Kondo peak

Furthermore, it was shown the unpaired spin S = 1/2, which is delocalized over the two Pc rings, still remained in the Jt-orbitals after absorption on Au(lll). Consequently, STS measurements also provided direct observation ofthe S = 1/2 radical on the TbPc2 molecules on Au(lll) whereby the indicative Kondo-peak could be switched off by tunnelling current pulses [215]. Indeed the tunnelling conductance (dl/dV) was analysed from STS experiments of TbPc2 on Au(lll) near the Fermi level showed a zero-bias peak (ZBP) in the spectra, which could be assigned as a Kondo resonance. Clear Kondo features for the molecules with 9 = 45° were observed when the tip was positioned over one ofthe lobes of TbPc2. 

A crystal field (CF) can strongly modify these standard properties of VF or HF systems if the CF level splitting is of the order /cbYk- Figures 10 and 11 show the shift and the deformation of the Kondo peak in the specific heat due to cubic CF splitting in this case. In fig. 11 one has an additional Schottky peak. 

The thermopower of concentrated VF systems or compounds shows a huge Kondo peak (see fig. 9) and in addition a low-temperature peak of opposite sign (Franz et al. 1978), which can be explained by inelastic spin-flip scattering between the 4f and conduction electrons and which is due to the RKKY interactions (Fischer 1989b). The thermopower can also strongly depend on CF effects and seems to be far from universal. 

Despite the fact that the GS model ignores the influence of the thermal broadening and of the coherence between the neighbour f states, the message of this study is that the weight of the Kondo peak in the spectra of heavy-fermion systems is too weak to be detected directly with the resolution and low temperatures which could be reached until now. In the light of this conclusion, the interpretation of recent spectroscopic studies devoted to the heavy-fermion problem in Ce and U systems (Parks et al. 1984, Arko et aL 1984, Allen et al. 1985) has to be reconsidered critically. 

As discussed in more detail in section 4 the exaet result for g (z) to leading order in l/Nf ean be ealeulated analytically for the ease [/ = oo. In the spin fluctuation limit -6f PNfA the corresponding spectral function has a Lorentzian peak of halfwidth NfA near z = 6f and sharp rise near the Fermi energy, whieh eorresponds to the onset of the Kondo peak, which has most of its weight in the BIS spectrum slightly above Sp. An analogous ealculation can be carried out for g (z). This shows in addition to the P-peak near + U a sharp P-peak just above the Fermi level. The position and width nk Ty lN[ of this Kondo or Abrikosov-Suhf... 

Equation (109) describes a sharp rise in the spectrum, determined by S, as s approaches p = 0 from below. In fig. 5 this is illustrated by the Nf = ao curves, In section 4.3 we demonstrate that this rise is the tail of a peak at e 5 on the BIS (e > 0) side of the spectrum. This peak is the Kondo peak discussed in section 3. To understand the origin of this feature we study the character of the corresponding final states. If we only consider the basis states (94) and (95) (order l/Nff for pf (e)) the first energy variable e in these states can be considered as a dummy index, since different values of e are not mixed by the matrix elements (97). Thus we can perform a variational calculation for each value of e and obtain a state... 

In fig. 19 results for the valence PES spectra of the Ce pnictides are shown (Gunnarsson and Schonhammer 1985b). The off-resonance spectra of the pnictides show spectra with a peak at — 2eV. For simplicity we have therefore used a simple triangular shape for V eY as shown in the insert. The figure shows results for both U = CO and for a finite U. In this case the finite U effects have a small influence on the spectra. The weight of the Kondo peak is also negligible. In these cases the hybridization effects dominate. The same conclusion was reached by Sakai et al. (1984). 

Appendix 1. Spin-orbit and crystal field split Kondo peaks... 

This analysis yields the spectrum shown in fig. 1, which has a peak at the Fermi level, which is in fact a tail of the Kondo peak, and several broad features located below the... 

Since all of these f photo-emission peaks are side bands of the basic Kondo peak, they are all proportional to the weight of the/° component in the ground state That is, the Kondo peaks represent processes whereby a single electron is added to the f level (for C/ff oo this requires the presence of an imoccupied f orbital in the initial state), the intensities of the side bands are all proportional to (1 - f). As the peaks do not have simple Lorentzian forms, they are asymmetric the total intensities are not straightforward to estimate. However, by assuming a Lorentzian shape, we have the estimates of the integrated intensities of the crystal field split Kondo side bands given by the expressions... 

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