VOLUME 88, NUMBER 19 PHYSICAL REVIEW LETTERS 13 MAY 2002 New Spectroscopy Solves an Old Puzzle: The Kondo Scale in Heavy Fermions C. Dallera, 1 M. Grioni, 2 A. Shukla, 3 G. Vankó, 3 J. L. Sarrao, 4 J. P. Rueff, 5 and D. L. Cox 6 1 INFM-Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy 2 IPN, Ecole Polytechnique Fédérale (EPFL), CH-1015 Lausanne, Switzerland 3 European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble, France 4 Los Alamos National Laboratory, Los Alamos, New Mexico 87545 5 Laboratoire de Chimie Physique, Université Pierre et Marie Curie, F-75231 Paris, France 6 Department of Physics, University of California, Davis, California 95616 (Received 28 December 2001; published 26 April 2002) Resonant inelastic x-ray scattering (RIXS) yields clear evidence of spectroscopic Kondo scales in heavy fermions. In YbInCu 4 and YbAgCu 4 RIXS probes the Yb 21 component of the hybrid ground state and the temperature dependence of the Yb 4f occupation. We report a sudden valence change at a phase transition in YbInCu 4 , but a continuous temperature dependence in YbAgCu 4 , consistent with the predictions of the Anderson impurity model, for a Kondo temperature T K  70 K. These results solve a long-standing controversy and establish RIXS as a quantitative probe of the electronic structure of strongly correlated electron systems. DOI: 10.1103/PhysRevLett.88.196403 PACS numbers: 71.28.+d, 71.20.Eh, 78.70.Ck, 78.70.Dm The occurrence of intermediate valence in cerium and ytterbium compounds reflects the peculiar nature of the quasiatomic 4f orbitals, and the mixing of different electronic configurations — e.g., Yb 31 (4f 13 ) and Yb 21 (4f 14 ) — in the quantum mechanical ground state [1]. According to the leading theoretical scenario for these materials — the Anderson impurity model (AIM) [2]— the 4f occupation n f , like other physical quantities, must vary with temperature in a universal, nontrivial way [3]. This dependence is controlled by the single parameter T T K . T K is the material-dependent characteristic Kondo temperature, which marks the crossover from local mo- ments at high temperatures to a low-temperature phase where spins are compensated by the conduction electrons. Thermodynamic measurements allow indirect in- ferences to be drawn about the value of n f  and its temperature dependence. The temperature scaling should be directly observable from spectroscopic measurements, but reports from photoemission (PES) on polycrystalline samples [4–7] have been disputed by results on single crystals [8]. These discrepancies could indicate the need for refinements of the AIM [9], but uncertainties arise because PES is surface sensitive and may not always probe bulk thermodynamic properties [10,11]. We present truly bulk-sensitive spectroscopic data on single crystal Yb compounds, which unambiguously demonstrate the Kondo temperature dependence predicted by theory. X-ray absorption (XAS) data at the Yb (Ce) L 2,3 (2p ! 5d) edges give convincing evidence of a temperature de- pendence in valence fluctuators [12,13] but are not free from pitfalls. The spectral changes are small, and quanti- tative analyses rely on the deconvolution of broad spec- tra and on assumptions on the underlying line shapes. Novel x-ray spectroscopies developed at third-generation synchrotron sources, namely, high-resolution XAS and resonant inelastic x-ray scattering (RIXS), open new op- portunities to test the fundamental theoretical prediction. RIXS experiments, where the deexcitation channels of the XAS final state are separately measured, are especially promising. By a proper choice of the parameters, the RIXS signal from a specific configuration in the hybrid ground state can be greatly enhanced, thus eliminating the need for arbitrary spectral decompositions. We used bulk sensitive (probing depth l  10 mm) high-resolution XAS and RIXS at the Yb L 3 edge to measure the temperature dependence of the valence in two representative and well-studied Yb compounds, YbInCu 4 and YbAgCu 4 , for which high-quality single crystals and comprehensive measurements of the physical properties are available [14,15]. YbInCu 4 exhibits a sharp valence transition at T V  42 K with a discrete change in n f , whereas YbAgCu 4 displays a continuous evolution of physical properties describable by a Kondo temperature T K  60 100 K. For both materials, physical properties such as the electronic specific heat, and the static and dy- namic magnetic susceptibilities, are well described by the AIM. In YbInCu 4 we find that the number of Yb 4f holes n h  suddenly drops below T V in excellent agreement with the thermodynamic and magnetic properties, but in stark contrast with surface-sensitive PES data [16–18]. In YbAgCu 4 , exploiting the resonant enhancement of the Yb 21 signal in the RIXS spectrum, we could follow with unprecedented accuracy the continuous temperature dependence of n h  and found it to obey the predicted Kondo scaling, with T K  70 K. Single crystals of YbInCu 4 and YbAgCu 4 were grown using a flux technique as reported previously [19]. The experiment was performed on beam line ID16 at European Synchrotron Radiation Facility. Radiation from an undulator source was monochromatized by a Si(111) monochromator and focused to a spot size of 130 3 50 mm 2 (H 3 V). The scattered x rays were 196403-1 0031-9007 02 88(19) 196403(4)$20.00 © 2002 The American Physical Society 196403-1