f 5 , and 27.8% f 6 for the ␦ phase while for the thin films the amount of f 5 and the localization strongly increase with reduced thickness. The obtained findings are in agreement with recent electronic structure calculations for ␦ Pu using local-density approximation with dynamical mean-field theory and with the branching-ratio analysis of the Pu N 4,5 edge in electron-energy-loss spectroscopy.

Investigation of the distribution of localised and extended states in amorphous MoOx

“…18 We find remarkable agreement with a model based on non-interacting band electrons, valid for extended states, for certain films but large disagreements for others, indicating that substantial numbers of localised states exist in some films. In the latter case, a small polaron method becomes appropriate for an understanding of the transport and the optical properties.…”

“…23 If the electrons are in band states then the occupation of the states is given by a statistical model. 18 This model assumes that electrons move independently in extended states that are occupied up to the Fermi level. The model is valid if the band width is large compared with the variation in the local potentials and the one-site electronic repulsion.…”

Nature of the 5f electronic structure of plutonium

“…5 as well) 95 . Though the δ-Pu sample used in this experiment is not pure element (containing 1.9 at.% Ga), such a large fraction for 5 f 6 configuration is hard to be understood and contrast to most of the DFT + DMFT 54,55 and experimental results 96 . Anyhow, our calculated results for δ-Pu are excellently consistent with the very recent DFT + DMFT results 55 , and close to the experimental results obtained by using the core-hole photoemission spectroscopy 96 .…”

The valence-fluctuating ground state of plutonium

“…Core-hole photoemission spectroscopy (12) and resonant x-ray emission spectroscopy (RXES) measurements (13), both of which probe the valence configuration on a very short time scale (τ ≈ 1 fs), find a multi-valence ground state in δ-Pu suggested by DMFT calculations (9), with reasonable agreement for the occupation of the 5f 4 , 5f 5 , and 5f 6 states (Table 1). Because these measurements only allow an essentially instantaneous snapshot of the electronic configuration, the corresponding virtual valence fluctuations remained hidden.…”

“…Average occupation of the 5f states in δ-Pu. The occupation of the 5f states in δ-Pu is shown as calculated by (DMFT) and measured by resonant x-ray emission spectroscopy (RXES) (13) and corehole photo-emission spectroscopy (CHPES) (12), respectively. We also list the corresponding effective moment µ eff of the three 5f states based on the intermediate coupling scheme (21 Occupation (CHPES) (%) 6(1) 66 (7) 28 (3) Effective Moment µ eff (µ B ) 2.88 1.225 0 Table 2.…”