Polarization analysis of K-edge resonant X-ray scattering of germanium

Abstract

The polarization of K-edge resonant scattering at the space group "forbidden" (0 0 6) reflection of Ge was measured as function of the azimuthal angle, ψ. The experimental results are compared to model calculations based on symmetry analysis of the resonant scattering tensors.PACS numbers: 61.10. Dp, 61.10.Eq, 78.70.Ck In the last few years the investigation of resonant scattering phenomena has allowed novel studies of antiferromagnetism (through resonant magnetic xray scattering 1 ) and, more recently, of orbital 2,3,4,5 and quadrupolar order 6 . Although much progress has been made in the theory and interpretation of these effects, a large number of open questions concerning the origin of the scattering remains.A characteristic feature of resonant scattering is its polarization dependence, which differs markedly from that of normal Thompson scattering. Indeed, polarization analysis (PA) has now been developed into a standard tool for the study of the aforementioned effects. In this communication I present a study of resonant x-ray scattering at the Ge K-edge with emphasis on the analysis of polarization effects. Anisotropic tensor susceptibility (ATS) scattering 7,8,9 and orbital/quadrupolar order resonances are intimately related as the scattering arises from the same transitions between core level and valence band electronic states 10 . Therefore systematic studies of a well-known reference system may lead to better understanding of the complex situation in compounds exhibiting orbital order.One may distinguish three different classes of ATS scattering, depending on the rank of the scattering tensor: The original experiment on NaBrO 3 may be described by second rank tensors corresponding to electric dipole (E1) transitions 7,8,9 . A later experiment on α−Fe 2 O 3 evidenced electric quadrupole (E2) transitions, which give rise to fourth rank tensors 11 . Finally, ATS scattering in Ge was attributed to rank three tensors. Two different origins of this tensor were proposed: An E1-E2 mixed resonance 12,13,14 , and an E1-E1 process combined with a displacement of the scattering atom due to thermal motion 15,16 . The subject is still under discussion 17,18 .The azimuthal dependence of the scattered beam intensity was calculated and experimentally verified by Templeton and Templeton 12 , but without polarization analysis. For some selected photon energies, the phase of the (0 0 6) and (2 2 2) resonant scattering was determined by Lee et al. 19 through the interference with Umweg reflections. Finally, Kokubun et al. 15 and Kirfel et al. 16 studied the temperature dependence of the (0 0 2) and (0 0 6) resonant scattering. They observed a strong increase of the intensity with increasing temperature, but only minor variations in the line shape of the resonance.They concluded that the dominant origin of resonant scattering lies in anisotropic thermal motion of the Ge atoms.The aim of the present experiment was to complement the existing body of experimental data to further study resonant x-ray scattering of odd-rank...

Magnetic and electronic structure of the layered rare-earth pnictideEuCd2Sb2

“…The sample was cooled below T N by a liquid helium flow cryostat in conjunction with an aluminium shield to reduce beam heating. The cryostat achieved a base temperature of 4.5 K, but due to beam heating we estimate the sample temperature to be about 5 K. As in a typical magnetic X-ray scattering experiment, the magnetic structure is determined by studying the azimuthal dependence of the scattered intensity with σ and π incident photons [22][23][24][25] . The intensity of the scattered beam was estimated with a AXUV100 avalanche photodiode with no polarization analysis.Therefore, when σpolarization was used, both the σ → σ and σ → π channels contributed to the scattered intensity.…”

Polarization anisotropy of X-ray atomic factors and `forbidden' resonant reflections

“…This anomalous temperature dependence was initially described in terms of a relatively simple autocorrelation model but significant improvement was later obtained upon introducing cooperative vibrations of the atoms. The spectral and polarization properties of the 006 reflection at ambient conditions were studied in detail by Detlefs (2004).…”

X-ray polarization: General formalism and polarization analysis

“…41 to measurements at different positions of η between 0 • and 180 • in steps of 30 • or less. Furthermore, the intensities should be recorded by rocking the analyzer crystal rather than the sample [32]; in this way artifacts from the variable resolution function are minimized.…”

“…upon rotation of the crystal about the scattering vector Q [23]) is completely free of adjustable parameters. For incident σ polarization the Poincaré-Stokes parameters of the scattered beam are given by [36,37,32], P 1 (θ, ψ) = sin 2 (2ψ) − sin 2 (θ) cos 2 (2ψ) sin 2 (2ψ) + sin 2 (θ) cos 2 (2ψ) (42)…”

“…Experimental data were taken as follows [32]: The photon energy was tuned to the maximum of the resonance, 11.096 keV. For each setting of the azimuth, the Ge (006) reflection was aligned.…”