E1 and E2 contributions to the L₃resonance line shape in antiferromagnetic holmium

Abstract

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...

Hard X-ray magnetochiral dichroism in a paramagnetic molecular 4f complex

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Itinerant and Localized Magnetization Dynamics in Antiferromagnetic Ho

“…The resonant x-ray diffraction process at the Ho L 3 absorption edge involves virtual transitions between 2p core levels and unoccupied valence states, dramatically enhancing the sensitivity to the magnetic ordering of the valence states involved in the transition. Thus, by choosing either an electric dipole (E1) or quadrupole (E2) transition, the 5d and the 4f electrons can be addressed separately due to the respective selection rules [22,23], as depicted in Fig. 1(a).…”

“…The spectrum shows two prominent peaks at 8.064 and 8.072 keV, below and above the Ho L 3 absorption edge at 8.070 keV, representing a strong resonant enhancement of the magnetic diffraction signal. These two features originate from the electric quadrupole (E2) and electric dipole (E1) transitions in the resonant scattering process, probing the ordered localized 4f and itinerant 5d moments, respectively [23,29].…”

Kramers-Kronig constrained modeling of soft x-ray reflectivity spectra: Obtaining depth resolution of electronic and chemical structure

“…Applications often require accurate resonant x-ray absorption spectra (commonly referred to as XAS, NEXAFS, or XANES) to interpret results. Such spectra are obtained either from measurement or some form of model calculation, and are often adequate for the problem at hand 11,12 . However, as resonant x-ray scattering applications become more refined, cases are encountered in which the spatial distribution of electronic structure itself is to be determined, and in such cases it is not obvious that measured or model optical spectra are sufficient.…”