Resonant X-Ray Scattering in Correlated Systems by Youichi Murakami & Sumio Ishihara

Author:Youichi Murakami & Sumio Ishihara
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

In many magnetic materials, magnetic moments are hosted by partially filled d or f orbitals of transition metals, lanthanides, or actinides. The empty d orbitals may be studied through E1 transitions from the 2p core states, as shown in Fig. 3a. Here, 2p states are split into higher-lying quartet () and lower-lying doublet () by a fairly large spin–orbit interaction. Thus the absorption edges from 2p (L) and 2p (L) are observed at separate energies. Large resonant enhancements of X-ray magnetic scattering are expected at L absorption edges in the d electron systems. However, L-edge resonant X-ray scattering has not been applied to many 3d/4d transition-metal compounds.

The L edges of 3d transition metals are located between 450 and 960 eV, as shown in Fig. 4. The corresponding wavelengths of 13–28 Å would be too long to satisfy the Bragg condition for many magnetic 3d transition-metal compounds. In magnetic 3d transition-metal compounds, K-edge resonant scattering at much shorter wavelength has been often utilized instead of L-edge resonant scattering. A large rising of the X-ray absorption at K edge is assigned to the E1-allowed intratomic 1s–4p transition. The spin state of 3d electrons affects the 4p energies to some extent through the Coulomb interaction. The consequent tiny spin-splitting in the 4p states may cause a weak resonant enhancement of the amplitude of X-ray magnetic scattering, as already indicated in Fig. 1. A weak peak due to 1s–3d transition might also be discerned at a few eV lower than the main absorption edge in the X-ray absorption spectrum (XAS). If the transition metal site is on an inversion center, the E2 transition is the dominant process for 1s–3d excitation. Thus, one cannot expect a large resonant enhancement of the magnetic scattering. If the local inversion symmetry is broken, the E1 transition matrix between 1 s and 3d becomes nonzero through the 3d–4p hybridization. The resonant magnetic scattering would be caused by both E1 and E2 transitions. As a consequence, some unique X-ray response may show up, as discussed in Sect. 6.

Fig. 4K, L, and M absorption edges for all elements. Filled symbols indicate the data for elements that often host magnetic moments. The data are obtained from Ref. [11]

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