Polarization dependence and symmetry analysis in indirectK-edge RIXS

Abstract

We present a study of the charge-transfer excitations in undoped Nd 2 CuO 4 using resonant inelastic X-ray scattering (RIXS) at the Cu K-edge. At the Brillouin zone center, azimuthal scans that rotate the incidentphoton polarization within the CuO 2 planes reveal weak fourfold oscillations. A comparison of spectra taken in different Brillouin zones reveals a spectral weight decrease at high energy loss from forward-to back-scattering. We show that these are scattered-photon polarization effects related to the properties of the observed electronic excitations. Each of the two effects constitutes about 10% of the inelastic signal while the '4p-as-spectator' approximation describes the remaining 80%. Raman selection rules can accurately model our data, and we conclude that the observed polarization-dependent RIXS features correspond to E g and B 1g charge-transfer excitations to non-bonding oxygen 2p bands, above 2.5 eV energy-loss, and to an E g d → d excitation at 1.65 eV.Raman scattering and optical spectroscopy have enabled tremendous contributions to the study of condensed matter systems. Both probes use ∼ 1 eV light and are limited to essentially zero momentum transfer. In order to investigate the charge response of a material throughout the Brillouin zone, photons in the X-ray regime must be used. X-ray Raman scattering, more commonly referred to as resonant inelastic X-ray scattering (RIXS), allows the measurement of the momentum dependence of charge excitations. Even though it has successfully been used to study the physics of a wide array of systems, 1-5 this resonant technique is relatively new and there is still much to learn about the details of its cross section.One of the strengths of conventional Raman scattering derives from the fact that the technique allows the determination of the symmetry of excitations by selecting the polarization of the incident and scattered photons. Only polarization dependent soft (or direct 6 ) X-ray RIXS studies, at the O K-edge or the Cu L-and M-edges of the cuprates, 7-11 have shown that photon polarization can be used to select different electronic excitations. In these cases, the photon polarization effects are understood to come from the direct interaction of the photoelectron, excited into the valence system, with the valence electrons. This is why this type of RIXS is commonly referred to as direct. 6 On the other hand, tuning the incident energy to the Cu K-edge excites the photoelectron into the Cu 4p band approximately 10-20 eV above the 3d valence levels. The relatively large separation in energy from the valence levels as well as the large spatial extent of the 4p orbital are believed to prevent the photoelectron from interacting with the valence system, and this type of RIXS is in turn referred to as indirect. 6 Accordingly, theoretical models of this type of RIXS accordingly do not include possible interactions of the 4p photoelectron with the valence system, 12-15 which is commonly referred to as the '4p-as-spectator' approximation.RIXS investigations of ...

Spin-orbit sensitive hard x-ray probe of the occupied and unoccupied5ddensity of states

“…39 However, electron-phonon interactions are observed at energy transfer below 1 eV 40 using indirect RIXS, where the photoexcited electron participates in the emission process (see, e.g., Refs. 23,24,40,and 41). The omission of multielectronic excitations in the present study is justified a posteriori by good agreement of the single-electron transition theory with the experimental data.…”

“…The importance of indirect and direct RIXS processes was discussed in Ref. 41 for Cu K-edge. A real-space multiple scattering Green's function formalism was adapted for resonant inelastic x-ray scattering.…”

Hard X-ray Resonant Inelastic X-ray Scattering at the Advanced Photon Source

“…Recently, Chabot-Couture et al [30] have used the polarization dependence, incident energy dependence, and most crucially, the azimuthal dependence of the charge transfer scattering to probe the symmetry of these excitations. By carefully normalizing data taken in the tetragonal cuprate, Nd 2 CuO 4 , at the zone center in a number of different Brillouin zones they were able to compare the scattering in each zone quantitatively.…”

K -edge and L3 -edge RIXS study of columnar and staggered quantum dimer phases of the square lattice Heisenberg model

“…In the K-edge process an electron transitions from the 1s 2 4p 0 → 1s 1 4p 1 → 1s 2 4p 0 . Within the 4p-spectator approximation the dynamics of the promoted electron is neglected [66]. Also, the 3d electrons state is not directly affected.…”