A detailed study of the angular, energy and polarization dependences of the electric dipolar (E1: 2p→5d) and quadrupolar (E2: 2p→4f) contributions to the x-ray scattering crosssection is presented for holmium in its basal plane spiral antiferromagnetic phase at the L 3 edge. The corresponding E1 and E2 scattering factors have been extracted from fits to the experimental energy line shapes taking into account for the first time a split dipole resonance. Using the imaginary part of the resonant scattering factors to retrieve the XMCD spectrum, we find qualitative agreement with the dichroic spectrum measured in transmission through a holmium foil. Derivation of the TMCS for magnetic moments lying in the a-b plane Appendix B. Fitting procedure References
IntroductionThe magnetism of rare-earth (RE) materials is of huge technological importance. Among other key applications, REs can be found in high-performance permanent magnets [1-3], as dopants in optical data storage devices [4,5] and in high speed magnetoelectronic devices [6,7]. An improved understanding of the electronic and magnetic properties of RE metals, including their interactions with other atoms in compounds and alloys, is crucial for developing future technologies. To this end, synchrotron x-rays are proving to be an important probe of RE magnetism [8,9]. Such experiments are carried out close to an atomic absorption edge by studying either absorptionnamely, x-ray magnetic dichroism, either with circularly (i.e. XMCD) or linearly (i.e. XMLD) polarized photons -or scattering, where scattering can be performed either in the elastic or inelastic regime, namely by x-ray resonant magnetic scattering (XRMS) or resonant inelastic x-ray scattering (RIXS) respectively.Controversy, however, surrounds the identification of E1 (dipolar) and E2 (quadrupolar) features in energy line shapes measured across the RE L 2,3 absorption edges in XRMS [10-12], XMCD [13][14][15][16] and RIXS [17,18]. The observation of a pre-edge peak (where the position of the "absorption edge″ itself is normally defined as the first inflection point of an absorption curve) has generally been interpreted as arising, purely, from E2 processes, whereas the higher energy peak has been attributed to E1 excitations. However, deviations from this understanding have appeared in the literature: in an XMCD study at the Yb L 3 absorption edge, where a dichroic signal observed at the edge was interpreted to be E2 in origin, while a lower energy feature was assigned to be E1 [19]; in an XRMS study at the Tb L 2,3 edges where (again) the low energy peak was interpreted to be E1 and the high energy peak to be E2 [20]. More importantly, a recent combined experiment and theory investigation of charge-magnetic x-ray resonant interference scattering (XRIS) -a technique which is a "subset" of elastic resonant scattering (i.e. XRMS) -carried out by Brown et al [21,22], studying ferro-and ferri-magnetic phases of the hexagonal close-packed, heavy RE metals (moments along the c-axis), has challenged the general i...