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Resonant and near-resonant inelastic X-ray scattering spectroscopy and lifetime-broadening-removed XANES of CuO
Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 277–280
Resonant and near-resonant inelastic X-ray scattering spectroscopy and lifetime-broadening-removed XANES of CuO Hisashi Hayashi a,∗ , Yasuo Udagawa a , Chi-Chang Kao b a
IMRAM, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan b NSLS, Brookhaven National Laboratory, Upton, New York, NY 11973, USA Available online 25 March 2004
Abstract Being a second order optical phenomenon, resonant inelastic X-ray scattering (RIXS) spectroscopy can be used to disentangle bound-state excitations from continuous absorption spectrum more effectively than ordinary first order absorption spectroscopy. When the excitation energy is lower than the K absorption threshold by about 10 eV or more, RIXS spectra observed approach a mirror image of 1s-core-hole lifetime-broadening-removed (LBR) XANES spectra, although the scattering intensity is prohibitively weak because of the unsatisfactory resonant condition employed. Approaching closer to the resonance, RIXS intensity increases by several orders of magnitude and concurrently observed is a surprisingly complicated set of spectra which heavily depends on the excitation energies. From each RIXS spectrum obtained under close to the resonant conditions, 1s-core-hole LBR-XANES or 1s- and 2p-core-hole LBR-XANES can be deduced by analytical method or numerical calculations. The RIXS-XANES method has been applied to CuO to reveal an existence of hidden electronic states near the absorption threshold. © 2004 Elsevier B.V. All rights reserved. Keywords: Resonant inelastic X-ray scattering; Lifetime-broadening-removed XANES; CuO; Unoccupied electronic states
1. Introduction The evolution of X-ray sources by third-generation synchrotron radiation facilities opens up new possibilities to apply resonant and near-resonant inelastic X-ray scattering; i.e., lifetime-broadening-removed (LBR)/free X-ray absorption near-edge structures (XANES) spectroscopy [1,2]. Since resonant inelastic X-ray scattering (RIXS) is a second order optical phenomenon [3], it can be used to disentangle bound-state excitations from continuous absorption spectrum more effectively than ordinary first order absorption spectroscopy as follows. 1s2p RIXS process is schematically illustrated in Fig. 1a. The following differential cross section of this type of resonant emission can be deduced from the well-known Kramers–Heisenberg equation under the assumption that post collision interaction effects are ignored [4]:
∗ Corresponding author. Tel.: +81-22-217-5385; fax: +81-22-217-5337. E-mail address: [email protected] (H. Hayashi).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.02.065
dσ(ω1 ) ∝ dω2
(ω2 /ω1 )(Ω1s +ω)(dg1s /dω) 2 /4¯h2 ) ((ω − (ω1 − Ω1s ))2 + Γ1s 2 /4¯h2 ) × ((ω − (ω1 − ω2 − Ω2p ))2 +Γ2p
dω
(1) ¯ ω2 are incident and scattered photon enerHere, h ¯ ω1 and h gies, h ¯ ω is the energy of the excited electron in the intermediate state, Γ 1s and Γ 2p are the widths of the 1s and 2p levels, the energies of which are represented by h ¯ Ω1s and h ¯ Ω2p . The dg1s /dω is proportional to the density of unoccupied states and the transition matrix elements of 1s electrons. The integrand of Eq. (1) is essentially the product of three functions having ω as a common variable; two Lorentzians, one (f1 ) centered at ω = ω1 − Ω1s with FWHM Γ1s /¯h and another (f2 ) centered at ω = ω1 − ω2 − Ω2p with FWHM Γ2p /¯h, and dg1s /dω. Let us assume that Γ 1s is much larger than Γ 2p and that dg1s /dω is characterized by a narrow discrete band corresponding to vacant 3d and two step functions near the absorption threshold followed by a continuum, which are reasonable approximations for CuO studied here. The three functions along the ω-axis can be depicted
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H. Hayashi et al. / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 277–280
der the approximation employed here, dg1s /dω derived from RIXS by Eq. (2) is free from lifetime-broadening by Γ 1s and the width is determined only by experimental resolution ( Eexp ) and Γ 2p . In this work, the above-mentioned RIXS-XANES method has been applied to CuO. The electronic structure of this compound has attracted renewed interest recently, because CuO shares the same basic building block (CuO4 parallelogram plane) with high-Tc materials. Revealed is an existence of hidden electronic states near the absorption threshold in CuO.
2. Experimental
Fig. 1. (a) A diagram of 1s2p resonant inelastic X-ray scattering (RIXS) process and (b) schematic presentation of lifetime-broadening-removed measurements by 1s2p RIXS. See text.
schematically for arbitrary chosen ω1 and ω2 , as shown in Fig. 1b. The scattering intensity is in principle determined by the overlap of these three functions. In RIXS measurements, ω1 is fixed and the scattering intensity is monitored as a function of ω2 , which is equivalent of sliding the sharp f2 along the ω-axis, while keeping f1 and dg1s /dω fixed as shown in Fig. 1b. Suppose ω1 − Ω1s is small, say ≤−10 eV, f1 tails off at ω > 0 and can be assumed a small constant. Then Eq. (1) is determined by the convolution of dg1s /dω with f2 , that is, broadening by Γ 1s is removed [1]. However, small f1 value makes the scattering intensity significantly low, imposing severe restriction to wide application. When ω1 − Ω1s approaches zero, f1 cannot be approximated to be a constant, and the scattering intensity is governed by the overlap of these three functions. It will be obvious, however, that in this case also the bandwidth of the scattering spectra is dominated by Γ 2p and not by Γ 1s because in the overlap region the f1 forms just a monotonously decreasing background. Under the approximation that Γ2p /2¯h 1, Eq. (1) can be transformed to a more transparent form [2,4] by using the K␣-emission energy h ¯ ωK␣ = h ¯ (Ω1s − Ω2p ) = 8047.8 eV and the absorption energy ωabs = Ω1s +ω = ωK␣ +ω1 −ω2 : dσ(ω1 ) (ω2 /ω1 )ωabs (dg1s /dωabs ) ∝ . 2 /4¯h2 dω2 (ω2 − ωK␣ )2 + Γ1s
(2)
This equation means that the cross section of 1s2p RIXS is, apart from the factor (ω2 /ω1 ) × ωabs , proportional to dg1s /dωabs multiplied by a Lorentzian centered at ωK␣ . Hence, it is possible to calculate dg1s /dω analytically from the experimental RIXS spectra directly, or vice versa. Un-
RIXS experiments were carried out at the BL47XU beamline at SPring-8. The experimental details were described elsewhere [2]. In short, incident X-rays (flux =∼ 1014 photons/s; spectral width = 0.9 eV at 8 keV) were horizontally focused by a cylindrically-bent mirror and irradiated onto the sample, with an ion chamber monitoring the beam intensity. The scattered radiation was analyzed with a spherically-bent φ 75 mm Si(4 4 4) crystal having an 820 mm radius of curvature, and detected by a scintillation counter. To acquire 1s2p RIXS spectra, the incident energy remained fixed and the scattered photon energy was analyzed by moving the analyzer and the detector synchronously. In these measurements, the active area of the analyzer was limited to 40 mm in diameter, which resulted in an overall energy resolution ( Eexp ) of 1.1 eV as determined by the FWHM of the elastic line. All data were taken on powder CuO at room temperature at a constant scattering angle of 80◦ .
3. Results Fig. 2 shows excitation energy dependence of RIXS spectra of CuO. Spectral shape and intensity change with excitation energy significantly. Excitation with X-ray energies well above the K-absorption edge energy (∼8986 eV) yields a single band at 8047.8 eV, which is the well-known Cu K␣1 fluorescence line (in Fig. 2 the K␣1 peak is out of the scale). As the excitation energy lowered below the K-edge, the main feature corresponding to the K␣1 (denoted A) is shifted down with its width broadened. By lowering the excitation energy to ∼8983 eV, a new branch, labeled B, appears. Another feature labeled C is prominent at the excitation energy around 8980 eV excitation. As the excitation energy further lowered, the peak energy of A continues to shift to lower energy, preserving the energy loss (Eloss ) of 939 eV. At the same time, the scattering intensities decrease monotonously. In contrast to the consecutive changes with excitation energy observed for A, the branch B is only observable within a small range of excitation energy, from ∼8981 to ∼8984 eV. Furthermore, the Eloss of the branch B
H. Hayashi et al. / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 277–280
279
Exp. Best-fit LBF-XANES A
B 8983.1eV
A B
C
8981.1eV
A
C 8979.1eV
A C 8977.1eV
Fig. 2. Excitation energy dependence of resonant inelastic X-ray scattering (RIXS) spectra of CuO as a function of excitation energy and emission energy.
Emission energy [eV]
8978
In the upper panel of Fig. 3 the RIXS spectra of CuO excited at several excitation energies are shown. In the lower panel shown by squares and triangles are LBR-XANES profiles of CuO analytically derived from some of the RIXS spectra by the use of Eq. (2). The inset shows 1s → 3d transition region below the absorption edge in an expanded scale. It is rather striking that, in spite of significant differences in RIXS spectra employed, LBR-XANES derived by Eq. (2) almost overlaps with each other. Although not shown for clarity of the figure, a use of RIXS spectra at other excitation energies produces almost the same results as long as the excitation energy is below about 8984 eV. In the lower panel of Fig. 3 conventional XANES is also shown. It is clear from the comparison that features in LBR-XANES are much more distinct than those in conventional XANES. This endorses that line-broadening by Γ 1s , which often hampers detailed analysis of conventional XANES, is removed in LBR-XANES derived from RIXS. In the derivation of Eq. (2) it has been assumed that Γ 2p is zero. Since the quality of the present RIXS data allows us to examine the profiles in detail numerically, attempted next is
8980
8982
8984
8986
Best-fit LBF XANES
a
4. Discussions 4.1. LBR- and LBF-XANES of CuO
b
c dg1s/d
varies with the excitation energy. On the other hand, Eloss for C remains constant (932 eV) and is independent of the excitation energy, as is the branch A. As the excitation energy is tuned to ∼8980 eV, which is the transition energy from 1 s to the vacant 3d [5], the band C is the strongest with the band width much narrower than the normal K␣1 fluorescence. These excitation energy dependencies of RIXS spectral features have been already reported [2,6].
8036 8040 8044 8048 8052
c 8976
8980
LBR-XANES analytically Obtained from 8977.1eV Exc. 8979.1 8981.1 8983.1
b 8984
Conventional XANES
8988
8992
8996
9000
Energy [eV]
Fig. 3. (Upper panel) Comparisons of the observed RIXS spectra (circles) and calculated ones (solid line) by the use of the best-fit dg1s /dω model at the excitation energies indicated in the figure. (Lower panel) The best-fit LBF-XANES (dg1s /dω) numerically obtained as well as LBR-XANES spectra analytically obtained from RIXS spectra of the upper panel. Conventional XANES is also shown in the lower panel for comparison.
to derive dg1s /dω by numerical simulation based on Eq. (1) without such an assumption. The dg1s /dω profiles obtained from this procedure correspond to lifetime-broadening-free (LBF) XANES. The procedures to extract LBF-XANES are described in detail elsewhere [2]. In the lower panel of Fig. 3, a dg1s /dω model that reproduces observed RIXS spectra best is shown. It is evident that dg1s /dω obtained here shows much more distinct features than those obtained from Eq. (2), 1s-LBR-XANES, demonstrating that the core-hole lifetimes of 2p as well as 1s are removed. It is also possible to calculate RIXS spectra from an assumed dg1s /dω by the use of Eq. (1). In the upper panel
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of Fig. 3 calculated RIXS profiles from the best-fit dg1s /dω model are compared with experimental RIXS spectra. It is clear that the observed RIXS spectra almost exactly coincide with the corresponding ones generated by the single dg1s /dω model. Roughly speaking, there are the following relations between dg1s /dω features and RIXS peaks. First, the main RIXS feature, which is indicated by A in Figs. 2 and 3, is essentially determined by the profile of the prominent features in XANES indicated by a in Fig. 3. The shape of the low-energy tail of the features, indicated by b, determines the RIXS feature B. The discrete 1s → 3d band c at 8980 eV is responsible to the prominent feature C in the RIXS spectra. From these observations it is confirmed that complicated behavior of the RIXS spectra, found in Figs. 2 and 3, can be explained quantitatively as the reflection of the LBF-XANES profile. LBR/LBF-XANES, therefore, can be derived from each inelastic X-ray scattering spectrum under near-resonant conditions. As was described in the previous section, if measured under ≤−10 eV off-resonant conditions, RIXS spectrum itself is almost equivalent to LBR-XANES [1]. However, weak scattering intensity at off-resonant conditions requires a long data accumulation period. On the other hand, if measured under close-to-resonant conditions (a few eV below the edge), 2–3 orders of magnitude intensity gain is achieved. An apparent disadvantage is that some calculations are required to deduce LBR/LBF-XANES spectrum from RIXS. Since the calculation is straightforward and can be carried out almost without resorting to any unambiguous or uncertain parameters, the advantage of near-resonant measurements far exceeds the disadvantage and warrants a wide application of the RIXS-XANES method.
Bocharov et al. [7] concluded that although the gross features of polarized XANES spectrum can be reproduced by the calculation, some discrepancies between experiment and theory still remain, the most significant one being the absence of the Cu 1s to 4pz dipole transition near 8983 eV in the experimental absorption spectra. In their convention, the z -axis is perpendicular to the CuO4 parallelogram plane. Our observation here clearly supports the calculation that there is an unoccupied state at ∼8983 eV in spite of the absence of distinct peak or shoulder in the X-ray absorption spectrum. Unfortunately, it is not possible with present experimental results from a powder sample to determine whether the transition is to the pz orbital or not. However, L3 absorption studies [8,9] on CuO show that there is no marked structure at high energy side of the strong peak due to the 2p → 3d transition, which suggests that the character of the state giving the band B is neither s nor d, but p dominant. Polarization dependent RIXS measurements and LBR/LBF-XANES deduced from them on single crystal CuO will make unambiguous determination of the symmetry of the states possible. The present results demonstrate the potential use of LBR/LBF XANES spectroscopy, which will provide valuable new information on the electronic states of metal compounds, including strongly correlated metal oxides, as well as stringent tests for electronic states calculations for these systems.
Acknowledgements This experiment was carried out at the SPring-8 under the proposal No. R02A47XU-0033N.
4.2. Hidden electronic states of CuO revealed by LBR/LBF-XANES References The existence of weak bound states b, which are hidden in the conventional K XANES spectrum of CuO, is especially interesting. In our previous RIXS work [6], the presence of state between 8980.8 and 8983.3 eV, has been revealed, but relatively low signal-to-noise (S/N) ratio of data prevents detailed examinations. The LBR/LBF XANES obtained here from RIXS spectra with much better S/N ratio (the lower panel of Fig. 3) indicates the tail feature of the hidden states; in the upper panel of Fig. 3 the features of the band B, including almost no dispersion, are completely reproduced by introducing the state b. Here, it should be noted that the gently decaying tail is not common in Cu LBR/LBF-XANES. For example, in another Cu(II) compound, CuCl2 ·2H2 O, the tail is rather steep, which results in barely observable RIXS feature B [1,2]. In a recent combined polarized (conventional) XANES and real-space multiple-scattering calculation study of CuO,
[1] H. Hayashi, Y. Udagawa, W.A. Caliebe, C.-C. Kao, Chem. Phys. Lett. 371 (2003) 125. [2] H. Hayashi, R. Takeda, Y. Udagawa, T. Nakamura, H. Miyagawa, H. Shoji, S. Nanao, N. Kawamura, Phys. Rev. B 68 (2003) 45122. [3] A. Kotani, S. Shin, Rev. Mod. Phys. 73 (2001) 203. [4] J. Tulkki, T. Åberg, J. Phys. B 15 (1982) L435. [5] N. Kosugi, H. Kondoh, H. Tajima, H. Kuroda, Chem. Phys. 135 (1989) 149. [6] H. Hayashi, Y. Udagawa, W.A. Caliebe, C.-C. Kao, Phys. Rev. B 66 (2002) 33105. [7] S. Bocharov, Th. Kirchner, G. Dräger, O. Šipr, A. Šimunek, Phys. Rev. B 63 (2001) 45104. [8] M. Grioni, J.B. Goedkoop, R. Schoorl, F.M.F. deGroot, J.C. Fuggle, F. Schäfer, E.E. Koch, G. Rossi, J.-M. Esteva, R.C. Karnatak, Phys. Rev. B 39 (1989) 1541. [9] L.H. Tjeng, C.T. Chen, S-W. Cheong, Phys. Rev. B 45 (1992) 8205.
Resonant and near-resonant inelastic X-ray scattering spectroscopy and lifetime-broadening-removed XANES of CuO Hisashi Hayashi a,∗ , Yasuo Udagawa a , Chi-Chang Kao b a
IMRAM, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan b NSLS, Brookhaven National Laboratory, Upton, New York, NY 11973, USA Available online 25 March 2004
Abstract Being a second order optical phenomenon, resonant inelastic X-ray scattering (RIXS) spectroscopy can be used to disentangle bound-state excitations from continuous absorption spectrum more effectively than ordinary first order absorption spectroscopy. When the excitation energy is lower than the K absorption threshold by about 10 eV or more, RIXS spectra observed approach a mirror image of 1s-core-hole lifetime-broadening-removed (LBR) XANES spectra, although the scattering intensity is prohibitively weak because of the unsatisfactory resonant condition employed. Approaching closer to the resonance, RIXS intensity increases by several orders of magnitude and concurrently observed is a surprisingly complicated set of spectra which heavily depends on the excitation energies. From each RIXS spectrum obtained under close to the resonant conditions, 1s-core-hole LBR-XANES or 1s- and 2p-core-hole LBR-XANES can be deduced by analytical method or numerical calculations. The RIXS-XANES method has been applied to CuO to reveal an existence of hidden electronic states near the absorption threshold. © 2004 Elsevier B.V. All rights reserved. Keywords: Resonant inelastic X-ray scattering; Lifetime-broadening-removed XANES; CuO; Unoccupied electronic states
1. Introduction The evolution of X-ray sources by third-generation synchrotron radiation facilities opens up new possibilities to apply resonant and near-resonant inelastic X-ray scattering; i.e., lifetime-broadening-removed (LBR)/free X-ray absorption near-edge structures (XANES) spectroscopy [1,2]. Since resonant inelastic X-ray scattering (RIXS) is a second order optical phenomenon [3], it can be used to disentangle bound-state excitations from continuous absorption spectrum more effectively than ordinary first order absorption spectroscopy as follows. 1s2p RIXS process is schematically illustrated in Fig. 1a. The following differential cross section of this type of resonant emission can be deduced from the well-known Kramers–Heisenberg equation under the assumption that post collision interaction effects are ignored [4]:
∗ Corresponding author. Tel.: +81-22-217-5385; fax: +81-22-217-5337. E-mail address: [email protected] (H. Hayashi).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.02.065
dσ(ω1 ) ∝ dω2
(ω2 /ω1 )(Ω1s +ω)(dg1s /dω) 2 /4¯h2 ) ((ω − (ω1 − Ω1s ))2 + Γ1s 2 /4¯h2 ) × ((ω − (ω1 − ω2 − Ω2p ))2 +Γ2p
dω
(1) ¯ ω2 are incident and scattered photon enerHere, h ¯ ω1 and h gies, h ¯ ω is the energy of the excited electron in the intermediate state, Γ 1s and Γ 2p are the widths of the 1s and 2p levels, the energies of which are represented by h ¯ Ω1s and h ¯ Ω2p . The dg1s /dω is proportional to the density of unoccupied states and the transition matrix elements of 1s electrons. The integrand of Eq. (1) is essentially the product of three functions having ω as a common variable; two Lorentzians, one (f1 ) centered at ω = ω1 − Ω1s with FWHM Γ1s /¯h and another (f2 ) centered at ω = ω1 − ω2 − Ω2p with FWHM Γ2p /¯h, and dg1s /dω. Let us assume that Γ 1s is much larger than Γ 2p and that dg1s /dω is characterized by a narrow discrete band corresponding to vacant 3d and two step functions near the absorption threshold followed by a continuum, which are reasonable approximations for CuO studied here. The three functions along the ω-axis can be depicted
278
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der the approximation employed here, dg1s /dω derived from RIXS by Eq. (2) is free from lifetime-broadening by Γ 1s and the width is determined only by experimental resolution ( Eexp ) and Γ 2p . In this work, the above-mentioned RIXS-XANES method has been applied to CuO. The electronic structure of this compound has attracted renewed interest recently, because CuO shares the same basic building block (CuO4 parallelogram plane) with high-Tc materials. Revealed is an existence of hidden electronic states near the absorption threshold in CuO.
2. Experimental
Fig. 1. (a) A diagram of 1s2p resonant inelastic X-ray scattering (RIXS) process and (b) schematic presentation of lifetime-broadening-removed measurements by 1s2p RIXS. See text.
schematically for arbitrary chosen ω1 and ω2 , as shown in Fig. 1b. The scattering intensity is in principle determined by the overlap of these three functions. In RIXS measurements, ω1 is fixed and the scattering intensity is monitored as a function of ω2 , which is equivalent of sliding the sharp f2 along the ω-axis, while keeping f1 and dg1s /dω fixed as shown in Fig. 1b. Suppose ω1 − Ω1s is small, say ≤−10 eV, f1 tails off at ω > 0 and can be assumed a small constant. Then Eq. (1) is determined by the convolution of dg1s /dω with f2 , that is, broadening by Γ 1s is removed [1]. However, small f1 value makes the scattering intensity significantly low, imposing severe restriction to wide application. When ω1 − Ω1s approaches zero, f1 cannot be approximated to be a constant, and the scattering intensity is governed by the overlap of these three functions. It will be obvious, however, that in this case also the bandwidth of the scattering spectra is dominated by Γ 2p and not by Γ 1s because in the overlap region the f1 forms just a monotonously decreasing background. Under the approximation that Γ2p /2¯h 1, Eq. (1) can be transformed to a more transparent form [2,4] by using the K␣-emission energy h ¯ ωK␣ = h ¯ (Ω1s − Ω2p ) = 8047.8 eV and the absorption energy ωabs = Ω1s +ω = ωK␣ +ω1 −ω2 : dσ(ω1 ) (ω2 /ω1 )ωabs (dg1s /dωabs ) ∝ . 2 /4¯h2 dω2 (ω2 − ωK␣ )2 + Γ1s
(2)
This equation means that the cross section of 1s2p RIXS is, apart from the factor (ω2 /ω1 ) × ωabs , proportional to dg1s /dωabs multiplied by a Lorentzian centered at ωK␣ . Hence, it is possible to calculate dg1s /dω analytically from the experimental RIXS spectra directly, or vice versa. Un-
RIXS experiments were carried out at the BL47XU beamline at SPring-8. The experimental details were described elsewhere [2]. In short, incident X-rays (flux =∼ 1014 photons/s; spectral width = 0.9 eV at 8 keV) were horizontally focused by a cylindrically-bent mirror and irradiated onto the sample, with an ion chamber monitoring the beam intensity. The scattered radiation was analyzed with a spherically-bent φ 75 mm Si(4 4 4) crystal having an 820 mm radius of curvature, and detected by a scintillation counter. To acquire 1s2p RIXS spectra, the incident energy remained fixed and the scattered photon energy was analyzed by moving the analyzer and the detector synchronously. In these measurements, the active area of the analyzer was limited to 40 mm in diameter, which resulted in an overall energy resolution ( Eexp ) of 1.1 eV as determined by the FWHM of the elastic line. All data were taken on powder CuO at room temperature at a constant scattering angle of 80◦ .
3. Results Fig. 2 shows excitation energy dependence of RIXS spectra of CuO. Spectral shape and intensity change with excitation energy significantly. Excitation with X-ray energies well above the K-absorption edge energy (∼8986 eV) yields a single band at 8047.8 eV, which is the well-known Cu K␣1 fluorescence line (in Fig. 2 the K␣1 peak is out of the scale). As the excitation energy lowered below the K-edge, the main feature corresponding to the K␣1 (denoted A) is shifted down with its width broadened. By lowering the excitation energy to ∼8983 eV, a new branch, labeled B, appears. Another feature labeled C is prominent at the excitation energy around 8980 eV excitation. As the excitation energy further lowered, the peak energy of A continues to shift to lower energy, preserving the energy loss (Eloss ) of 939 eV. At the same time, the scattering intensities decrease monotonously. In contrast to the consecutive changes with excitation energy observed for A, the branch B is only observable within a small range of excitation energy, from ∼8981 to ∼8984 eV. Furthermore, the Eloss of the branch B
H. Hayashi et al. / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 277–280
279
Exp. Best-fit LBF-XANES A
B 8983.1eV
A B
C
8981.1eV
A
C 8979.1eV
A C 8977.1eV
Fig. 2. Excitation energy dependence of resonant inelastic X-ray scattering (RIXS) spectra of CuO as a function of excitation energy and emission energy.
Emission energy [eV]
8978
In the upper panel of Fig. 3 the RIXS spectra of CuO excited at several excitation energies are shown. In the lower panel shown by squares and triangles are LBR-XANES profiles of CuO analytically derived from some of the RIXS spectra by the use of Eq. (2). The inset shows 1s → 3d transition region below the absorption edge in an expanded scale. It is rather striking that, in spite of significant differences in RIXS spectra employed, LBR-XANES derived by Eq. (2) almost overlaps with each other. Although not shown for clarity of the figure, a use of RIXS spectra at other excitation energies produces almost the same results as long as the excitation energy is below about 8984 eV. In the lower panel of Fig. 3 conventional XANES is also shown. It is clear from the comparison that features in LBR-XANES are much more distinct than those in conventional XANES. This endorses that line-broadening by Γ 1s , which often hampers detailed analysis of conventional XANES, is removed in LBR-XANES derived from RIXS. In the derivation of Eq. (2) it has been assumed that Γ 2p is zero. Since the quality of the present RIXS data allows us to examine the profiles in detail numerically, attempted next is
8980
8982
8984
8986
Best-fit LBF XANES
a
4. Discussions 4.1. LBR- and LBF-XANES of CuO
b
c dg1s/d
varies with the excitation energy. On the other hand, Eloss for C remains constant (932 eV) and is independent of the excitation energy, as is the branch A. As the excitation energy is tuned to ∼8980 eV, which is the transition energy from 1 s to the vacant 3d [5], the band C is the strongest with the band width much narrower than the normal K␣1 fluorescence. These excitation energy dependencies of RIXS spectral features have been already reported [2,6].
8036 8040 8044 8048 8052
c 8976
8980
LBR-XANES analytically Obtained from 8977.1eV Exc. 8979.1 8981.1 8983.1
b 8984
Conventional XANES
8988
8992
8996
9000
Energy [eV]
Fig. 3. (Upper panel) Comparisons of the observed RIXS spectra (circles) and calculated ones (solid line) by the use of the best-fit dg1s /dω model at the excitation energies indicated in the figure. (Lower panel) The best-fit LBF-XANES (dg1s /dω) numerically obtained as well as LBR-XANES spectra analytically obtained from RIXS spectra of the upper panel. Conventional XANES is also shown in the lower panel for comparison.
to derive dg1s /dω by numerical simulation based on Eq. (1) without such an assumption. The dg1s /dω profiles obtained from this procedure correspond to lifetime-broadening-free (LBF) XANES. The procedures to extract LBF-XANES are described in detail elsewhere [2]. In the lower panel of Fig. 3, a dg1s /dω model that reproduces observed RIXS spectra best is shown. It is evident that dg1s /dω obtained here shows much more distinct features than those obtained from Eq. (2), 1s-LBR-XANES, demonstrating that the core-hole lifetimes of 2p as well as 1s are removed. It is also possible to calculate RIXS spectra from an assumed dg1s /dω by the use of Eq. (1). In the upper panel
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of Fig. 3 calculated RIXS profiles from the best-fit dg1s /dω model are compared with experimental RIXS spectra. It is clear that the observed RIXS spectra almost exactly coincide with the corresponding ones generated by the single dg1s /dω model. Roughly speaking, there are the following relations between dg1s /dω features and RIXS peaks. First, the main RIXS feature, which is indicated by A in Figs. 2 and 3, is essentially determined by the profile of the prominent features in XANES indicated by a in Fig. 3. The shape of the low-energy tail of the features, indicated by b, determines the RIXS feature B. The discrete 1s → 3d band c at 8980 eV is responsible to the prominent feature C in the RIXS spectra. From these observations it is confirmed that complicated behavior of the RIXS spectra, found in Figs. 2 and 3, can be explained quantitatively as the reflection of the LBF-XANES profile. LBR/LBF-XANES, therefore, can be derived from each inelastic X-ray scattering spectrum under near-resonant conditions. As was described in the previous section, if measured under ≤−10 eV off-resonant conditions, RIXS spectrum itself is almost equivalent to LBR-XANES [1]. However, weak scattering intensity at off-resonant conditions requires a long data accumulation period. On the other hand, if measured under close-to-resonant conditions (a few eV below the edge), 2–3 orders of magnitude intensity gain is achieved. An apparent disadvantage is that some calculations are required to deduce LBR/LBF-XANES spectrum from RIXS. Since the calculation is straightforward and can be carried out almost without resorting to any unambiguous or uncertain parameters, the advantage of near-resonant measurements far exceeds the disadvantage and warrants a wide application of the RIXS-XANES method.
Bocharov et al. [7] concluded that although the gross features of polarized XANES spectrum can be reproduced by the calculation, some discrepancies between experiment and theory still remain, the most significant one being the absence of the Cu 1s to 4pz dipole transition near 8983 eV in the experimental absorption spectra. In their convention, the z -axis is perpendicular to the CuO4 parallelogram plane. Our observation here clearly supports the calculation that there is an unoccupied state at ∼8983 eV in spite of the absence of distinct peak or shoulder in the X-ray absorption spectrum. Unfortunately, it is not possible with present experimental results from a powder sample to determine whether the transition is to the pz orbital or not. However, L3 absorption studies [8,9] on CuO show that there is no marked structure at high energy side of the strong peak due to the 2p → 3d transition, which suggests that the character of the state giving the band B is neither s nor d, but p dominant. Polarization dependent RIXS measurements and LBR/LBF-XANES deduced from them on single crystal CuO will make unambiguous determination of the symmetry of the states possible. The present results demonstrate the potential use of LBR/LBF XANES spectroscopy, which will provide valuable new information on the electronic states of metal compounds, including strongly correlated metal oxides, as well as stringent tests for electronic states calculations for these systems.
Acknowledgements This experiment was carried out at the SPring-8 under the proposal No. R02A47XU-0033N.
4.2. Hidden electronic states of CuO revealed by LBR/LBF-XANES References The existence of weak bound states b, which are hidden in the conventional K XANES spectrum of CuO, is especially interesting. In our previous RIXS work [6], the presence of state between 8980.8 and 8983.3 eV, has been revealed, but relatively low signal-to-noise (S/N) ratio of data prevents detailed examinations. The LBR/LBF XANES obtained here from RIXS spectra with much better S/N ratio (the lower panel of Fig. 3) indicates the tail feature of the hidden states; in the upper panel of Fig. 3 the features of the band B, including almost no dispersion, are completely reproduced by introducing the state b. Here, it should be noted that the gently decaying tail is not common in Cu LBR/LBF-XANES. For example, in another Cu(II) compound, CuCl2 ·2H2 O, the tail is rather steep, which results in barely observable RIXS feature B [1,2]. In a recent combined polarized (conventional) XANES and real-space multiple-scattering calculation study of CuO,
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