J. Phys. Soc. Jpn. 84, 033702 (2015) [4 Pages]
LETTERS

Final-State Interaction in the L3 X-ray Absorption Spectra of Mixed-Valence Ce and Yb Compounds

+ Affiliations
1Photon Factory, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan2RIKEN SPring-8 Center, Sayo, Hyogo 679-5148, Japan

X-ray absorption spectroscopy (XAS) at the L3 edge of mixed-valence Ce and Yb compounds is a powerful tool for measuring the valence of Ce and Yb ions, but in order to obtain the valence in the ground state it is necessary to analyze the effect of the final-state interaction on XAS profiles, which gives rise to some correction for the XAS-derived valence. We theoretically compare the difference in the final-state interaction for Ce and Yb compounds whose ground states are in the electron–hole symmetry. It is found that the correction for the valence by the final-state interaction is much larger for Ce than for Yb, even if the valences in the ground state are the same. In order to discuss the mechanism of this observation, we define two different final-state interactions: (i) the final-state hybridization between the 4f0 and 4f1 configurations and (ii) that between the 4f1 and 4f2 configurations. Among (i) and (ii) of Ce and Yb compounds, (ii) of Ce compounds is much larger than other interactions, because the core hole potential is attractive for the Ce 4f electron but repulsive for the Yb 4f hole.

©2015 The Physical Society of Japan

References

  • 1 See, for instance, F. M. F. de Groot and A. Kotani, Core Level Spectroscopy of Solids (CRC Press, Boca Raton, FL, 2008). CrossrefGoogle Scholar
  • 2 H. Yamaoka, I. Jarrige, N. Tsujii, A. Kotani, J.-F. Lin, F. Honda, R. Settai, Y. Ōnuki, N. Hiraoka, H. Ishii, and K.-D. Tsuei, J. Phys. Soc. Jpn. 80, 124701 (2011). 10.1143/JPSJ.80.124701 LinkGoogle Scholar
  • 3 T. Nakamura, Y. H. Matsuda, J.-L. Her, K. Kindo, S. Michimura, T. Inami, M. Mizumaki, N. Kawamura, M. Suzuki, B. Chen, H. Ohta, K. Yoshimura, and A. Kotani, J. Phys. Soc. Jpn. 81, 114702 (2012). 10.1143/JPSJ.81.114702 LinkGoogle Scholar
  • 4 I. Jarrige, H. Yamaoka, J.-P. Rueff, J.-F. Lin, M. Taguchi, N. Hiraoka, H. Ishii, K. D. Tsuei, K. Imura, T. Matsumura, A. Ochiai, H. S. Suzuki, and A. Kotani, Phys. Rev. B 87, 115107 (2013). 10.1103/PhysRevB.87.115107 CrossrefGoogle Scholar
  • 5 J.-P. Rueff, S. Raymond, M. Taguchi, M. Sikora, J.-P. Itié, F. Baudelet, D. Braithwaite, G. Knebel, and D. Jaccard, Phys. Rev. Lett. 106, 186405 (2011). 10.1103/PhysRevLett.106.18640521635111 CrossrefGoogle Scholar
  • 6 H. Yamaoka, Y. Zekko, A. Kotani, I. Jarrige, N. Tsujii, J.-F. Lin, J. Mizuki, H. Abe, H. Kitazawa, N. Hiraoka, H. Ishii, and K.-D. Tsuei, Phys. Rev. B 86, 235131 (2012). 10.1103/PhysRevB.86.235131 CrossrefGoogle Scholar
  • 7 A. Fernandez-Pañella, V. Balédent, D. Braithwaite, L. Paolasini, R. Verbeni, G. Lapertot, and J.-P. Rueff, Phys. Rev. B 86, 125104 (2012). 10.1103/PhysRevB.86.125104 CrossrefGoogle Scholar
  • 8 T. Mazet, D. Malterre, M. Francois, C. Dallera, M. Grioni, and G. Monaco, Phys. Rev. Lett. 111, 096402 (2013). 10.1103/PhysRevLett.111.09640224033054 CrossrefGoogle Scholar
  • 9 A. Kotani, Eur. Phys. J. B 85, 31 (2012). 10.1140/epjb/e2011-20577-y CrossrefGoogle Scholar
  • 10 A. Kotani, Eur. Phys. J. B 72, 375 (2009). 10.1140/epjb/e2009-00362-5 CrossrefGoogle Scholar
  •   (11) Unfortunately, in the calculation in Ref. 10, the effect of the 4f2 configuration was disregarded, so that the difference between the final-state interactions for the Ce and Yb systems could not be discussed. Google Scholar
  •   (12) On the right-hand side of \(|\tilde{f}^{0}\rangle \), \(|\tilde{f}^{1}\rangle \), and \(|\tilde{f}^{2}\rangle \), we explicitly write the states that hybridize directly by V. Actually, \(|f^{2}\rangle \) is included in \(|\tilde{f}^{0}\rangle \), and \(|f^{0}\rangle \) is also included in \(|\tilde{f}^{2}\rangle \) through indirect hybridization. Therefore, there is an interference between the final-state interactions (i) and (ii), but here we disregard the interference for simplicity. In our numerical calculations, the indirect hybridization is also taken into account, and then the interference between (i) and (ii), as well as the orthogonality between \(|\tilde{f}^{0}\rangle \) and \(|\tilde{f}^{2}\rangle \), is recovered. Google Scholar
  •   (13) From the numerical calculations of the final-state interaction by changing the width W of the conduction band, V and \(\epsilon _{f}\) are changed to keep TK and \(n_{f}^{(\text{e})}\) (or \(n_{f}^{(\text{h})}\)) unchanged for each W (see Ref. 10), we can show that the final-state interaction depends on W. In the limit of vanishing W, as in our simplified model (Fig. 4), the final-state interaction (ii) for Yb is negligible compared with (i) for Yb, but for W = 4 eV, (i) and (ii) for Yb are comparable. Our conclusion that the final-state interaction (ii) for Ce is much larger than the other final-state interactions for Ce and Yb is always valid for any realistic values of W. Google Scholar
  •   (14) Ce and Yb compounds with a strong hybridization (typically TK > 100 K) are often called valence-fluctuation compounds, and those with a weak hybridization (typically TK < 50 K) are called heavy-fermion compounds. In the present paper, we combine both cases and denote all of them as mixed-valence compounds. Google Scholar
  • 15 O. Gunnarsson and K. Schönhammer, Phys. Rev. B 28, 4315 (1983). 10.1103/PhysRevB.28.4315 CrossrefGoogle Scholar