Developments of Lifetime-broadening-removed XANES Spectroscopy X-ray absorption near-edge structure (XANES) is a powerful technique for studying electronic states around selected atomic species. XANES features are, however, often smeared out because of the natural lifetime width of the core holes. Intense monochromatic X-rays available at SPring-8 have made it possible to experimentally substantiate the observation of lifetime-broadening-removed (LBR) XANES from resonant inelastic X-ray scattering (RIXS) spectra [1]. In this article using CuO data it is demonstrated that 1 s -LBR-XANES and 1 s as well as 2 p -LBR or lifetime-broadening-free (LB F ) XANES can be deduced from experimental RIXS spectra. T he experiments were carried out at beamline BL47XU . T he RIXS from powder CuO was analy z ed with a spherically bent φ 75 mm Si( 444 ) crystal having an 8 20 mm radius of curvature, and detected by a scintillation counter. T he overall resolution was 1.1 e V . F igure 1 shows the excitation energy dependence of 1 s 2 p RIXS spectra of CuO [1]. Spectral shape and intensity change with excitation energy significantly. Excitation with X-ray energies well above the K - absorption edge energy yields a single band, which is the well- k nown Cu K α 1 . As the excitation energy is decreased, the main feature corresponding to the K α 1 (A) is shifted down with its width broadened. By decreasing the excitation energy to ~ ~ 8 9 8 3 e V , a new branch (B) appears. Another feature labeled C is prominent at the excitation energy below 8 9 8 3 e V , and is the strongest at the 1 s → 3 d transition energy, 8 9 8 0 e V [ 2 ]. T he differential cross section of 1 s 2 p RIXS process can be deduced from the well- k nown K ramers- H eisenberg equation [1, 3 ] : H ere, ω 1 and ω 2 are incident and scattered photon energies, is the energy of the excited electron, and Γ 1 s and Γ 2 p are the widths of the 1 s and 2 p levels, the energies of which are represented by Ω 1 s and Ω 2 p , respectively. T he dg 1 s / d ω corresponds to LB F - XANES profile. where ω abs = Ω 1 s + ω . Equation ( 2 ) allows us to calculate dg 1 s / d ω analytically from the experimental RIXS spectra directly. T he dg 1 s / d ω derived (LBR- XANES) is free from the Γ 1 s broadening and the width is determined only by Γ 2 p . Fig. 1. Excitation energy dependence of RIXS spectra of CuO as a function of excitation energy and emission energy. d σ ( ω 1 ) d ω 2 ( ω 2 / ω 1 ) ( Ω 1 s + ω ) ( d g 1 s / d ω ) ( ( Ω 1 s + ω – ω 1 ) 2 + Γ 1 s /4 2 )( ( Ω 2 p + ω 2 + ω – ω 1 ) 2 + Γ 2 p /4 2 ) 2 2 d ω d σ ( ω 1 ) d ω 2 ( ω 2 / ω 1 ) ω abs ( d g 1 s / d ω abs ) ( Ω 1 s – Ω 2 p – ω 2 ) 2 + Γ 1 s /4 2 2 , U nder the approximation that Γ 2 p / << 1, Eq. (1) can be transformed in to Eq. ( 2 ) [1, 3 ] : ( 2 ) (1) 8988 8986 8984 8982 8980 8978 8050 8045 8040 8035 CuO In the upper panel of F ig. 2 , the RIXS spectra of CuO excited at several energies ( ‘ Exp. ’ ) are shown. T he LBR-XANES profiles analytically derived from them are plotted in the lower panel. T he inset shows 1 s → 3 d transition region in an expanded scale. It is notable that, despite of significant differences in RIXS h h h h h ω h h h h Emission Energy (eV) 75 References [ 1] H. Hayashi e t al. : Phys. Rev. B 68 (2003) 45122. [2] N. Kosugi e t al. : Chem. Phys. 135 ( 1989) 149. [3] J. Tulkki e t al. : J.Phys. B 15 ( 1982) L435. [4] H. Hayashi, R. Takeda, M. Kawata, Y. Udagawa, Y. Watanabe, T. Takano, S. Nanao, N. Kawamura, T. Uefuji and K. Yamada: J. Electron Spectrosc. Relat. Phenom. 136 (2004)199. Hisashi Hayashi IMRAM, Tohoku University E-mail: hayashi@tagen.tohoku.ac.jp Fig. 2. Upper panel: comparisons of the observed RIXS spectra (circles) and calculated ones (solid line) using the best- fit dg 1 s /d ω model. Lower panel: the best-fit LBF-XANES (dg 1 s /d ω ) numerically obtained as well as LBR-XANES spectra analytically obtained from RIXS spectra of the upper panel. Conventional XANES is also shown for comparison. Excitation Energy (eV) 89 80 8984 8988 8992 8996 dg 1 s / d ω ω Emission Energy (eV) 8036 80 40 8044 8048 8052 s p ectra, the LBR-XANES derived almost overlaps with each other. Thus, complicated RIXS behavior can be fully explained as the reflection of the LBR- XANES: the RIXS features, A, B, and C, are determined by the XANES features, a, b, and c, respectively [1]. The LBR-XANES is much more distinct th an con ve n ti o nal XANE S, w h ic h suggests that Γ 1 s broadening is removed. s Since the quality of the present RIXS data allows us to examine the profiles in detail numerically, deriving dg 1 s / d / / ω d d on the basis of Eq. (1) without assuming Γ 2 p / << 1 was attempted nex t. The dg 1 s / d ω t hus o bt a ine d corresponds to LBF-XANES. The dg 1 s / d / / ω d d that reproduces the observed RIXS spectra best and the calculated RIXS profiles (ʻBest-fit LBF-XANESʼ ) are shown in the lower and the upper panels of Fig. 2, respectively. In the u p p e r p a n e l , i t i s f o u n d t h a t t h e observed RIXS spectra almost exactly coincide with the calculations by the best-fit dg 1 s / d / / ω d d . ω ω In the lower panel, it is evident that the best-fit dg 1 s / d / / ω d d shows much more distinct features than those analytically obtained, demonstrating that the lifetimes of 2 p as well as 1 s are removed. Many exciting applications of the LBR- or LBF-XANES spectroscopy, e.g., for high-Tc materials [4], can be envisaged. h h 6 6 6 6 6 6 6 6 6 6 6 6 6 6 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 7 7 7 7 7 7 7 7 7 76 76 76 76 76 76 76 76 76 76 76 76 76 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
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