Applicability of the Spin-Orbit Sum Rule for the Actinide<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>5</mml:mn><mml:mi>f</mml:mi></mml:math>States

Laan, G. van der; Moore, K. T.; Tobin, J. G.; Chung, B W; Wall, M. A.; Schwartz, Adam J.

doi:10.1103/physrevlett.93.097401

Cited by 165 publications

(189 citation statements)

References 22 publications

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“…The latter result is rather surprising, since in spite of the fact that the Th 4d core level is more shallow than the Zr 2p of Hf 2p and lies in between the Ti 2p and La 3d, the core-valence interactions do not spoil the sum rule for the 5f states. Our calculations showed that B 0 varies between only 0.59 and 0.60 for the light actinides (see Table I) and, therefore, are very close to the statistical ratio [15]. This means that the EELS and XAS branching ratios depend almost solely on the 5f spin-orbit expectation value per hole, and thus we now have an unambiguous probe for the 5f spin-orbit interaction.…”

Section: Of 15supporting

confidence: 64%

“…However, for the 5f states of the actinides the spin-orbit interaction is much stronger, giving a significant mixing of the Hund's rule ground state by other LS states with the same J value. Hence, the LS states will be less pure and there is a tendency towards the jj coupling limit [14,15]. The choice of the coupling limit has profound implications for the expectation value of the spin-orbit interaction, as well as for any other orbital-related interactions, such as the orbital magnetic moment.…”

Section: Spin-orbit Interaction and Branching Ratiomentioning

confidence: 99%

“…The situation is favorable for the M 4,5 and N 4,5 edges of the actinides, given the small exchange interactions between the 3d and 4d core levels and the 5f states [15]. The latter result is rather surprising, since in spite of the fact that the Th 4d core level is more shallow than the Zr 2p of Hf 2p and lies in between the Ti 2p and La 3d, the core-valence interactions do not spoil the sum rule for the 5f states.…”

Section: Of 15mentioning

confidence: 99%

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Probing the population of the spin–orbit split levels in the actinide 5f states

et al. 2006

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Spin-orbit interaction in the 5f states is believed to strongly influence exotic behaviors observed in actinides metals and compounds. Understanding these interactions and how they relate to the actinide series is of considerable importance. To address this issue, the branching ratio of the white-line peaks of the N 4,5 edges for the light actinide metals, -Th, -U, and -Pu were recorded using electron energy-loss spectroscopy (EELS) in a transmission electron microscope (TEM) and synchrotron-radiation-based x-ray absorption spectroscopy (XAS). Using the spin-orbit sum rule and the branching ratios from both experimental spectra and many-electron atomic spectral calculations, accurate values of the spin-orbit interaction, and thus the relative occupation of the j = 5/2 and 7/2 levels, are determined for the actinide 5f states. Results show that the spin-orbit sum rule works very well with both EELS and XAS spectra, needing little or no correction. This is important, since the high spatial resolution of a TEM can be used to overcome the problems of single crystal growth often encountered with actinide metals, allowing acquisition of EELS spectra, and subsequent spin-orbit analysis, from nm-sized regions.The relative occupation numbers obtained by our method have been compared with recent theoretical results and show a good agreement in their trend.

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Section: Of 15supporting

confidence: 64%

Section: Spin-orbit Interaction and Branching Ratiomentioning

confidence: 99%

Section: Of 15mentioning

confidence: 99%

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Probing the population of the spin–orbit split levels in the actinide 5f states

et al. 2006

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“…Also the M 4,5 edge of the rare earth has large errors, but the edges of the 4d, 5d, and 5f systems have negligible errors due to the mixing of the spin-orbit split components. 8 Crocombette et al 9 also tested the effective spin sum rule theoretically. For an octahedral system at 300 K they found that the sum-rule value for ͗S z ͘ is ϳ10% too small for 3d 6 , 3d 7 , and 3d 8 .…”

Section: ͑⍀͒D⍀ ͑1͒mentioning

confidence: 99%

“…The effective spin sum rule has been theoretically simulated and tested by Teramura et al 7 They calculated the expectation values of the effective spin ͗SE z ͘ and compared them with simulated effective spin sum-rule values ͓SE z sum ͔. van der Laan et al 8 used the ratio of the G 1 ͑pd͒ Slater integral and the core hole spin-orbit coupling to estimate the purity of the L 2 and L 3 edges and as such the accuracy of the effective spin-orbit sum rule. They found the largest error for the L edges of 3d transition metals.…”

Section: ͑⍀͒D⍀ ͑1͒mentioning

confidence: 99%

Accuracy of the spin sum rule in XMCD for the transition-metalLedges from manganese to copper

2009

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The effective spin sum rule is widely used in the quantitative analysis of x-ray magnetic circular dichroism spectra. Here, this important, though imperfect, sum rule is reviewed with a detailed analysis of the various sources for errors and deviations. The simulations confirm that the final state effects of the core level spin-orbit coupling and the core-valence exchange interactions ͑multiplet effects͒ are linearly related with the effective spin sum-rule error. Within the charge transfer multiplet approach, we have analyzed these effects, in combination with the interactions affecting the magnetic ground state, including the crystal field strength, the charge transfer effects, the exchange ͑magnetic͒ field, and the 3d spin-orbit coupling. We find that for the late transition-metal systems, the error in the effective spin moment is between 5% and 10%, implying that for covalent and/or metallic systems the effective spin sum rule is precise to within 5-10 %. The error for 3d 5 systems is ϳ30% and for 3d 4 systems, the error is very large, implying that, without further information, the derived effective spin sum-rule values for 3d 4 systems have no meaning.

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Valence Fluctuation of Uranium Ions in Uranium Sesquinitride Revealed by Dynamical Mean‐field Theory Merged with Density Functional Theory

Cao

et al. 2023

ChemPhysChem

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The electronic properties, in particular, the occupation number of 5f electrons and the valence state of U ions in uranium sesquinitride (U2N3) are studied by using density functional theory (DFT) calculations merged with dynamical mean‐field theory (DMFT). The results demonstrate that j=5/2 and j=7/2 manifolds are in the weakly correlated metallic and weakly correlated insulating regimes, respectively. The quasi‐particle weights indicate that LS coupling scheme is more feasible for 5f electrons, which are not in the orbital‐selective localized state. The weighted summation of the occupation probabilities of 5fn (n=0,1,2,3,4) atomic configurations suggests that 5f electrons have the inter‐configuration fluctuation, or the mixed‐valence state for U ions, together with an average occupation number of 5f electrons n5f∼2.234, which is in good agreement with the electron localization function (ELF) and occupation analysis based on other DFT‐based calculations. The 5fn‐mixing‐driven inter‐configuration fluctuation might originate from the dual nature of 5f electrons, and the flexible electronic configuration of U ions. Finally, the so‐called quasiparticle band structure is also discussed.

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Applicability of the Spin-Orbit Sum Rule for the Actinide5fStates

Cited by 165 publications

References 22 publications

Probing the population of the spin–orbit split levels in the actinide 5f states

Probing the population of the spin–orbit split levels in the actinide 5f states

Accuracy of the spin sum rule in XMCD for the transition-metalLedges from manganese to copper

Valence Fluctuation of Uranium Ions in Uranium Sesquinitride Revealed by Dynamical Mean‐field Theory Merged with Density Functional Theory

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