Incident photon energy dependence of the resonant x-ray magnetic scattering cross section of a samarium film

Abstract

Resonant x-ray magnetic scattering is widely used as an element selective probe of magnetism in solids. The present work deals with a different, less frequently addressed aspect: the electronic shell selectivity. Due to the complexity of the atomic effects inherent to the resonant process and at the origin of the electronic shell selectivity, the data are generally considered on a qualitative basis. Here, we try to extend the arguments to a semiquantitative level. We show, through a detailed spectroscopic study of the resonance at the ${L}_{2}$ and ${L}_{3}$ edges of samarium in a single-crystal epitaxial film, how the exploitation of the atomic effects can lead to a deeper understanding of long-range magnetic order in this material. At the ${L}_{2,3}$ edges of rare earths, dipole resonances carry information on the polarization of the $5d$ band, whereas quadrupole resonances reflect the polarization of the $4f$ shell. The narrow width of the $4f$ band permits the interpretation of the quadrupole resonance below the ${L}_{3}$ edge using atomic considerations. A systematic study of the dependence of the $4f$ quadrupole resonance on wave-vector transfer shows that, within our resolution, the magnitude of the $4f$ moments in samarium is independent of the local environment (cubic or hexagonal). On the other hand, the energy dependence of the dipole resonance at and above the ${L}_{2}$ and ${L}_{3}$ absorption edges shows two maxima and is interpreted in the framework of an extended density of $5d$ states. Finally, the relative temperature dependences of the dipole and quadrupole resonances sheds light upon the respective contributions of the $4f$ and $5d$ levels to the long-range magnetic order in samarium.