Intermediate Valence in Yb Compounds Probed by RIXS and 4f Photoemission

1. Intermediate Valence in Yb Compounds Probed by RIXS and 4f Photoemission Serguei L. Molodtsov,European XFEL & Freiberg University of Technology S.L. Molodtsov, European XFEL & TU Freiberg

2. Cooperators Studies were performed by: Dresden University: K. Kummer (ESRF), D. Vyalikh, Yu. Kucherenko, S. Danzenbächer, M. Holder, C. Laubschat ESRF (ID16): S. Huotari and L. Simonelli Spring-8 (BL25SU): T. Muro, Y. Kato and T. Kinoshita MPI CPfS Dresden: C. Krellner and C. Geibel S.L. Molodtsov, European XFEL & TU Freiberg

3. Electron configuration: n m 2 [Xe]4f5d6s Atomic potential Lanthanoide : f - electrons Correlated f-materials Periodic table of the elements S.L. Molodtsov, European XFEL & TU Freiberg

4. Yb Rh Rh Lanthanoide : f - electrons Correlated f-materials: YbRh2Si2 Correlated f-Materials Periodic table of the elements S.L. Molodtsov, European XFEL & TU Freiberg

5. Correlated f-materials: Mixed-valent Ce and Yb systems E E DOS f ef0 EF EF f electron promotion energy Ufd may be compensated by increase of the system cohesive energy DUC d d ef1 f DOS Ufd >> DUC – stable configuration fn [f1 for Ce; f14(h0) for Yb] Ufd << D UC – stable configuration fn-1 [f0 for Ce, f13 (h1) for Yb] Ufd~DUC – mixed-valent system fv, (n-1) < v < n S.L. Molodtsov, European XFEL & TU Freiberg

6. Mixed valence: ef1andef0are almost equally possibleefficient hopping short lifetimebroad EF peak Kondo: starting from ef1, probability to haveef0is very low hopping is rear long lifetime sharp Kondo resonance Kondo From mixed-valent to Kondo behavior (Ce) Why exact knowledge of intermediate valencyis important ? E ef2 Uff f states ef0 EF Ufd ef1 S.L. Molodtsov, European XFEL & TU Freiberg

7. Intermediete valency from photoemission Ce: εf = -1.5 eV Δ = 1.0 eV Yb: εf = -0.05 eV Δ = 0.3 eV Uff = 7 eV J.-M. Imer & E. Wuilloud, Z. Phys. B 66, 153 (1987). SIAM calculations GSP breaks down, since it underestimates experimental intensity at EF. Final-state hybridization should be included in consideration! S.L. Molodtsov, European XFEL & TU Freiberg

8. Final-state hybridization is included! Ce: εf = -1.5 eV Δ = 1.0 eV Yb: εf = -0.05 eV Δ = 0.3 eV Uff = 7 eV O. Gunnarsson & K. Schönhammer, PRB 31, 4815 (1985) SIAM calculations In case final state hybridization and finite valence-band width are considered better agreement between theory and experiments can be achieved S.L. Molodtsov, European XFEL & TU Freiberg

9. Intermediete valency of YbRh2Si2 from photoemission Divalent (2+) contribution into the ground state is considerably overestimated in photoemission experiments S.L. Molodtsov, European XFEL & TU Freiberg

10. RIXS at L3 edge 2p54f14 configuration energetically preferred due to its better core-hole screening. Because of possible d→f electron hopping, the 2+ line thus might enter overemphasized into the spectra Constant emission energy (CEE) and constant excited energy (CXE) spectra can be calculated S.L. Molodtsov, European XFEL & TU Freiberg

11. Intermediarte valency from RIXS CXE at excitation energy of 2+ resonance is preferable for analysis of almost 3+ system with ζ = 1 for CEE scan and ζ < 1 for CXE scan S.L. Molodtsov, European XFEL & TU Freiberg

12. Intermetallic rare-earth materials: YbRh2Si2 Typical single-crystalline samples S.L. Molodtsov, European XFEL & TU Freiberg

13. Intermetallic rare-earth materials: YbRh2Si2 Yb Rh Si Quasi-layered structure, cleave between Yb (blue) and Si (green) layers S.L. Molodtsov, European XFEL & TU Freiberg

14. Yb Rh Si Characterization of cleaved samples: YbRh2Si2 S.L. Molodtsov, European XFEL & TU Freiberg

15. Surface Yb Rh Si Bulk Characterization of cleaved samples: YbRh2Si2 S.L. Molodtsov, European XFEL & TU Freiberg

16. Evaluation of photoemission spectra Intermediate valency 2.93 for bulk is observed (2.88 in GSP) Best fit for Δ = 0.26 eV S.L. Molodtsov, European XFEL & TU Freiberg

17. Evaluation of RIXS spectra Intensity map of the Yb Lα1 fluorescence yield for YbRh2Si2 CEE and CXE cuts through the 2+ resonance are indicated by white and red circles, respectively S.L. Molodtsov, European XFEL & TU Freiberg

18. CEE cut through the intensity map XAS measured in total fluorescence yield (TFY) mode and RIXS spectra in CEE mode of YbRh2Si2 Spectral broadening is no longer defined by the lifetime of the deep 2p core hole (TFY-XAS), but by the much shallower 3d core hole (CEE) S.L. Molodtsov, European XFEL & TU Freiberg

19. CXE cut through the intensity map Emission intensity curve along the CXE cut (excitation into 2+ resonance) indicated by red circles in fig. below Originally small 2+ intensity is now comparable to that of the 3+ resonance, despite the only small 2+ divalent admixture in the ground state. But, further normalization is required! S.L. Molodtsov, European XFEL & TU Freiberg

20. Absolute intensity normalization ζ = 0.13 Information on the absolute intensity ratio between the 2+ and 3+ peaks in their respective resonance maxima can be obtained comparing CEE and CXE cuts crossing maximum of the 2+ signal in the intensity map S.L. Molodtsov, European XFEL & TU Freiberg

21. Evaluation of RIXS spectra Δ = 0.26 eV from photoemission Intermediate valency: 2.93 from CEE scan and 2.92 from CEE scan (2.89 and 2.88 in GSP) S.L. Molodtsov, European XFEL & TU Freiberg

22. Summary Valency 2.95 is inferred from low-excitation measurements of the Kondo temperature (20 K) Both RIXS and photoemission approaches to determine valency fail if only initial-state properties are accounted for (2+ contribution is overestimated) Consideration of final-state hybridization is necessary to obtain correct valency S.L. Molodtsov, European XFEL & TU Freiberg

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24. Heisenberg RIXS (hRIXS) @ XFEL.EU Spokesperson: Alexander Föhlisch, Helmholtz-Zentrum-Berlin, Potsdam University, Germany Consortium members: Cooperation of representatives of 20 distinguished research institutions from 7 European countries: Germany, Italy, Switzerland, Sweden, the Netherlands, Finland and France S.L. Molodtsov, European XFEL & TU Freiberg

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