Mixed valence arises in strongly-correlated solids from the conflict between the natural tendency of electrons to form extended bands, and the opposing tendency to occupy atomic-like, localised states. This leads to spectacular physical properties including Kondo and heavy fermion behaviour as well as unconventional magnetism and superconductivity.

A typical manifestation of such many-body interactions in solids are small energy scales. In intermediate valence systems, like many cerium and ytterbium compounds, the characteristic scale is the energy separation between the hybrid singlet ground state and the first excited magnetic states, which defines the Kondo temperature T_K. Photoemission could directly probe the Kondo scale, but is severely limited by its surface sensitivity, and results are highly controversial. In contrast, resonant inelastic X-ray scattering (RIXS) in the hard X-ray energy range is a truly bulk probe of electronic states. Like other resonant core-hole spectroscopies it is also element-specific and sensitive to the electronic configuration. These advantages are clearly demonstrated by a RIXS study of the typical Kondo system YbAgCu₄.

The principle of the measurement is summarised in Figure 60. The ground state |_G> of YbAgCu₄ is a coherent superposition of the Yb²⁺ (4f¹⁴, n_h = 0) and Yb²⁺(4f¹³, n_h = 1) configurations. At T = 0, the estimated number of 4f holes is n_h = 0.87, and the valence is v = (2 + n_h) = 2.87, but excited magnetic states (n_h = 1) lying at an energy ~ k_BT_K above the ground state are thermally populated. As a consequence n_h, and the valence, vary with temperature as a characteristic function of T/T_K reflecting the existence of a Kondo scale [1]. Photon absorption at the Yb L₃ edge (8.95 keV) leads to intermediate states of mainly 2p⁵4f¹⁴dⁿ⁺¹ and 2p⁵4f¹³dⁿ⁺¹ character, separated by 7 eV by the strong 4f-core hole Coulomb interaction. These states can decay radiatively to the L₁ RIXS final states 3d⁹4f¹⁴dⁿ⁺¹ (2+) and 3d⁹4f¹³dⁿ⁺¹ (3+). At beamline ID16, we measured these decay channels for excitation energies varying through the Yb L₃ (2p_3/2) absorption edge. The emitted radiation was analysed by a Si (620) Rowland circle spectrometer.

Fig. 60: Total energy level scheme for an Yb ion in YbAgCu4. The arrows indicate the relevant XAS and RIXS transitions.

Distinct 2+ and 3+ features are observed both in absorption (XAS) and RIXS spectra (Figure 61). They are resonantly and separately enhanced when the excitation energy h_in is swept through the Yb L₃ absorption edge. When the excitation energy is tuned to the 2+ XAS feature, the signal from the minority Yb²⁺ configuration dominates the spectrum. We followed continuously the temperature evolution of this signal. Its intensity, proportional to (1 - <n_h(T)>), exhibits a 100% variation from 0.13 at 15 K to 0.065 at 300 K (Figure 62), revealing the existence of the underlying Kondo scale. The experimental curve is accurately reproduced by a calculation performed within the non-crossing approximation (NCA) for the Anderson Impurity Model (AIM). The fit yields a Kondo temperature T_K = 70 K, which agrees well with indirect estimates from magnetic and thermodynamic data. For comparison, we show in the same figure the results of an analogous RIXS measurement on the isoelectronic compound YbInCu₄. This material exhibits a first-order valence transition (from 2.96 to 2.83) at T_C = 42 K, and therefore is not a typical Kondo system. As expected, the intensity of the 2+ signal suddenly drops at T_C.

Fig. 61: RIXS spectra of YbAgCu4, excited along the Yb2+ feature of the XAS (inset). The 2+ feature is resonantly enhanced in the RIXS spectra.

The correspondence between bulk-sensitive RIXS results and thermodynamic properties confirms that the AIM is applicable to spectroscopic properties. It is remarkable that spectral changes, which are controlled by the small Kondo energy scale (~ 6 meV), are readily observed by RIXS in spite of the much larger excitation energy (~ 9 keV) and energy resolution (~ 1 eV). RIXS appears to be an extremely interesting probe of electronic configuration and strong correlations, with possible extension to studies of the electronic properties of solids under extreme conditions of pressure and magnetic fields.

Fig. 62: Temperature dependence of the 2+ RIXS intensity in YbAgCu4, compared with an NCA calculation for TK = 70 K. Selected spectra show the temperature dependence (inset). The case of YbInCu4 (dashed line), which exhibits a valence transition at 42 K, is shown for comparison.

References
[1] N.E. Bickers et al., Phys. Rev. B 36, 2036 (1987).

Principal Publication and Authors
C. Dallera (a), M. Grioni (b), A. Shukla (c), G. Vankó (c), J. Sarrao (d), J.-P. Rueff (e), D.L. Cox (f), Phys. Rev. Lett. 88, 196403 (2002).
(a) INFM - Politecnico di Milano (Italy)
(b) Ecole Polytechnique Fédérale de Lausanne (Switzerland)
(c) ESRF
(d) Los Alamos National Laboratory (USA)
(e) Université Pierre et Marie Curie, Paris (France)
(f) University of California, Davis (USA)