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• W2166223140 abstract "Sum rules for magnetic x-ray dichroism, relating the signals of the spin-orbit split core level absorption edges to the ground-state spin and orbital operators, are expressed in $mathrm{jj}$-coupled operators. These sum rules can be used in the region of intermediate coupling by taking into account the cross term between the $j=lifmmodepmelsetextpmfi{}frac{1}{2}$ ground-state levels and are, therefore, particularly useful in the study of actinides. The calculated expectation values for the ground-state moments of the actinide ions in intermediate coupling show that the spin-orbit-induced operators, such as the magnetic-dipole term, differ strongly from their Hund's rule ground-state values. We also prove the general rule that, when there is a perturbing interaction which is weak compared to the spin-orbit interaction, the ratio of operators with the same total moment remains constant. This condition is usually fulfilled for the crystal-field interaction in the lanthanides and actinides. The values of the ground-state moments as a function of $f$ count give rise to an interesting trend in the dichroism of the spin-orbit split-core edges. The branching ratio of the $3d$ and $4d$ circular dichroism signal gradually increases from nearly zero for $5{f}^{1}$ to ensuremath{sim}0.4 for $5{f}^{5}$ and is close to unity for a more than half-filled shell. The unusual behavior of the branching ratio can be related to the higher (lower) value of the magnetic dipole term, ${T}_{z}$, for a less (more) than half-filled shell of the actinides in the presence of spin-orbit interaction. Uranium compounds will have a much larger value of ${T}_{z}$ than the corresponding $4f$ compounds. Its precise value can be used as a measure for the $f$ count." @default.
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• W2166223140 date "1996-06-01" @default.
• W2166223140 modified "2023-10-13" @default.
• W2166223140 title "X-ray-absorption sum rules in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>jj</mml:mi></mml:math>-coupled operators and ground-state moments of actinide ions" @default.
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• W2166223140 doi "https://doi.org/10.1103/physrevb.53.14458" @default.
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