Residual-density mapping and site-selective determination of anomalous scattering factors to examine the origin of the FeKpre-edge peak of magnetite

Abstract

The electron-density distribution and the contribution to anomalous scattering factors for Fe ions in magnetite have been analyzed by X-ray resonant scattering at the pre-edge of Fe K absorption. Synchrotron X-ray experiments were carried out using a conventional four-circle diffractometer in the right-handed circular polarization. Difference-Fourier synthesis was applied with a difference in structure factors measured on and off the pre-edge (E(on) = 7.1082 keV, E(off) = 7.1051 keV). Electron-density peaks due to X-ray resonant scattering were clearly observed for both A and B sites. The real part of the anomalous scattering factor f' has been determined site-independently, based on the crystal-structure refinements, to minimize the squared residuals at the Fe K pre-edge. The f' values obtained at E(on) and E(off) are -7.063 and -6.682 for the A site and -6.971 and -6.709 for the B site, which are significantly smaller than the values of -6.206 and -5.844, respectively, estimated from the Kramers-Kronig transform. The f' values at E(on) are reasonably smaller than those at E(off). Our results using a symmetry-based consideration suggest that the origin of the pre-edge peak is Fe ions occupying both A and B sites, where p-d mixing is needed with hybridized electrons of Fe in both sites overlapping the neighbouring O atoms.

Resonant and non-resonant magnetic scatterings with circularly polarized X-rays: magnetic scattering factor and electron density of gadolinium iron garnet

“…Therefore, if circular polarization experiments are performed in an ideal condition, charge and magnetic scattering factors given by equations (8) and (10), respectively, may be of the same order. In circular polarization experiments of Fe 3 O 4 at the Fe K edge, similar asymmetrical ratios are reported as ÁI/2I = À0.070 for the 266 reflection and ÁI/2I = 0.074 for the 026 reflection (Okube & Sasaki, 2014), in comparison with À6 Â 10 À4 and 1 Â 10 À3 for XMCD (Okube et al, 2012). In summary, the appearance of positive-negativepositive peaks is reminiscent of the ÁI/2I peaks, although the ÁI/2I spectrum is much narrower than the XMCD one in terms of peak width.…”

Site-specific electronic structures of ferrimagnetic Fe3O4 measured by resonant X-ray magnetic scattering

“…The atomic scattering factor for charge scattering is defined as f = f 0 + f 0 + if 00 , where f 0 represents the Thomson elastic scattering, and f 0 and f 00 represent the resonant scattering. The values of f 0 , f 0 and f 00 used in this study were taken from published tables (Inter-International Tables for X-ray Crystallography, 1974) and from the Kramers-Kronig transform (Okube et al, 2012).…”

“…(6). Displacement parameters with constraints of 11 = 22 = 33 and 12 = 13 = 23 are 11 = 0.001408 (4) and 12 = 0 for the A site, 11 = 0.001893 (3) and 12 = 0.000184 (4) for the B site, and 11 = 0.001861 (7) and 12 = À0.00012 (1) for the O site (Okube et al, 2012). Table 2 X-ray energy and asymmetric ratios observed for several reflections in RXMS measurements in the vicinity of the Fe K edge.…”

“…In the pre-edge peak, the dipole electronic transition in the O h symmetry is prohibited by the selection rule. However, the intrinsic site symmetry of D 3d for the B site allows such a transition with the second neighbouring Fe atoms (Okube et al, 2012). Schematic diagrams of the DOS for Fe 3d at the A and B sites of magnetite, based on LSDA calculations (Anisimov et al, 1996).…”

Accurate determination of anomalous scattering factor near FeKabsorption edge

“…In this study, through the measurement of X-ray resonant scattering in the Fe K pre-edge, anomalous scattering factors of Fe have been determined site-independently. A related article has been published elsewhere [11]. Since the result on f'(E) depends on the probability of electron transition, our approach would contribute to the quantitative discussion on the electronic states in magnetite.…”