Intermediate Valence in Yb Compounds Probed by RIXS and 4f

8 th International Conference on Inelastic X-Ray Scattering IXS-2013, May 12-15, Menlo Park

Intermediate Valence in Yb Compounds

Probed by RIXS and 4f Photoemission

Serguei L. Molodtsov, European XFEL & Freiberg University of Technology

1

S.L. Molodtsov, European XFEL & TU Freiberg


Cooperators

Studies were performed by:

Dresden University :

ESRF (ID16):

Spring-8 (BL25SU):

MPI CPfS Dresden:

K. Kummer (ESRF) , D. Vyalikh,

Yu. Kucherenko, S. Danzenbächer,

M. Holder, C. Laubschat

S. Huotari and L. Simonelli

T. Muro, Y. Kato and T. Kinoshita

C. Krellner and C. Geibel

2



Correlated f-materials

Periodic table n m 2

[Xe] 4f 5d 6s

Atomic potential

3

Lanthanoide

:

S.L. Molodtsov, European XFEL & TU Freiberg f - electrons


Correlated f-materials: YbRh

2

Si

2

4

Correlated f-Materials

Periodic table of the elements

Lanthanoide

:

S.L. Molodtsov, European XFEL & TU Freiberg f - electrons


Correlated f-materials: Mixed-valent Ce and Yb systems

E

DOS f d e

E

F f

1 f d

DOS

E e f

0

E

F f electron promotion energy U fd may be compensated by increase of the system cohesive energy

D

U

C

5

U fd

U fd

>>

D

U

C

– stable configuration f n [f 1 for Ce; f 14 (h 0 ) for Yb]

<<

D

U

C

– stable configuration f n-1 [f 0 for Ce, f 13 (h 1 ) for Yb]

U fd

~ D

U

C

– mixed-valent system f v , (n-1) < v < n



From mixed-valent to Kondo behavior (Ce)

E

6

Why exact knowledge of intermediate valency is important ?

e f

2 f states

U ff

Mixed valence: e f

1 and e f

0 are almost equally possible short lifetime efficient hopping broad E

F peak

Kondo e f

0

E

F e f

1

U fd

Kondo: starting from e f

1 , probability to have e f

0 is very low hopping is rear long lifetime sharp Kondo resonance



Intermediete valency from photoemission

SIAM calculations

Ce:

ε f

= -1.5 eV

Δ = 1.0 eV

Yb:

ε f

= -0.05 eV

Δ = 0.3 eV

U ff

= 7 eV

J.-M. Imer & E. Wuilloud,

Z. Phys. B 66 , 153 (1987).

7

GSP breaks down, since it underestimates experimental intensity at E

F

. Final-state hybridization should be included in consideration!



Final-state hybridization is included!

SIAM calculations

Ce:

ε f

= -1.5 eV

Δ = 1.0 eV

Yb:

ε f

= -0.05 eV

Δ = 0.3 eV

U ff

= 7 eV

O. Gunnarsson &

K. Schönhammer,

PRB 31 , 4815 (1985)

8

In case final state hybridization and finite valence-band width are considered better agreement between theory and experiments can be achieved



Intermediete valency of YbRh

2

Si

2 from photoemission

9

Divalent (2 + ) contribution into the ground state is considerably overestimated in photoemission experiments



RIXS at L

3 edge

10

2 p 5 4 f 14 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



Intermediarte valency from RIXS

CXE at excitation energy of 2 + resonance is preferable for analysis of almost 3 + system

11 with ζ = 1 for CEE scan and ζ < 1 for CXE scan



Intermetallic rare-earth materials: YbRh

2

Si

2 12

Typical single-crystalline samples



Intermetallic rare-earth materials: YbRh

2

Si

2

Yb

Rh

Si

13

Quasi-layered structure, cleave between Yb (blue) and Si (green) layers



Characterization of cleaved samples: YbRh

2

Si

2

Yb

Rh

Si

14



Characterization of cleaved samples: YbRh

2

Si

2

Surface

15

Yb

Rh

Si

Bulk



Evaluation of photoemission spectra

16

Best fit for Δ = 0.26 eV


Intermediate valency 2.93 for bulk is observed

(2.88 in GSP)


Evaluation of RIXS spectra

Intensity map of the Yb Lα

1 fluorescence yield for YbRh

2

Si

2

17

CEE and CXE cuts through the 2 + resonance are indicated by white and red circles, respectively



CEE cut through the intensity map

XAS measured in total fluorescence yield (TFY) mode and RIXS spectra in

CEE mode of YbRh

2

Si

2

18

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)



CXE cut through the intensity map

Emission intensity curve along the CXE cut (excitation into 2 + resonance) indicated by red circles in fig. below

19

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!



Absolute intensity normalization

20

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



Evaluation of RIXS spectra

Δ = 0.26 eV from photoemission

21

Intermediate valency: 2.93 from CEE scan and 2.92 from CEE scan

(2.89 and 2.88 in GSP)



Summary

22

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



European XFEL (XFEL.EU)

23

Superconducting LINAC technology provides 27.000 light pulses/s with duration down to a few fs each. It makes XFEL.EU attractive for photonhungry and time-resolved experiments.



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

24



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25



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26



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27



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28



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29



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30



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31


You are very welcome to plan your

IXS/RIXS

experiments at the European XFEL

32


Intermediate Valence in Yb Compounds Probed by RIXS and 4f

Intermediate Valence in Yb Compounds

Probed by RIXS and 4f Photoemission

Surface

Spokesperson

Consortium members

You are very welcome to plan your

IXS/RIXS

experiments at the European XFEL

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Intermediate Valence in Yb Compounds Probed by RIXS and 4f