We examine the degree of $5f$ electron localization in ${\text{URu}}_2{\text{Si}}_2$ using spin-orbit sum rule analysis of the U $N_{4,5}$ $\left(4d\to 5f\right)$ edge. When compared to $\alpha -\text{U}$ metal, US, USe, and UTe, which have increasing localization of the $5f$ states, we find that the $5f$ states of ${\text{URu}}_2{\text{Si}}_2$ are more localized, although not entirely. Spin-orbit analysis shows that intermediate coupling is the correct angular momentum coupling mechanism for ${\text{URu}}_2{\text{Si}}_2$ when the $5f$ electron count is between 2.6 and 2.8. These results have direct ramifications for theoretical assessment of the hidden order state of ${\text{URu}}_2{\text{Si}}_2$, where the degree of localization of the $5f$ electrons and their contribution to the Fermi surface are critical.

• Received 20 May 2010

DOI:https://doi.org/10.1103/PhysRevB.82.033103