The low temperature resistivity minimum, together with the overall reduction of the magnetic moment, are two of the main macroscopic identifiers of the Kondo effect. The effect occurs when a localised impurity is found close to the Fermi surface of a non-magnetic host. For temperatures that are lower than the Kondo temperature, TK, the spin of the impurity is compensated by the conduction electrons and the resulting magnetic moment is reduced. Whereas above the Kondo temperature, Kondo systems behave as local moment systems. According to the prevailing single impurity Anderson model, it is the hybridisation between the impurities and the conduction states that results, for T < TK, in a non-magnetic ground state. The fingerprint of this state in the photoemission spectrum is the Kondo resonance. The cross-over from low temperature (T < TK) to high temperature (T > TK) is associated with a decrease of the resonance’s intensity, as the ground state is destroyed by thermally activated spin fluctuations. Whether or not a description in terms of this model is appropriate has been strongly debated. For cerium (Ce) compounds, the surface sensitivity of most of the previous photoemission investigations, together with an often uncertain identification of the 4f contribution to the photoemitted intensity, are the underlying causes of the conflicting results. Hence, 4f spectra that are more representative of the bulk are needed.

Soft X-ray resonant photoemission spectroscopy performed at the ID08 beamline has allowed us to identify bulk-representative 4f spectral features for CeCo2Ge2, a single-crystalline compound whose Kondo temperature is TK ~ 120 K. In fact, by tuning the photon energy to the Ce M5 absorption edge (h ~ 880 eV), both bulk and orbital selectivity are obtained; the first due to the increase of the inelastic mean free path for incoming energies belonging to the soft X-ray range, the second due to the enhancement of the 4f intensity by more than one order of magnitude if compared to off-resonance conditions.

Fig. 121: Temperature-dependent, resonant, angle-integrated valence band spectra. h ~ 880 eV. The arrows indicate the position of the Kondo resonance and the spin-orbit partner respectively. EF = 0 eV.

Figure 121 shows the angle-integrated valence band of CeCo2Ge2 measured at several temperatures ranging from T = 20 K to T = 145 K. Despite the fact that the intensity is strongest at 20 K, the shape of the two low temperature spectra is very similar. In particular, two features are observed: the most intense, found at approximately 70 meV binding energy, is the Kondo resonance, whereas the other, positioned at approximately 270 meV, is the spin-orbit partner. As the temperature is raised from 90 K to 110 K, a decrease is observed in the overall intensity, together with a smearing out of the spin-orbit partner. By increasing the temperature further, the signal below 350 meV remains unchanged whereas the intensity of the Kondo resonance continues to decrease. In agreement with the impurity model, we therefore observe a temperature dependence that reflects the progressive breakdown of the singlet ground state.

Fig. 122: Resonant, angle-resolved, valence band spectrum. h ~ 880 eV and T = 20 K. The binding energy is plotted as a function of kpar and the colour map indicates the intensity. Top: three dimensional representation. Bottom: two dimensional projection. The dispersing feature is shown by the dashed line. EF = 0 eV.

Figure 122 shows the angle-resolved valence band of CeCo2Ge2 for T = 20 K. These data fail to confirm the applicability of the impurity model in its simplest form as, at the heart of the model, is the postulate that both the intensity and the binding energy of the Kondo resonance are constant functions of the momentum component parallel to the surface, kpar. Figure 122 indicates the contrary, that the nature of this feature varies. Indeed, the spectral weight is mostly concentrated within ± 0.7 Å-1 from the centre of the Brillouin zone (kpar = 0 Å-1) and a clear intensity modulation of the Kondo resonance is observed. Most intriguingly, a weak but visible spin-orbit-partner-like feature is seen dispersing towards higher binding energies.

The data reveal clear 4f bulk-like features whose temperature dependence is in agreement with the predictions of the impurity model. The major exceptions to this scenario are given by the localisation of the 4f intensity close to the centre of the Brillouin zone and the dispersion of what may be the spin-orbit partner, as observed in Figure 122. We refer to a renormalised f-d mixing model, that retains the underlying physics of the impurity approach but is further complicated by a more sophisticated screening mechanism, as a candidate for explaining both the temperature dependence of the Kondo resonance’s intensity and its observed directional character.

 

In memory of Kenneth Larsson.

 

Principal Publication and Authors

F. Venturini (a), J.C. Cezar (a), C. De Nadaï (a), P.C. Canfield (b), N.B. Brookes (a), J. Phys.: Condens. Matter 18, 9221 (2006).
(a) ESRF
(b) Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, U.S.A.